diff --git a/docs/index.html b/docs/index.html index 57368e0..f8e769c 100644 --- a/docs/index.html +++ b/docs/index.html @@ -281,8 +281,9 @@

Getting started

  • skeletor.pre.fix_mesh() to fix the mesh
  • skeletor.pre.simplify() to simplify the mesh
  • skeletor.pre.contract() to contract the mesh [1]
    • -
  • skeletor.skeletonize.vertex_clusters() to generate a skeleton
    • +
  • skeletor.skeletonize.by_vertex_clusters() to generate a skeleton
  • skeletor.post.clean_up() to clean up some potential issues with the skeleton
    • +
  • skeletor.post.smooth() to smooth the skeleton
  • skeletor.post.radii() to extract radii either by k-nearest neighbours or ray-casting
    • @@ -560,184 +561,185 @@

    Top-level functions and classes

    97 1. `skeletor.pre.fix_mesh()` to fix the mesh 98 2. `skeletor.pre.simplify()` to simplify the mesh 99 3. `skeletor.pre.contract()` to contract the mesh [1] -100 4. `skeletor.skeletonize.vertex_clusters()` to generate a skeleton +100 4. `skeletor.skeletonize.by_vertex_clusters()` to generate a skeleton 101 5. `skeletor.post.clean_up()` to clean up some potential issues with the skeleton -102 6. `skeletor.post.radii()` to extract radii either by k-nearest neighbours or ray-casting -103 -104In my experience there is no one-size-fits-all. You will have to play around to -105find the right approach and parameters to get nice skeletons for your meshes. -106If you need help just open an [issue](https://github.com/navis-org/skeletor/issues). -107 -108Also check out the Gotchas below! -109 -110# Examples -111 -112First load the example mesh (a fruit fly neuron): -113 -114```Python -115>>> import skeletor as sk -116>>> mesh = sk.example_mesh() -117>>> mesh -118<trimesh.Trimesh(vertices.shape=(6582, 3), faces.shape=(13772, 3))> -119``` -120 -121Next see if there is stuff to fix in the mesh (degenerate faces, duplicate -122vertices, etc.): -123 -124```Python -125>>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False) -126>>> fixed -127<trimesh.Trimesh(vertices.shape=(6213, 3), faces.shape=(12805, 3))> -128``` -129 -130Now for tubular meshes like this neuron, the "wave front" skeletonization method -131performs really well: it works by casting waves across the mesh and collapsing -132the resulting rings into a skeleton (kinda like when you throw a stone in a -133pond and track the expanding ripples). -134 -135```Python -136>>> skel = sk.skeletonize.by_wavefront(fixed, waves=1, step_size=1) -137>>> skel -138<Skeleton(vertices=(1258, 3), edges=(1194, 2), method=wavefront)> -139``` -140 -141All skeletonization methods return a `Skeleton` object. These are just -142convenient objects to bundle the various outputs of the skeletonization. -143 -144```Python -145>>> # x/y/z location of skeleton vertices (nodes) -146>>> skel.vertices -147array([[16744, 36720, 26407], -148 ..., -149 [22076, 23217, 24472]]) -150>>> # child -> parent edges -151>>> skel.edges -152array([[ 64, 31], -153 ..., -154 [1257, 1252]]) -155>>> # Mapping for mesh to skeleton vertex indices -156>>> skel.mesh_map -157array([ 157, 158, 1062, ..., 525, 474, 547]) -158>>> # SWC table -159>>> skel.swc.head() -160 node_id parent_id x y z radius -1610 0 -1 16744.005859 36720.058594 26407.902344 0.000000 -1621 1 -1 5602.751953 22266.756510 15799.991211 7.542587 -1632 2 -1 16442.666667 14999.978516 10887.916016 5.333333 -164``` -165 -166SWC is a commonly used format for saving skeletons. `Skeleton` objects -167have a method for quickly saving a correctly formatted SWC file: -168 -169```Python -170>>> skel.save_swc('~/Documents/my_skeleton.swc') -171``` -172 -173If you installed `pyglet` (see above) you can also use `trimesh`'s plotting -174capabilities to inspect the results: -175 -176```Python -177>>> skel.show(mesh=True) -178``` -179 -180<img src="https://github.com/navis-org/skeletor/raw/master/_static/example1.png" alt="skeletor_example" width="100%"/> -181 -182That looks pretty good already but let's run some pro-forma postprocessing. -183 -184```Python -185>>> sk.post.clean_up(skel, inplace=True) -186<Skeleton(vertices=(1071, 3), edges=(1070, 2))> -187``` -188 -189So that would be a full pipeline mesh to skeleton. Don't expect your own meshes -190to produce such nice results off the bat though. Chances are you will need to -191play around to find the right recipe. If you don't know where to start, I suggest -192you try out mesh contraction + vertex clustering first: -193 -194```Python -195>>> import skeletor as sk -196>>> # Load the example mesh that ships with skeletor -197>>> mesh = sk.example_mesh() -198>>> # Alternatively use trimesh to load/construct your own mesh: -199>>> # import trimesh as tm -200>>> # mesh = tm.Trimesh(vertices, faces) -201>>> # mesh = tm.load_mesh('some/mesh.obj') -202>>> # Run some general clean-up (see docstring for details) -203>>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False) -204>>> # Contract mesh to 10% (0.1) of original volume -205>>> cont = sk.pre.contract(fixed, epsilon=0.1) -206>>> # Skeletonize -207>>> skel = sk.skeletonize.by_vertex_clusters(cont, sampling_dist=100) -208>>> # Replace contracted mesh with original for postprocessing and plotting -209>>> skel.mesh = fixed -210>>> # Add radii (vertex cluster method does not do that automatically) -211>>> sk.post.radii(skel, method='knn') -212>>> skel.show(mesh=True) -213``` -214 -215# Gotchas -216 -217- while this is a general purpose library, my personal focus is on neurons and -218 this has certainly influenced things like default parameter values and certain -219 post-processing steps -220- meshes need to be triangular (we are using `trimesh`) -221- use `sk.pre.simplify` if your mesh is very complex (half a million vertices is -222 where things start getting sluggish) -223- a good mesh contraction is often half the battle but it can be tricky to get -224 to work -225- if the mesh consists of multiple disconnected pieces the skeleton will -226 likewise be fragmented (i.e. will have multiple roots) -227- it's often a good idea to fix issues with the skeleton in postprocessing rather -228 than trying to get the skeletonization to be perfect -229 -230# Benchmarks -231 -232<img src="https://github.com/navis-org/skeletor/raw/master/benchmarks/benchmark_2.png" alt="skeletor_benchmark" width="100%"/> -233 -234[Benchmarks](https://github.com/navis-org/skeletor/blob/master/benchmarks/skeletor_benchmark.ipynb) -235were run on a 2018 MacBook Pro (2.2 GHz Core i7, 32Gb memory) with optional -236`fastremap` dependency installed. Note some of these functions (e.g. -237contraction and TEASAR/vertex cluster skeletonization) vary a lot in -238speed based on parameterization. -239 -240# What about algorithm `X`? -241 -242`skeletor` contains some algorithms that I found easy enough to implement -243and useful for my work with neurons. If you have some interesting paper/approach -244that could make a nice addition to `skeletor`, please get in touch on Github. -245Pull requests are always welcome! -246 -247# References -248 -249`[1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.` -250 -251The abstract and the paper can be found [here](http://visgraph.cse.ust.hk/projects/skeleton/). -252Also see [this](https://www.youtube.com/watch?v=-H7n59YQCRM&feature=youtu.be) YouTube video. -253 -254Some of the code in skeletor was modified from the -255[Py_BL_MeshSkeletonization](https://github.com/aalavandhaann/Py_BL_MeshSkeletonization) -256addon created by #0K Srinivasan Ramachandran and published under GPL3. -257 -258# Top-level functions and classes -259At top-level we only expose `example_mesh()` and the `Skeleton` class (which -260you probably won't ever need to touch manually). Everything else is neatly -261tucked away into submodules (see side-bar or above table). -262 -263""" -264 -265__version__ = "1.3.0" -266__version_vector__ = (1, 3, 0) -267 -268from . import skeletonize -269from . import pre -270from . import post -271 -272from .skeletonize.base import Skeleton -273from .data import example_mesh -274 -275__docformat__ = "numpy" -276 -277__all__ = ['Skeleton', 'example_mesh', 'pre', 'post', 'skeletonize'] +102 6. `skeletor.post.smooth()` to smooth the skeleton +103 7. `skeletor.post.radii()` to extract radii either by k-nearest neighbours or ray-casting +104 +105In my experience there is no one-size-fits-all. You will have to play around to +106find the right approach and parameters to get nice skeletons for your meshes. +107If you need help just open an [issue](https://github.com/navis-org/skeletor/issues). +108 +109Also check out the Gotchas below! +110 +111# Examples +112 +113First load the example mesh (a fruit fly neuron): +114 +115```Python +116>>> import skeletor as sk +117>>> mesh = sk.example_mesh() +118>>> mesh +119<trimesh.Trimesh(vertices.shape=(6582, 3), faces.shape=(13772, 3))> +120``` +121 +122Next see if there is stuff to fix in the mesh (degenerate faces, duplicate +123vertices, etc.): +124 +125```Python +126>>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False) +127>>> fixed +128<trimesh.Trimesh(vertices.shape=(6213, 3), faces.shape=(12805, 3))> +129``` +130 +131Now for tubular meshes like this neuron, the "wave front" skeletonization method +132performs really well: it works by casting waves across the mesh and collapsing +133the resulting rings into a skeleton (kinda like when you throw a stone in a +134pond and track the expanding ripples). +135 +136```Python +137>>> skel = sk.skeletonize.by_wavefront(fixed, waves=1, step_size=1) +138>>> skel +139<Skeleton(vertices=(1258, 3), edges=(1194, 2), method=wavefront)> +140``` +141 +142All skeletonization methods return a `Skeleton` object. These are just +143convenient objects to bundle the various outputs of the skeletonization. +144 +145```Python +146>>> # x/y/z location of skeleton vertices (nodes) +147>>> skel.vertices +148array([[16744, 36720, 26407], +149 ..., +150 [22076, 23217, 24472]]) +151>>> # child -> parent edges +152>>> skel.edges +153array([[ 64, 31], +154 ..., +155 [1257, 1252]]) +156>>> # Mapping for mesh to skeleton vertex indices +157>>> skel.mesh_map +158array([ 157, 158, 1062, ..., 525, 474, 547]) +159>>> # SWC table +160>>> skel.swc.head() +161 node_id parent_id x y z radius +1620 0 -1 16744.005859 36720.058594 26407.902344 0.000000 +1631 1 -1 5602.751953 22266.756510 15799.991211 7.542587 +1642 2 -1 16442.666667 14999.978516 10887.916016 5.333333 +165``` +166 +167SWC is a commonly used format for saving skeletons. `Skeleton` objects +168have a method for quickly saving a correctly formatted SWC file: +169 +170```Python +171>>> skel.save_swc('~/Documents/my_skeleton.swc') +172``` +173 +174If you installed `pyglet` (see above) you can also use `trimesh`'s plotting +175capabilities to inspect the results: +176 +177```Python +178>>> skel.show(mesh=True) +179``` +180 +181<img src="https://github.com/navis-org/skeletor/raw/master/_static/example1.png" alt="skeletor_example" width="100%"/> +182 +183That looks pretty good already but let's run some pro-forma postprocessing. +184 +185```Python +186>>> sk.post.clean_up(skel, inplace=True) +187<Skeleton(vertices=(1071, 3), edges=(1070, 2))> +188``` +189 +190So that would be a full pipeline mesh to skeleton. Don't expect your own meshes +191to produce such nice results off the bat though. Chances are you will need to +192play around to find the right recipe. If you don't know where to start, I suggest +193you try out mesh contraction + vertex clustering first: +194 +195```Python +196>>> import skeletor as sk +197>>> # Load the example mesh that ships with skeletor +198>>> mesh = sk.example_mesh() +199>>> # Alternatively use trimesh to load/construct your own mesh: +200>>> # import trimesh as tm +201>>> # mesh = tm.Trimesh(vertices, faces) +202>>> # mesh = tm.load_mesh('some/mesh.obj') +203>>> # Run some general clean-up (see docstring for details) +204>>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False) +205>>> # Contract mesh to 10% (0.1) of original volume +206>>> cont = sk.pre.contract(fixed, epsilon=0.1) +207>>> # Skeletonize +208>>> skel = sk.skeletonize.by_vertex_clusters(cont, sampling_dist=100) +209>>> # Replace contracted mesh with original for postprocessing and plotting +210>>> skel.mesh = fixed +211>>> # Add radii (vertex cluster method does not do that automatically) +212>>> sk.post.radii(skel, method='knn') +213>>> skel.show(mesh=True) +214``` +215 +216# Gotchas +217 +218- while this is a general purpose library, my personal focus is on neurons and +219 this has certainly influenced things like default parameter values and certain +220 post-processing steps +221- meshes need to be triangular (we are using `trimesh`) +222- use `sk.pre.simplify` if your mesh is very complex (half a million vertices is +223 where things start getting sluggish) +224- a good mesh contraction is often half the battle but it can be tricky to get +225 to work +226- if the mesh consists of multiple disconnected pieces the skeleton will +227 likewise be fragmented (i.e. will have multiple roots) +228- it's often a good idea to fix issues with the skeleton in postprocessing rather +229 than trying to get the skeletonization to be perfect +230 +231# Benchmarks +232 +233<img src="https://github.com/navis-org/skeletor/raw/master/benchmarks/benchmark_2.png" alt="skeletor_benchmark" width="100%"/> +234 +235[Benchmarks](https://github.com/navis-org/skeletor/blob/master/benchmarks/skeletor_benchmark.ipynb) +236were run on a 2018 MacBook Pro (2.2 GHz Core i7, 32Gb memory) with optional +237`fastremap` dependency installed. Note some of these functions (e.g. +238contraction and TEASAR/vertex cluster skeletonization) vary a lot in +239speed based on parameterization. +240 +241# What about algorithm `X`? +242 +243`skeletor` contains some algorithms that I found easy enough to implement +244and useful for my work with neurons. If you have some interesting paper/approach +245that could make a nice addition to `skeletor`, please get in touch on Github. +246Pull requests are always welcome! +247 +248# References +249 +250`[1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.` +251 +252The abstract and the paper can be found [here](http://visgraph.cse.ust.hk/projects/skeleton/). +253Also see [this](https://www.youtube.com/watch?v=-H7n59YQCRM&feature=youtu.be) YouTube video. +254 +255Some of the code in skeletor was modified from the +256[Py_BL_MeshSkeletonization](https://github.com/aalavandhaann/Py_BL_MeshSkeletonization) +257addon created by #0K Srinivasan Ramachandran and published under GPL3. +258 +259# Top-level functions and classes +260At top-level we only expose `example_mesh()` and the `Skeleton` class (which +261you probably won't ever need to touch manually). Everything else is neatly +262tucked away into submodules (see side-bar or above table). +263 +264""" +265 +266__version__ = "1.3.0" +267__version_vector__ = (1, 3, 0) +268 +269from . import skeletonize +270from . import pre +271from . import post +272 +273from .skeletonize.base import Skeleton +274from .data import example_mesh +275 +276__docformat__ = "numpy" +277 +278__all__ = ['Skeleton', 'example_mesh', 'pre', 'post', 'skeletonize'] diff --git a/docs/search.js b/docs/search.js index 1ff7b54..1c886c2 100644 --- a/docs/search.js +++ b/docs/search.js @@ -1,6 +1,6 @@ window.pdocSearch = (function(){ /** elasticlunr - http://weixsong.github.io * Copyright (C) 2017 Oliver Nightingale * Copyright (C) 2017 Wei Song * MIT Licensed */!function(){function e(e){if(null===e||"object"!=typeof e)return e;var t=e.constructor();for(var n in e)e.hasOwnProperty(n)&&(t[n]=e[n]);return t}var t=function(e){var n=new t.Index;return n.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),e&&e.call(n,n),n};t.version="0.9.5",lunr=t,t.utils={},t.utils.warn=function(e){return function(t){e.console&&console.warn&&console.warn(t)}}(this),t.utils.toString=function(e){return void 0===e||null===e?"":e.toString()},t.EventEmitter=function(){this.events={}},t.EventEmitter.prototype.addListener=function(){var e=Array.prototype.slice.call(arguments),t=e.pop(),n=e;if("function"!=typeof t)throw new TypeError("last argument must be a function");n.forEach(function(e){this.hasHandler(e)||(this.events[e]=[]),this.events[e].push(t)},this)},t.EventEmitter.prototype.removeListener=function(e,t){if(this.hasHandler(e)){var n=this.events[e].indexOf(t);-1!==n&&(this.events[e].splice(n,1),0==this.events[e].length&&delete this.events[e])}},t.EventEmitter.prototype.emit=function(e){if(this.hasHandler(e)){var t=Array.prototype.slice.call(arguments,1);this.events[e].forEach(function(e){e.apply(void 0,t)},this)}},t.EventEmitter.prototype.hasHandler=function(e){return e in this.events},t.tokenizer=function(e){if(!arguments.length||null===e||void 0===e)return[];if(Array.isArray(e)){var n=e.filter(function(e){return null===e||void 0===e?!1:!0});n=n.map(function(e){return t.utils.toString(e).toLowerCase()});var i=[];return n.forEach(function(e){var n=e.split(t.tokenizer.seperator);i=i.concat(n)},this),i}return e.toString().trim().toLowerCase().split(t.tokenizer.seperator)},t.tokenizer.defaultSeperator=/[\s\-]+/,t.tokenizer.seperator=t.tokenizer.defaultSeperator,t.tokenizer.setSeperator=function(e){null!==e&&void 0!==e&&"object"==typeof e&&(t.tokenizer.seperator=e)},t.tokenizer.resetSeperator=function(){t.tokenizer.seperator=t.tokenizer.defaultSeperator},t.tokenizer.getSeperator=function(){return t.tokenizer.seperator},t.Pipeline=function(){this._queue=[]},t.Pipeline.registeredFunctions={},t.Pipeline.registerFunction=function(e,n){n in t.Pipeline.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+n),e.label=n,t.Pipeline.registeredFunctions[n]=e},t.Pipeline.getRegisteredFunction=function(e){return e in t.Pipeline.registeredFunctions!=!0?null:t.Pipeline.registeredFunctions[e]},t.Pipeline.warnIfFunctionNotRegistered=function(e){var n=e.label&&e.label in this.registeredFunctions;n||t.utils.warn("Function is not registered with pipeline. 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this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oWhat is skeletor?\n\n

    Unlike its namesake, this skeletor\ndoes not (yet) seek to conquer Eternia but to turn meshes into skeletons.

    \n\n

    Before we get started some terminology:

    \n\n
      \n
    • a mesh is something that consists of vertices and faces
      • \n
    • a skeleton is a (hierarchical) tree-like structure consisting of vertices\n(also called nodes) and edges that connect them
      • \n
    \n\n

    Skeletons are useful for a range of reasons. For example:

    \n\n
      \n
    1. Typically smaller (less vertices) than the mesh
      2. \n
    2. Have an implicit sense of topology (e.g. \"this node is distal to that node\")
      3. \n
    \n\n

    Extracting skeletons from meshes (or other types of data such as voxels) is\nnon-trivial and there are a great many research papers exploring various\ndifferent approaches (see Google scholar).

    \n\n

    skeletor implements some algorithms that I found useful in my work with\nneurons. In my experience there is unfortuntely no magic bullet when it\ncomes to skeletonization and chances are you will have to fiddle around a bit\nto get decent results.

    \n\n

    Installation

    \n\n

    From PyPI:

    \n\n
    \n
    pip3 install skeletor\n
    \n
    \n\n

    For the bleeding-edge version from Github:

    \n\n
    \n
    pip3 install git+https://github.com/navis-org/skeletor@master\n
    \n
    \n\n

    Getting started

    \n\n

    A skeletonization pipeline typically consists of:

    \n\n
      \n
    1. Some pre-processing of the mesh (e.g. fixing some potential errors like\ndegenerate faces, unreferenced vertices, etc.)
      2. \n
    2. The skeletonization itself
      3. \n
    3. Some post-processing of the skeleton (e.g. adding radius information, smoothing, etc.)
      4. \n
    \n\n
    \n\n

    Here is a complete list of available functions:

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n
    functiondescription
    example data
    skeletor.example_mesh()load an example mesh
    pre-processing
    skeletor.pre.fix_mesh()fix some common errors found in meshes
    skeletor.pre.remesh()re-generate mesh (uses Blender 3D)
    skeletor.pre.simplify()reduce mesh complexity (uses Blender 3D)
    skeletor.pre.contract()contract mesh to facilitate skeletonization [1]
    skeletonization
    skeletor.skeletonize.by_wavefront()very fast, works well for tubular meshes (like neurons)
    skeletor.skeletonize.by_vertex_clusters()very fast but needs mesh to be contracted (see above)
    skeletor.skeletonize.by_edge_collapse()presented in [1] but never got this to work well
    skeletor.skeletonize.by_teasar()very fast and robust, works on mesh surface
    skeletor.skeletonize.by_tangent_ball()very fast, best on smooth meshes
    postprocessing
    skeletor.post.clean_up()fix some potential errors in the skeleton
    skeletor.post.radii()add radius information using various method
    skeletor.post.smooth()smooth the skeleton
    skeletor.post.remove_bristles()remove single-node bristles from the skeleton
    skeletor.post.despike()smooth out jumps in the skeleton
    \n\n
    \n\n

    See docstrings of the respective functions for details.

    \n\n

    A pipeline might look like this:

    \n\n
      \n
    1. skeletor.pre.fix_mesh() to fix the mesh
      2. \n
    2. skeletor.pre.simplify() to simplify the mesh
      3. \n
    3. skeletor.pre.contract() to contract the mesh [1]
      4. \n
    4. skeletor.skeletonize.vertex_clusters() to generate a skeleton
      5. \n
    5. skeletor.post.clean_up() to clean up some potential issues with the skeleton
      6. \n
    6. skeletor.post.radii() to extract radii either by k-nearest neighbours or ray-casting
      7. \n
    \n\n

    In my experience there is no one-size-fits-all. You will have to play around to\nfind the right approach and parameters to get nice skeletons for your meshes.\nIf you need help just open an issue.

    \n\n

    Also check out the Gotchas below!

    \n\n

    Examples

    \n\n

    First load the example mesh (a fruit fly neuron):

    \n\n
    \n
    >>> import skeletor as sk\n>>> mesh = sk.example_mesh()\n>>> mesh\n<trimesh.Trimesh(vertices.shape=(6582, 3), faces.shape=(13772, 3))>\n
    \n
    \n\n

    Next see if there is stuff to fix in the mesh (degenerate faces, duplicate\nvertices, etc.):

    \n\n
    \n
    >>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False)\n>>> fixed\n<trimesh.Trimesh(vertices.shape=(6213, 3), faces.shape=(12805, 3))>\n
    \n
    \n\n

    Now for tubular meshes like this neuron, the \"wave front\" skeletonization method\nperforms really well: it works by casting waves across the mesh and collapsing\nthe resulting rings into a skeleton (kinda like when you throw a stone in a\npond and track the expanding ripples).

    \n\n
    \n
    >>> skel = sk.skeletonize.by_wavefront(fixed, waves=1, step_size=1)\n>>> skel\n<Skeleton(vertices=(1258, 3), edges=(1194, 2), method=wavefront)>\n
    \n
    \n\n

    All skeletonization methods return a Skeleton object. These are just\nconvenient objects to bundle the various outputs of the skeletonization.

    \n\n
    \n
    >>> # x/y/z location of skeleton vertices (nodes)\n>>> skel.vertices\narray([[16744, 36720, 26407],\n       ...,\n       [22076, 23217, 24472]])\n>>> # child -> parent edges\n>>> skel.edges\narray([[  64,   31],\n       ...,\n       [1257, 1252]])\n>>> # Mapping for mesh to skeleton vertex indices\n>>> skel.mesh_map\narray([ 157,  158, 1062, ...,  525,  474,  547])\n>>> # SWC table\n>>> skel.swc.head()\n   node_id  parent_id             x             y             z    radius\n0        0         -1  16744.005859  36720.058594  26407.902344  0.000000\n1        1         -1   5602.751953  22266.756510  15799.991211  7.542587\n2        2         -1  16442.666667  14999.978516  10887.916016  5.333333\n
    \n
    \n\n

    SWC is a commonly used format for saving skeletons. Skeleton objects\nhave a method for quickly saving a correctly formatted SWC file:

    \n\n
    \n
    >>> skel.save_swc('~/Documents/my_skeleton.swc')\n
    \n
    \n\n

    If you installed pyglet (see above) you can also use trimesh's plotting\ncapabilities to inspect the results:

    \n\n
    \n
    >>> skel.show(mesh=True)\n
    \n
    \n\n

    \"skeletor_example\"

    \n\n

    That looks pretty good already but let's run some pro-forma postprocessing.

    \n\n
    \n
    >>> sk.post.clean_up(skel, inplace=True)\n<Skeleton(vertices=(1071, 3), edges=(1070, 2))>\n
    \n
    \n\n

    So that would be a full pipeline mesh to skeleton. Don't expect your own meshes\nto produce such nice results off the bat though. Chances are you will need to\nplay around to find the right recipe. If you don't know where to start, I suggest\nyou try out mesh contraction + vertex clustering first:

    \n\n
    \n
    >>> import skeletor as sk\n>>> # Load the example mesh that ships with skeletor\n>>> mesh = sk.example_mesh()\n>>> # Alternatively use trimesh to load/construct your own mesh:\n>>> # import trimesh as tm\n>>> # mesh = tm.Trimesh(vertices, faces)\n>>> # mesh = tm.load_mesh('some/mesh.obj')\n>>> # Run some general clean-up (see docstring for details)\n>>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False)\n>>> # Contract mesh to 10% (0.1) of original volume\n>>> cont = sk.pre.contract(fixed, epsilon=0.1)\n>>> # Skeletonize\n>>> skel = sk.skeletonize.by_vertex_clusters(cont, sampling_dist=100)\n>>> # Replace contracted mesh with original for postprocessing and plotting\n>>> skel.mesh = fixed\n>>> # Add radii (vertex cluster method does not do that automatically)\n>>> sk.post.radii(skel, method='knn')\n>>> skel.show(mesh=True)\n
    \n
    \n\n

    Gotchas

    \n\n
      \n
    • while this is a general purpose library, my personal focus is on neurons and\nthis has certainly influenced things like default parameter values and certain\npost-processing steps
      • \n
    • meshes need to be triangular (we are using trimesh)
      • \n
    • use sk.pre.simplify if your mesh is very complex (half a million vertices is\nwhere things start getting sluggish)
      • \n
    • a good mesh contraction is often half the battle but it can be tricky to get\nto work
      • \n
    • if the mesh consists of multiple disconnected pieces the skeleton will\nlikewise be fragmented (i.e. will have multiple roots)
      • \n
    • it's often a good idea to fix issues with the skeleton in postprocessing rather\nthan trying to get the skeletonization to be perfect
      • \n
    \n\n

    Benchmarks

    \n\n

    \"skeletor_benchmark\"

    \n\n

    Benchmarks\nwere run on a 2018 MacBook Pro (2.2 GHz Core i7, 32Gb memory) with optional\nfastremap dependency installed. Note some of these functions (e.g.\ncontraction and TEASAR/vertex cluster skeletonization) vary a lot in\nspeed based on parameterization.

    \n\n

    What about algorithm X?

    \n\n

    skeletor contains some algorithms that I found easy enough to implement\nand useful for my work with neurons. If you have some interesting paper/approach\nthat could make a nice addition to skeletor, please get in touch on Github.\nPull requests are always welcome!

    \n\n

    References

    \n\n

    [1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.

    \n\n

    The abstract and the paper can be found here.\nAlso see this YouTube video.

    \n\n

    Some of the code in skeletor was modified from the\nPy_BL_MeshSkeletonization\naddon created by #0K Srinivasan Ramachandran and published under GPL3.

    \n\n

    Top-level functions and classes

    \n\n

    At top-level we only expose example_mesh() and the Skeleton class (which\nyou probably won't ever need to touch manually). Everything else is neatly\ntucked away into submodules (see side-bar or above table).

    \n"}, "skeletor.Skeleton": {"fullname": "skeletor.Skeleton", "modulename": "skeletor", "qualname": "Skeleton", "kind": "class", "doc": "

    Class representing a skeleton.

    \n\n

    Typically returned as results from a skeletonization.

    \n\n
    Attributes
    \n\n
      \n
    • swc (pd.DataFrame, optional):\nSWC table.
      • \n
    • vertices ((N, 3) array):\nVertex (node) positions.
      • \n
    • edges ((M, 2) array):\nIndices of connected vertex pairs.
      • \n
    • radii ((N, ) array, optional):\nRadii for each vertex (node) in the skeleton.
      • \n
    • mesh (trimesh, optional):\nThe original mesh.
      • \n
    • mesh_map (array, optional):\nSame length as mesh. Maps mesh vertices to vertices (nodes)\nin the skeleton.
      • \n
    • skel_map (array of arrays, optional):\nInverse of mesh_map: maps skeleton vertices (nodes) to mesh\nvertices.
      • \n
    • method (str, optional):\nWhich method was used to generate the skeleton.
      • \n
    \n"}, "skeletor.Skeleton.__init__": {"fullname": "skeletor.Skeleton.__init__", "modulename": "skeletor", "qualname": "Skeleton.__init__", "kind": "function", "doc": "

    \n", "signature": "(swc, mesh=None, mesh_map=None, method=None)"}, "skeletor.Skeleton.swc": {"fullname": "skeletor.Skeleton.swc", "modulename": "skeletor", "qualname": "Skeleton.swc", "kind": "variable", "doc": "

    \n"}, "skeletor.Skeleton.mesh": {"fullname": "skeletor.Skeleton.mesh", "modulename": "skeletor", "qualname": "Skeleton.mesh", "kind": "variable", "doc": "

    \n"}, "skeletor.Skeleton.mesh_map": {"fullname": "skeletor.Skeleton.mesh_map", "modulename": "skeletor", "qualname": "Skeleton.mesh_map", "kind": "variable", "doc": "

    \n"}, "skeletor.Skeleton.method": {"fullname": "skeletor.Skeleton.method", "modulename": "skeletor", "qualname": "Skeleton.method", "kind": "variable", "doc": "

    \n"}, "skeletor.Skeleton.edges": {"fullname": "skeletor.Skeleton.edges", "modulename": "skeletor", "qualname": "Skeleton.edges", "kind": "variable", "doc": "

    Return skeleton edges.

    \n"}, "skeletor.Skeleton.vertices": {"fullname": "skeletor.Skeleton.vertices", "modulename": "skeletor", "qualname": "Skeleton.vertices", "kind": "variable", "doc": "

    Return skeleton vertices (nodes).

    \n"}, "skeletor.Skeleton.radius": {"fullname": "skeletor.Skeleton.radius", "modulename": "skeletor", "qualname": "Skeleton.radius", "kind": "variable", "doc": "

    Return radii.

    \n"}, "skeletor.Skeleton.skeleton": {"fullname": "skeletor.Skeleton.skeleton", "modulename": "skeletor", "qualname": "Skeleton.skeleton", "kind": "variable", "doc": "

    Skeleton as trimesh Path3D.

    \n"}, "skeletor.Skeleton.skel_map": {"fullname": "skeletor.Skeleton.skel_map", "modulename": "skeletor", "qualname": "Skeleton.skel_map", "kind": "variable", "doc": "

    Skeleton vertex (nodes) to mesh vertices. Based on mesh_map.

    \n"}, "skeletor.Skeleton.leafs": {"fullname": "skeletor.Skeleton.leafs", "modulename": "skeletor", "qualname": "Skeleton.leafs", "kind": "variable", "doc": "

    Leaf nodes (includes root).

    \n"}, "skeletor.Skeleton.reindex": {"fullname": "skeletor.Skeleton.reindex", "modulename": "skeletor", "qualname": "Skeleton.reindex", "kind": "function", "doc": "

    Clean up skeleton.

    \n", "signature": "(self, inplace=False):", "funcdef": "def"}, "skeletor.Skeleton.copy": {"fullname": "skeletor.Skeleton.copy", "modulename": "skeletor", "qualname": "Skeleton.copy", "kind": "function", "doc": "

    Return copy of the skeleton.

    \n", "signature": "(self):", "funcdef": "def"}, "skeletor.Skeleton.get_graph": {"fullname": "skeletor.Skeleton.get_graph", "modulename": "skeletor", "qualname": "Skeleton.get_graph", "kind": "function", "doc": "

    Generate networkX representation of the skeletons.

    \n\n

    Distance between nodes will be used as edge weights.

    \n\n
    Returns
    \n\n
      \n
    • networkx.DiGraph
      • \n
    \n", "signature": "(self):", "funcdef": "def"}, "skeletor.Skeleton.get_segments": {"fullname": "skeletor.Skeleton.get_segments", "modulename": "skeletor", "qualname": "Skeleton.get_segments", "kind": "function", "doc": "

    Generate a list of linear segments while maximizing segment lengths.

    \n\n
    Parameters
    \n\n
      \n
    • weight ('weight' | None, optional):\nIf \"weight\" use physical, geodesic length to determine\nsegment length. If None use number of nodes (faster).
      • \n
    • return_lengths (bool):\nIf True, also return lengths of segments according to weight.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • segments (list):\nSegments as list of lists containing node IDs. List is\nsorted by segment lengths.
      • \n
    • lengths (list):\nLength for each segment according to weight. Only provided\nif return_lengths is True.
      • \n
    \n", "signature": "(self, weight='weight', return_lengths=False):", "funcdef": "def"}, "skeletor.Skeleton.save_swc": {"fullname": "skeletor.Skeleton.save_swc", "modulename": "skeletor", "qualname": "Skeleton.save_swc", "kind": "function", "doc": "

    Save skeleton in SWC format.

    \n\n
    Parameters
    \n\n
      \n
    • filepath (path-like):\nFilepath to save SWC to.
      • \n
    \n", "signature": "(self, filepath):", "funcdef": "def"}, "skeletor.Skeleton.scene": {"fullname": "skeletor.Skeleton.scene", "modulename": "skeletor", "qualname": "Skeleton.scene", "kind": "function", "doc": "

    Return a Scene object containing the skeleton.

    \n\n
    Returns
    \n\n
      \n
    • scene (trimesh.scene.scene.Scene):\nContains the skeleton and optionally the mesh.
      • \n
    \n", "signature": "(self, mesh=False, **kwargs):", "funcdef": "def"}, "skeletor.Skeleton.show": {"fullname": "skeletor.Skeleton.show", "modulename": "skeletor", "qualname": "Skeleton.show", "kind": "function", "doc": "

    Render the skeleton in an opengl window. Requires pyglet.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (bool):\nIf True, will render transparent mesh on top of the\nskeleton.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scene (trimesh.scene.Scene):\nScene with skeleton in it.
      • \n
    \n", "signature": "(self, mesh=False, **kwargs):", "funcdef": "def"}, "skeletor.example_mesh": {"fullname": "skeletor.example_mesh", "modulename": "skeletor", "qualname": "example_mesh", "kind": "function", "doc": "

    Load and return example mesh.

    \n\n

    The example mesh is a fruit fly neuron (an olfactory projection neuron of\nthe DA1 glomerulus) segmented from an EM image data set. It is part of the\nJanelia hemibrain data set (see here) [1].

    \n\n
    References
    \n\n

    [1] Louis K. Scheffer et al., eLife. 2020. doi: 10.7554/eLife.57443\nA connectome and analysis of the adult Drosophila central brain

    \n\n
    Returns
    \n\n
      \n
    • trimesh.Trimesh
      • \n
    \n\n
    Examples
    \n\n
    \n
    >>> import skeletor as sk\n>>> # Load this example mesh\n>>> mesh = sk.example_mesh()\n
    \n
    \n", "signature": "():", "funcdef": "def"}, "skeletor.post": {"fullname": "skeletor.post", "modulename": "skeletor.post", "kind": "module", "doc": "

    The skeletor.post module contains functions to post-process skeletons after\nskeletonization.

    \n\n

    Fixing issues with skeletons

    \n\n

    Depending on your mesh, pre-processing and the parameters you chose for\nskeletonization, chances are that your skeleton will not come out perfectly.

    \n\n

    skeletor.post.clean_up can help you solve some potential issues:

    \n\n
      \n
    • skeleton nodes (vertices) that outside or right on the surface instead of\ncentered inside the mesh
      • \n
    • superfluous \"hairs\" on otherwise straight bits
      • \n
    \n\n

    skeletor.post.smooth will smooth out the skeleton.

    \n\n

    skeletor.post.despike can help you remove spikes in the skeleton where\nsingle nodes are out of aligment.

    \n\n

    skeletor.post.remove_bristles will remove bristles from the skeleton.

    \n\n

    Computing radius information

    \n\n

    Only skeletor.skeletonize.by_wavefront() provides radii off the bat. For all\nother methods, you might want to run skeletor.post.radii can help you\n(re-)generate radius information for the skeletons.

    \n"}, "skeletor.post.radii": {"fullname": "skeletor.post.radii", "modulename": "skeletor.post", "qualname": "radii", "kind": "function", "doc": "

    Extract radii for given skeleton table.

    \n\n
    Important
    \n\n

    This function really only produces useful radii if the skeleton is centered\ninside the mesh. by_wavefront does that by default whereas all other\nskeletonization methods don't. Your best bet to get centered skeletons is\nto contract the mesh first (sk.pre.contract).

    \n\n
    Parameters
    \n\n
      \n
    • s (skeletor.Skeleton):\nSkeleton to clean up.
      • \n
    • mesh (trimesh.Trimesh, optional):\nOriginal mesh (e.g. before contraction). If not provided will\nuse the mesh associated with s.
      • \n

    • method (\"knn\" | \"ray\"):\nWhether and how to add radius information to each node::

      \n\n
        \n
      • \"knn\" uses k-nearest-neighbors to get radii: fast but\npotential for being very wrong
        • \n
      • \"ray\" uses ray-casting to get radii: slower but sometimes\nless wrong
        • \n
      • \n
    • aggregate (\"mean\" | \"median\" | \"max\" | \"min\" | \"percentile75\"):\nFunction used to aggregate radii over sample (i.e. across\nk nearest-neighbors or ray intersections)
      • \n
    • validate (bool):\nIf True, will try to fix potential issues with the mesh\n(e.g. infinite values, duplicate vertices, degenerate faces)\nbefore skeletonization. Note that this might make changes to\nyour mesh inplace!
      • \n
    • **kwargs: Keyword arguments are passed to the respective method:
      • \n
    \n\n

    For method \"knn\"::

    \n\n
    n :             int (default 5)\n                Radius will be the mean over n nearest-neighbors.\n
    \n\n

    For method \"ray\"::

    \n\n
    n_rays :        int (default 20)\n                Number of rays to cast for each node.\nprojection :    \"sphere\" (default) | \"tangents\"\n                Whether to cast rays in a sphere around each node or in a\n                circle orthogonally to the node's tangent vector.\nfallback :      \"knn\" (default) | None | number\n                If a point is outside or right on the surface of the mesh\n                the raycasting will return nonesense results. We can either\n                ignore those cases (``None``), assign a arbitrary number or\n                we can fall back to radii from k-nearest-neighbors (``knn``).\n
    \n\n
    Returns
    \n\n
      \n
    • None: But attaches radius to the skeleton's SWC table. Existing\nvalues are replaced!
      • \n
    \n", "signature": "(\ts,\tmesh=None,\tmethod='knn',\taggregate='mean',\tvalidate=False,\t**kwargs):", "funcdef": "def"}, "skeletor.post.clean_up": {"fullname": "skeletor.post.clean_up", "modulename": "skeletor.post", "qualname": "clean_up", "kind": "function", "doc": "

    Clean up the skeleton.

    \n\n

    This function bundles a bunch of procedures to clean up the skeleton:

    \n\n
      \n
    1. Remove twigs that are running parallel to their parent branch
      2. \n
    2. Move nodes outside the mesh back inside (or at least snap to surface)
      3. \n
    \n\n

    Note that this is not a magic bullet and some of this will not work (well)\nif the original mesh was degenerate (e.g. internal faces or not watertight)\nto begin with.

    \n\n
    Parameters
    \n\n
      \n
    • s (skeletor.Skeleton):\nSkeleton to clean up.
      • \n
    • mesh (trimesh.Trimesh, optional):\nOriginal mesh (e.g. before contraction). If not provided will\nuse the mesh associated with s.
      • \n
    • validate (bool):\nIf True, will try to fix potential issues with the mesh\n(e.g. infinite values, duplicate vertices, degenerate faces)\nbefore cleaning up. Note that this might change your mesh\ninplace!
      • \n
    • inplace (bool):\nIf False will make and return a copy of the skeleton. If True,\nwill modify the s inplace.
      • \n
    • **kwargs: Keyword arguments are passed to the bundled function.
      • \n
    \n\n

    For skeletor.postprocessing.drop_parallel_twigs::

    \n\n

    theta : float (default 0.01)\n For each twig we generate the dotproduct between the tangent\n vectors of it and its parents. If these line up perfectly the\n dotproduct will equal 1. theta determines how much that\n value can differ from 1 for us to still prune the twig: higher\n theta = more pruning.

    \n\n
    Returns
    \n\n
      \n
    • s_clean (skeletor.Skeleton):\nHopefully improved skeleton.
      • \n
    \n", "signature": "(s, mesh=None, validate=False, inplace=False, **kwargs):", "funcdef": "def"}, "skeletor.post.smooth": {"fullname": "skeletor.post.smooth", "modulename": "skeletor.post", "qualname": "smooth", "kind": "function", "doc": "

    Smooth skeleton using rolling windows.

    \n\n
    Parameters
    \n\n
      \n
    • s (skeletor.Skeleton):\nSkeleton to be processed.
      • \n
    • window (int, optional):\nSize (N observations) of the rolling window in number of\nnodes.
      • \n
    • to_smooth (list):\nColumns of the node table to smooth. Should work with any\nnumeric column (e.g. 'radius').
      • \n
    • inplace (bool):\nIf False will make and return a copy of the skeleton. If\nTrue, will modify the s inplace.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • s (skeletor.Skeleton):\nSkeleton with smoothed node table.
      • \n
    \n", "signature": "(\ts,\twindow: int = 3,\tto_smooth: list = ['x', 'y', 'z'],\tinplace: bool = False):", "funcdef": "def"}, "skeletor.post.despike": {"fullname": "skeletor.post.despike", "modulename": "skeletor.post", "qualname": "despike", "kind": "function", "doc": "

    Remove spikes in skeleton.

    \n\n

    For each node A, the euclidean distance to its next successor (parent)\nB and that node's successor C (i.e A->B->C) is computed. If\n\\( \\frac{dist(A,B)}{dist(A,C)}>sigma \\), node B is considered a spike\nand realigned between A and C.

    \n\n
    Parameters
    \n\n
      \n
    • x (skeletor.Skeleton):\nSkeleton to be processed.
      • \n
    • sigma (float | int, optional):\nThreshold for spike detection. Smaller sigma = more\naggressive spike detection.
      • \n
    • max_spike_length (int, optional):\nDetermines how long (# of nodes) a spike can be.
      • \n
    • inplace (bool, optional):\nIf False, a copy of the neuron is returned.
      • \n
    • reverse (bool, optional):\nIf True, will also walk the segments from proximal\nto distal. Use this to catch spikes on e.g. terminal\nnodes.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • s skeletor.Skeleton: Despiked neuron.
      • \n
    \n", "signature": "(s, sigma=5, max_spike_length=1, inplace=False, reverse=False):", "funcdef": "def"}, "skeletor.post.remove_bristles": {"fullname": "skeletor.post.remove_bristles", "modulename": "skeletor.post", "qualname": "remove_bristles", "kind": "function", "doc": "

    Remove \"bristles\" that sometimes occurr along the backbone.

    \n\n

    Works by finding terminal twigs that consist of only a single node.

    \n\n
    Parameters
    \n\n
      \n
    • s (skeletor.Skeleton):\nSkeleton to clean up.
      • \n
    • mesh (trimesh.Trimesh, optional):\nOriginal mesh (e.g. before contraction). If not provided will\nuse the mesh associated with s.
      • \n
    • los_only (bool):\nIf True, will only remove bristles that are in line of sight of\ntheir parent. If False, will remove all single-node bristles.
      • \n
    • inplace (bool):\nIf False will make and return a copy of the skeleton. If True,\nwill modify the s inplace.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • s (skeletor.Skeleton):\nSkeleton with single-node twigs removed.
      • \n
    \n", "signature": "(s, mesh=None, los_only=False, inplace=False):", "funcdef": "def"}, "skeletor.pre": {"fullname": "skeletor.pre", "modulename": "skeletor.pre", "kind": "module", "doc": "

    The skeletor.pre module contains functions to pre-process meshes before\nskeletonization.

    \n\n

    Fixing faulty meshes

    \n\n

    Some skeletonization methods are susceptible to faulty meshes (degenerate faces,\nwrong normals, etc.). If your skeleton looks off, it might be worth a shot\ntrying to fix the mesh using skeletor.pre.fix_mesh().

    \n\n

    Mesh contraction

    \n\n

    As a rule of thumb: the more your mesh looks like a skeleton, the easier it is\nto extract one (duh). Mesh contraction using skeletor.pre.contract() [1] can\nhelp you to get your mesh \"in shape\".

    \n\n
    References
    \n\n

    [1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh\n contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.

    \n"}, "skeletor.pre.fix_mesh": {"fullname": "skeletor.pre.fix_mesh", "modulename": "skeletor.pre", "qualname": "fix_mesh", "kind": "function", "doc": "

    Try to fix some common problems with mesh.

    \n\n
      \n
    1. Remove infinite values
      2. \n
    2. Merge duplicate vertices
      3. \n
    3. Remove duplicate and degenerate faces
      4. \n
    4. Remove unreference vertices
      5. \n
    5. Drop winglets (faces that have only one adjacent face)
      6. \n
    6. Fix normals (Optional)
      7. \n
    7. Remove disconnected fragments (Optional)
      8. \n
    \n\n
    Parameters
    \n\n
      \n
    • mesh (mesh-like object):\nMesh to fix. Must have .vertices and .faces\nproperties.
      • \n
    • remove_disconnected (False | int):\nIf a number is given, will iterate over the mesh's\nconnected components and remove those consisting of\nless than the given number of vertices. For example,\nremove_disconnected=5 will drop parts of the\nmesh that consist of five or less connected\nvertices.
      • \n
    • inplace (bool):\nIf True, will perform fixes on the input mesh.\nIf False, will make a copy first. This is silently\nignored if mesh is not already a trimesh.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • fixed mesh (trimesh.Trimesh):
      • \n
    \n", "signature": "(\tmesh,\tremote_infinite=True,\tmerge_duplicate_verts=True,\tremove_degenerate_faces=True,\tremove_unreferenced_verts=True,\tdrop_winglets=True,\tfix_normals=False,\tremove_disconnected=False,\tinplace=False):", "funcdef": "def"}, "skeletor.pre.simplify": {"fullname": "skeletor.pre.simplify", "modulename": "skeletor.pre", "qualname": "simplify", "kind": "function", "doc": "

    Simplify mesh using Blender 3D.

    \n\n

    Uses Blender's \"decimate\" modifier in \"collapse\" mode.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (trimesh.Trimesh):\nMesh to simplify.
      • \n
    • ratio (float):\nFactor to which to reduce faces. For example, a ratio of 0.5 will\nreduce the number of faces to 50%.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • trimesh.Trimesh: Simplified mesh.
      • \n
    \n", "signature": "(mesh, ratio):", "funcdef": "def"}, "skeletor.pre.remesh": {"fullname": "skeletor.pre.remesh", "modulename": "skeletor.pre", "qualname": "remesh", "kind": "function", "doc": "

    Remesh mesh using Blender 3D.

    \n\n

    Uses Blender's \"remesh\" modifier in \"voxel\" mode.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (trimesh.Trimesh):\nMesh to remesh.
      • \n
    • voxel_size (float):\nSize of individual voxels (edge length).
      • \n
    • adaptivity (float):\nReduces final face count where detail is not important.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • trimesh.Trimesh: Remeshed mesh.
      • \n
    \n", "signature": "(mesh, voxel_size=50, adaptivity=5):", "funcdef": "def"}, "skeletor.pre.contract": {"fullname": "skeletor.pre.contract", "modulename": "skeletor.pre", "qualname": "contract", "kind": "function", "doc": "

    Contract mesh.

    \n\n

    In a nutshell: this function contracts the mesh by applying rounds of\n_constraint_ Laplacian smoothing. This function can be fairly expensive\nand I highly recommend you play around with SL to contract the\nmesh in as few steps as possible. The contraction doesn't have to be perfect\nfor good skeletonization results (<10%, i.e. epsilon<0.1).

    \n\n

    Also: parameterization matters a lot! Default parameters will get you there\nbut playing around with SL and WH0 might speed things up by an order of\nmagnitude.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (mesh obj):\nThe mesh to be contracted. Can be any object (e.g.\na trimesh.Trimesh) that has .vertices and .faces\nproperties or a tuple (vertices, faces) or a dictionary\n{'vertices': vertices, 'faces': faces}.\nVertices and faces must be (N, 3) numpy arrays.
      • \n
    • epsilon (float (0-1), optional):\nTarget contraction rate as measured by the sum of all face\nareas in the contracted versus the original mesh. Algorithm\nwill stop once mesh is contracted below this threshold.\nDepending on your mesh (number of faces, shape) reaching a\nstrong contraction can be extremely costly with comparatively\nlittle benefit for the subsequent skeletonization. Note that\nthe algorithm might stop short of this target if iter_lim\nor time_lim is reached first or if the sum of face areas\nis increasing from one iteration to the next instead of\ndecreasing.
      • \n
    • iter_lim (int (>1), optional):\nMaximum rounds of contractions.
      • \n
    • time_lim (int, optional):\nMaximum run time in seconds. Note that this limit is not\nchecked during but after each round of contraction. Hence,\nthe actual total time will likely overshoot time_lim.
      • \n
    • precision (float, optional):\nSets the precision for finding the least-square solution.\nThis is the main determinant for speed vs quality: lower\nvalues will take (much) longer but will get you closer to an\noptimally contracted mesh. Higher values will be faster but\nthe iterative contractions might stop early.
      • \n
    • SL (float, optional):\nFactor by which the contraction matrix is multiplied for\neach iteration. Higher values = quicker contraction, lower\nvalues = more likely to get you an optimal contraction.
      • \n
    • WH0 (float, optional):\nInitial weight factor for the attraction constraints.\nThe ratio of the initial weights WL0 and WH0\ncontrols the smoothness and the degree of contraction of the\nfirst iteration result, thus it determines the amount of\ndetails retained in subsequent and final contracted meshes:\nhigher WH0 = more details retained.
      • \n
    • WL0 (\"auto\" | float):\nInitial weight factor for the contraction constraints. By\ndefault (\"auto\"), this will be set to 1e-3 * sqrt(A)\nwith A being the average face area. This ensures that\ncontraction forces scale with the coarseness of the mesh.
      • \n

    • operator (\"cotangent\" | \"umbrella\"):\nWhich Laplacian operator to use:

      \n\n
        \n
      • The \"cotangent\" operator (default) takes both topology\nand geometry of the mesh into account and is hence a\nbetter descriptor of the curvature flow. This is the\noperator used in the original paper.
        • \n
      • The \"umbrella\" operator (aka \"uniform weighting\") uses\nonly topological features of the mesh. This also makes\nit more robust against flaws in the mesh! Use it when\nthe cotangent operator produces oddly contracted meshes.
        • \n
      • \n
    • progress (bool):\nWhether or not to show a progress bar.
      • \n
    • validate (bool):\nIf True, will try to fix potential issues with the mesh\n(e.g. infinite values, duplicate vertices, degenerate faces)\nbefore collapsing. Degenerate meshes can lead to effectively\ninfinite runtime for this function!
      • \n
    \n\n
    Returns
    \n\n
      \n
    • trimesh.Trimesh: Contracted copy of original mesh. The final contraction rate\nis attached to the mesh as .epsilon property.
      • \n
    \n\n
    References
    \n\n

    [1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh\n contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.

    \n", "signature": "(\tmesh,\tepsilon=1e-06,\titer_lim=100,\ttime_lim=None,\tprecision=1e-07,\tSL=2,\tWH0=1,\tWL0='auto',\toperator='cotangent',\tprogress=True,\tvalidate=True):", "funcdef": "def"}, "skeletor.skeletonize": {"fullname": "skeletor.skeletonize", "modulename": "skeletor.skeletonize", "kind": "module", "doc": "

    The skeletor.skeletonize module contains functions to for skeletonization\nof meshes.

    \n\n

    There are several approaches to skeletonizing a mesh. Which one to pick depends\n(among other things) on the shape of your mesh and the skeleton quality you want\nto get out of it. In general, unless you mesh already looks like a tube I\nrecommend looking into mesh contraction 4.

    \n\n

    Please see the documentation of the individual functions for details but here\nis a quick summary:

    \n\n\n\n\n \n \n \n \n \n \n\n\n\n\n \n \n \n \n \n \n\n\n \n \n \n \n \n \n\n\n \n \n \n \n \n \n\n\n \n \n \n \n \n \n\n\n \n \n \n \n \n \n\n\n
    functionspeedrobustradii 1mesh map 2description
    skeletor.skeletonize.by_wavefront()+++++yesyesworks well for tubular meshes
    skeletor.skeletonize.by_vertex_clusters()+++noyesbest with contracted meshes 3
    skeletor.skeletonize.by_teasar()+++noyesworks on mesh surface
    skeletor.skeletonize.by_tangent_ball()++0yesyesworks with mesh normals
    skeletor.skeletonize.by_edge_collapse()-0nonopublished with [1] - never got this to work well
    \n\n

    References

    \n\n

    [1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.

    \n\n
    \n
    \n
      \n
    1. \n

      radii can also be added in postprocessing with skeletor.post.radii() ↩

      \n
      2. \n\n
    2. \n

      a mapping from the meshes vertices to skeleton nodes ↩

      \n
      3. \n\n
    3. \n

      use skeletor.pre.contract() ↩

      \n
      4. \n\n
    4. \n

      use skeletor.pre.contract() ↩

      \n
      5. \n
    \n
    \n"}, "skeletor.skeletonize.by_teasar": {"fullname": "skeletor.skeletonize.by_teasar", "modulename": "skeletor.skeletonize", "qualname": "by_teasar", "kind": "function", "doc": "

    Skeletonize a mesh mesh using the TEASAR algorithm [1].

    \n\n

    This algorithm finds the longest path from a root vertex, invalidates all\nvertices that are within inv_dist. Then picks the second longest (and\nstill valid) path and does the same. Rinse & repeat until all vertices have\nbeen invalidated. It's fast + works very well with tubular meshes, and with\ninv_dist you have control over the level of detail. Note that by its\nnature the skeleton will be exactly on the surface of the mesh.

    \n\n

    Based on the implementation by Sven Dorkenwald, Casey Schneider-Mizell and\nForrest Collman in meshparty (https://github.com/sdorkenw/MeshParty).

    \n\n
    Parameters
    \n\n
      \n
    • mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}.
      • \n
    • inv_dist (int | float):\nDistance along the mesh used for invalidation of vertices.\nThis controls how detailed (or noisy) the skeleton will be.
      • \n
    • min_length (float, optional):\nIf provided, will skip any branch that is shorter than\nmin_length. Use this to get rid of noise but note that\nit will lead to vertices not being mapped to skeleton nodes.\nSuch vertices will show up with index -1 in\nSkeleton.mesh_map.
      • \n
    • root (int, optional):\nVertex ID of a root. If not provided will use 0.
      • \n
    • progress (bool, optional):\nIf True, will show progress bar.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
      • \n
    \n\n
    References
    \n\n

    [1] Sato, M., Bitter, I., Bender, M. A., Kaufman, A. E., & Nakajima, M.\n (n.d.). TEASAR: tree-structure extraction algorithm for accurate and\n robust skeletons. In Proceedings the Eighth Pacific Conference on\n Computer Graphics and Applications. IEEE Comput. Soc.\n https://doi.org/10.1109/pccga.2000.883951

    \n", "signature": "(mesh, inv_dist, min_length=None, root=None, progress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_wavefront": {"fullname": "skeletor.skeletonize.by_wavefront", "modulename": "skeletor.skeletonize", "qualname": "by_wavefront", "kind": "function", "doc": "

    Skeletonize a mesh using wave fronts.

    \n\n

    The algorithm tries to find rings of vertices and collapse them to\ntheir center. This is done by propagating a wave across the mesh starting at\na single seed vertex. As the wave travels across the mesh we keep track of\nwhich vertices are are encountered at each step. Groups of connected\nvertices that are \"hit\" by the wave at the same time are considered rings\nand subsequently collapsed. By its nature this works best with tubular meshes.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}.
      • \n
    • waves (int):\nNumber of waves to run across the mesh. Each wave is\ninitialized at a different vertex which produces slightly\ndifferent rings. The final skeleton is produced from a mean\nacross all waves. More waves produce higher resolution\nskeletons but also introduce more noise.
      • \n
    • origins (int | list of ints, optional):\nVertex ID(s) where the wave(s) are initialized. If we run\nout of origins (either because less origins than waves\nor because no origin for one of the connected components)\nwill fall back to semi-random origin.
      • \n
    • step_size (int):\nValues greater 1 effectively lead to binning of rings. For\nexample a stepsize of 2 means that two adjacent vertex rings\nwill be collapsed to the same center. This can help reduce\nnoise in the skeleton (and as such counteracts a large\nnumber of waves).
      • \n
    • radius_agg (\"mean\" | \"median\" | \"max\" | \"min\" | \"percentile75\" | \"percentile25\"):\nFunction used to aggregate radii over sample (i.e. the\nvertices forming a ring that we collapse to its center).
      • \n
    • progress (bool):\nIf True, will show progress bar.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
      • \n
    \n", "signature": "(\tmesh,\twaves=1,\torigins=None,\tstep_size=1,\tradius_agg='mean',\tprogress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_vertex_clusters": {"fullname": "skeletor.skeletonize.by_vertex_clusters", "modulename": "skeletor.skeletonize", "qualname": "by_vertex_clusters", "kind": "function", "doc": "

    Skeletonize a (contracted) mesh by clustering vertices.

    \n\n

    The algorithm traverses the mesh graph and groups vertices together that\nare within a given distance to each other. This uses the geodesic\n(along-the-mesh) distance, not simply the Eucledian distance. Subsequently\nthese groups of vertices are collapsed and re-connected respecting the\ntopology of the input mesh.

    \n\n

    The graph traversal is fast and scales well, so this method is well suited\nfor meshes with lots of vertices. On the downside: this implementation is\nnot very clever and you might have to play around with the parameters\n(mostly sampling_dist) to get decent results.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}.
      • \n
    • sampling_dist (float | int):\nMaximal distance at which vertices are clustered. This\nparameter should be tuned based on the resolution of your\nmesh (see Examples).
      • \n

    • cluster_pos (\"median\" | \"center\"):\nHow to determine the x/y/z coordinates of the collapsed\nvertex clusters (i.e. the skeleton's nodes)::

      \n\n
        \n
      • \"median\": Use the vertex closest to cluster's center of\nmass.
        • \n
      • \"center\": Use the center of mass. This makes for smoother\nskeletons but can lead to nodes outside the mesh.
        • \n
      • \n
    • progress (bool):\nIf True, will show progress bar.
      • \n
    \n\n
    Examples
    \n\n
    \n
    >>> import skeletor as sk\n>>> mesh = sk.example_mesh()\n>>> cont = sk.pre.contract(mesh, epsilon=0.1)\n>>> skel = sk.skeletonize.vertex_cluster(cont)\n>>> skel.mesh = mesh\n
    \n
    \n\n
    Returns
    \n\n
      \n
    • skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
      • \n
    \n", "signature": "(mesh, sampling_dist, cluster_pos='median', progress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_edge_collapse": {"fullname": "skeletor.skeletonize.by_edge_collapse", "modulename": "skeletor.skeletonize", "qualname": "by_edge_collapse", "kind": "function", "doc": "

    Skeletonize a (contracted) mesh by iteratively collapsing edges.

    \n\n

    This algorithm (described in [1]) iteratively collapses edges that are part\nof a face until no more faces are left. Edges are chosen based on a cost\nfunction that penalizes collapses that would change the shape of the object\nor would introduce long edges.

    \n\n

    This is somewhat sensitive to the dimensions of the input mesh: too large\nand you might experience slow-downs or numpy OverflowErrors; too low and\nyou might get skeletons that don't quite match the mesh (e.g. too few nodes).\nIf you experience either, try down- or up-scaling your mesh, respectively.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}.
      • \n
    • shape_weight (float, optional):\nWeight for shape costs which penalize collapsing edges that\nwould drastically change the shape of the object.
      • \n
    • sample_weight (float, optional):\nWeight for sampling costs which penalize collapses that\nwould generate prohibitively long edges.
      • \n
    • progress (bool):\nIf True, will show progress bar.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
      • \n
    \n\n
    References
    \n\n

    [1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh\n contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.

    \n", "signature": "(mesh, shape_weight=1, sample_weight=0.1, progress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_tangent_ball": {"fullname": "skeletor.skeletonize.by_tangent_ball", "modulename": "skeletor.skeletonize", "qualname": "by_tangent_ball", "kind": "function", "doc": "

    Skeletonize a mesh by finding the maximal tangent ball.

    \n\n

    This algorithm casts a ray from every mesh vertex along its inverse normals\n(requires ncollpyde). It then creates a sphere that is tangent to the\nvertex and to where the ray hit the inside of a face on the opposite side.\nNext it drops spheres that overlap with another, larger sphere. Modified\nfrom [1].

    \n\n

    The method works best on smooth meshes and is rather sensitive to errors in\nthe mesh such as incorrect normals (see skeletor.pre.fix_mesh), internal\nfaces, noisy surface (try smoothing or downsampling) or holes in the mesh.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
      • \n
    \n\n
    Examples
    \n\n
    \n
    >>> import skeletor as sk\n>>> mesh = sk.example_mesh()\n>>> fixed = sk.pre.fix_mesh(mesh, fix_normals=True, remove_disconnected=10)\n>>> skel = sk.skeletonize.by_tangent_ball(fixed)\n
    \n
    \n\n
    References
    \n\n

    [1] Ma, J., Bae, S.W. & Choi, S. 3D medial axis point approximation using\n nearest neighbors and the normal field. Vis Comput 28, 7\u201319 (2012).\n https://doi.org/10.1007/s00371-011-0594-7

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    What is skeletor?

    \n\n

    Unlike its namesake, this skeletor\ndoes not (yet) seek to conquer Eternia but to turn meshes into skeletons.

    \n\n

    Before we get started some terminology:

    \n\n
      \n
    • a mesh is something that consists of vertices and faces
      • \n
    • a skeleton is a (hierarchical) tree-like structure consisting of vertices\n(also called nodes) and edges that connect them
      • \n
    \n\n

    Skeletons are useful for a range of reasons. For example:

    \n\n
      \n
    1. Typically smaller (less vertices) than the mesh
      2. \n
    2. Have an implicit sense of topology (e.g. \"this node is distal to that node\")
      3. \n
    \n\n

    Extracting skeletons from meshes (or other types of data such as voxels) is\nnon-trivial and there are a great many research papers exploring various\ndifferent approaches (see Google scholar).

    \n\n

    skeletor implements some algorithms that I found useful in my work with\nneurons. In my experience there is unfortuntely no magic bullet when it\ncomes to skeletonization and chances are you will have to fiddle around a bit\nto get decent results.

    \n\n

    Installation

    \n\n

    From PyPI:

    \n\n
    \n
    pip3 install skeletor\n
    \n
    \n\n

    For the bleeding-edge version from Github:

    \n\n
    \n
    pip3 install git+https://github.com/navis-org/skeletor@master\n
    \n
    \n\n

    Getting started

    \n\n

    A skeletonization pipeline typically consists of:

    \n\n
      \n
    1. Some pre-processing of the mesh (e.g. fixing some potential errors like\ndegenerate faces, unreferenced vertices, etc.)
      2. \n
    2. The skeletonization itself
      3. \n
    3. Some post-processing of the skeleton (e.g. adding radius information, smoothing, etc.)
      4. \n
    \n\n
    \n\n

    Here is a complete list of available functions:

    \n\n\n\n\n \n \n\n\n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n \n \n\n\n
    functiondescription
    example data
    skeletor.example_mesh()load an example mesh
    pre-processing
    skeletor.pre.fix_mesh()fix some common errors found in meshes
    skeletor.pre.remesh()re-generate mesh (uses Blender 3D)
    skeletor.pre.simplify()reduce mesh complexity (uses Blender 3D)
    skeletor.pre.contract()contract mesh to facilitate skeletonization [1]
    skeletonization
    skeletor.skeletonize.by_wavefront()very fast, works well for tubular meshes (like neurons)
    skeletor.skeletonize.by_vertex_clusters()very fast but needs mesh to be contracted (see above)
    skeletor.skeletonize.by_edge_collapse()presented in [1] but never got this to work well
    skeletor.skeletonize.by_teasar()very fast and robust, works on mesh surface
    skeletor.skeletonize.by_tangent_ball()very fast, best on smooth meshes
    postprocessing
    skeletor.post.clean_up()fix some potential errors in the skeleton
    skeletor.post.radii()add radius information using various method
    skeletor.post.smooth()smooth the skeleton
    skeletor.post.remove_bristles()remove single-node bristles from the skeleton
    skeletor.post.despike()smooth out jumps in the skeleton
    \n\n
    \n\n

    See docstrings of the respective functions for details.

    \n\n

    A pipeline might look like this:

    \n\n
      \n
    1. skeletor.pre.fix_mesh() to fix the mesh
      2. \n
    2. skeletor.pre.simplify() to simplify the mesh
      3. \n
    3. skeletor.pre.contract() to contract the mesh [1]
      4. \n
    4. skeletor.skeletonize.by_vertex_clusters() to generate a skeleton
      5. \n
    5. skeletor.post.clean_up() to clean up some potential issues with the skeleton
      6. \n
    6. skeletor.post.smooth() to smooth the skeleton
      7. \n
    7. skeletor.post.radii() to extract radii either by k-nearest neighbours or ray-casting
      8. \n
    \n\n

    In my experience there is no one-size-fits-all. You will have to play around to\nfind the right approach and parameters to get nice skeletons for your meshes.\nIf you need help just open an issue.

    \n\n

    Also check out the Gotchas below!

    \n\n

    Examples

    \n\n

    First load the example mesh (a fruit fly neuron):

    \n\n
    \n
    >>> import skeletor as sk\n>>> mesh = sk.example_mesh()\n>>> mesh\n<trimesh.Trimesh(vertices.shape=(6582, 3), faces.shape=(13772, 3))>\n
    \n
    \n\n

    Next see if there is stuff to fix in the mesh (degenerate faces, duplicate\nvertices, etc.):

    \n\n
    \n
    >>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False)\n>>> fixed\n<trimesh.Trimesh(vertices.shape=(6213, 3), faces.shape=(12805, 3))>\n
    \n
    \n\n

    Now for tubular meshes like this neuron, the \"wave front\" skeletonization method\nperforms really well: it works by casting waves across the mesh and collapsing\nthe resulting rings into a skeleton (kinda like when you throw a stone in a\npond and track the expanding ripples).

    \n\n
    \n
    >>> skel = sk.skeletonize.by_wavefront(fixed, waves=1, step_size=1)\n>>> skel\n<Skeleton(vertices=(1258, 3), edges=(1194, 2), method=wavefront)>\n
    \n
    \n\n

    All skeletonization methods return a Skeleton object. These are just\nconvenient objects to bundle the various outputs of the skeletonization.

    \n\n
    \n
    >>> # x/y/z location of skeleton vertices (nodes)\n>>> skel.vertices\narray([[16744, 36720, 26407],\n       ...,\n       [22076, 23217, 24472]])\n>>> # child -> parent edges\n>>> skel.edges\narray([[  64,   31],\n       ...,\n       [1257, 1252]])\n>>> # Mapping for mesh to skeleton vertex indices\n>>> skel.mesh_map\narray([ 157,  158, 1062, ...,  525,  474,  547])\n>>> # SWC table\n>>> skel.swc.head()\n   node_id  parent_id             x             y             z    radius\n0        0         -1  16744.005859  36720.058594  26407.902344  0.000000\n1        1         -1   5602.751953  22266.756510  15799.991211  7.542587\n2        2         -1  16442.666667  14999.978516  10887.916016  5.333333\n
    \n
    \n\n

    SWC is a commonly used format for saving skeletons. Skeleton objects\nhave a method for quickly saving a correctly formatted SWC file:

    \n\n
    \n
    >>> skel.save_swc('~/Documents/my_skeleton.swc')\n
    \n
    \n\n

    If you installed pyglet (see above) you can also use trimesh's plotting\ncapabilities to inspect the results:

    \n\n
    \n
    >>> skel.show(mesh=True)\n
    \n
    \n\n

    \"skeletor_example\"

    \n\n

    That looks pretty good already but let's run some pro-forma postprocessing.

    \n\n
    \n
    >>> sk.post.clean_up(skel, inplace=True)\n<Skeleton(vertices=(1071, 3), edges=(1070, 2))>\n
    \n
    \n\n

    So that would be a full pipeline mesh to skeleton. Don't expect your own meshes\nto produce such nice results off the bat though. Chances are you will need to\nplay around to find the right recipe. If you don't know where to start, I suggest\nyou try out mesh contraction + vertex clustering first:

    \n\n
    \n
    >>> import skeletor as sk\n>>> # Load the example mesh that ships with skeletor\n>>> mesh = sk.example_mesh()\n>>> # Alternatively use trimesh to load/construct your own mesh:\n>>> # import trimesh as tm\n>>> # mesh = tm.Trimesh(vertices, faces)\n>>> # mesh = tm.load_mesh('some/mesh.obj')\n>>> # Run some general clean-up (see docstring for details)\n>>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False)\n>>> # Contract mesh to 10% (0.1) of original volume\n>>> cont = sk.pre.contract(fixed, epsilon=0.1)\n>>> # Skeletonize\n>>> skel = sk.skeletonize.by_vertex_clusters(cont, sampling_dist=100)\n>>> # Replace contracted mesh with original for postprocessing and plotting\n>>> skel.mesh = fixed\n>>> # Add radii (vertex cluster method does not do that automatically)\n>>> sk.post.radii(skel, method='knn')\n>>> skel.show(mesh=True)\n
    \n
    \n\n

    Gotchas

    \n\n
      \n
    • while this is a general purpose library, my personal focus is on neurons and\nthis has certainly influenced things like default parameter values and certain\npost-processing steps
      • \n
    • meshes need to be triangular (we are using trimesh)
      • \n
    • use sk.pre.simplify if your mesh is very complex (half a million vertices is\nwhere things start getting sluggish)
      • \n
    • a good mesh contraction is often half the battle but it can be tricky to get\nto work
      • \n
    • if the mesh consists of multiple disconnected pieces the skeleton will\nlikewise be fragmented (i.e. will have multiple roots)
      • \n
    • it's often a good idea to fix issues with the skeleton in postprocessing rather\nthan trying to get the skeletonization to be perfect
      • \n
    \n\n

    Benchmarks

    \n\n

    \"skeletor_benchmark\"

    \n\n

    Benchmarks\nwere run on a 2018 MacBook Pro (2.2 GHz Core i7, 32Gb memory) with optional\nfastremap dependency installed. Note some of these functions (e.g.\ncontraction and TEASAR/vertex cluster skeletonization) vary a lot in\nspeed based on parameterization.

    \n\n

    What about algorithm X?

    \n\n

    skeletor contains some algorithms that I found easy enough to implement\nand useful for my work with neurons. If you have some interesting paper/approach\nthat could make a nice addition to skeletor, please get in touch on Github.\nPull requests are always welcome!

    \n\n

    References

    \n\n

    [1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.

    \n\n

    The abstract and the paper can be found here.\nAlso see this YouTube video.

    \n\n

    Some of the code in skeletor was modified from the\nPy_BL_MeshSkeletonization\naddon created by #0K Srinivasan Ramachandran and published under GPL3.

    \n\n

    Top-level functions and classes

    \n\n

    At top-level we only expose example_mesh() and the Skeleton class (which\nyou probably won't ever need to touch manually). Everything else is neatly\ntucked away into submodules (see side-bar or above table).

    \n"}, "skeletor.Skeleton": {"fullname": "skeletor.Skeleton", "modulename": "skeletor", "qualname": "Skeleton", "kind": "class", "doc": "

    Class representing a skeleton.

    \n\n

    Typically returned as results from a skeletonization.

    \n\n
    Attributes
    \n\n
      \n
    • swc (pd.DataFrame, optional):\nSWC table.
      • \n
    • vertices ((N, 3) array):\nVertex (node) positions.
      • \n
    • edges ((M, 2) array):\nIndices of connected vertex pairs.
      • \n
    • radii ((N, ) array, optional):\nRadii for each vertex (node) in the skeleton.
      • \n
    • mesh (trimesh, optional):\nThe original mesh.
      • \n
    • mesh_map (array, optional):\nSame length as mesh. Maps mesh vertices to vertices (nodes)\nin the skeleton.
      • \n
    • skel_map (array of arrays, optional):\nInverse of mesh_map: maps skeleton vertices (nodes) to mesh\nvertices.
      • \n
    • method (str, optional):\nWhich method was used to generate the skeleton.
      • \n
    \n"}, "skeletor.Skeleton.__init__": {"fullname": "skeletor.Skeleton.__init__", "modulename": "skeletor", "qualname": "Skeleton.__init__", "kind": "function", "doc": "

    \n", "signature": "(swc, mesh=None, mesh_map=None, method=None)"}, "skeletor.Skeleton.swc": {"fullname": "skeletor.Skeleton.swc", "modulename": "skeletor", "qualname": "Skeleton.swc", "kind": "variable", "doc": "

    \n"}, "skeletor.Skeleton.mesh": {"fullname": "skeletor.Skeleton.mesh", "modulename": "skeletor", "qualname": "Skeleton.mesh", "kind": "variable", "doc": "

    \n"}, "skeletor.Skeleton.mesh_map": {"fullname": "skeletor.Skeleton.mesh_map", "modulename": "skeletor", "qualname": "Skeleton.mesh_map", "kind": "variable", "doc": "

    \n"}, "skeletor.Skeleton.method": {"fullname": "skeletor.Skeleton.method", "modulename": "skeletor", "qualname": "Skeleton.method", "kind": "variable", "doc": "

    \n"}, "skeletor.Skeleton.edges": {"fullname": "skeletor.Skeleton.edges", "modulename": "skeletor", "qualname": "Skeleton.edges", "kind": "variable", "doc": "

    Return skeleton edges.

    \n"}, "skeletor.Skeleton.vertices": {"fullname": "skeletor.Skeleton.vertices", "modulename": "skeletor", "qualname": "Skeleton.vertices", "kind": "variable", "doc": "

    Return skeleton vertices (nodes).

    \n"}, "skeletor.Skeleton.radius": {"fullname": "skeletor.Skeleton.radius", "modulename": "skeletor", "qualname": "Skeleton.radius", "kind": "variable", "doc": "

    Return radii.

    \n"}, "skeletor.Skeleton.skeleton": {"fullname": "skeletor.Skeleton.skeleton", "modulename": "skeletor", "qualname": "Skeleton.skeleton", "kind": "variable", "doc": "

    Skeleton as trimesh Path3D.

    \n"}, "skeletor.Skeleton.skel_map": {"fullname": "skeletor.Skeleton.skel_map", "modulename": "skeletor", "qualname": "Skeleton.skel_map", "kind": "variable", "doc": "

    Skeleton vertex (nodes) to mesh vertices. Based on mesh_map.

    \n"}, "skeletor.Skeleton.leafs": {"fullname": "skeletor.Skeleton.leafs", "modulename": "skeletor", "qualname": "Skeleton.leafs", "kind": "variable", "doc": "

    Leaf nodes (includes root).

    \n"}, "skeletor.Skeleton.reindex": {"fullname": "skeletor.Skeleton.reindex", "modulename": "skeletor", "qualname": "Skeleton.reindex", "kind": "function", "doc": "

    Clean up skeleton.

    \n", "signature": "(self, inplace=False):", "funcdef": "def"}, "skeletor.Skeleton.copy": {"fullname": "skeletor.Skeleton.copy", "modulename": "skeletor", "qualname": "Skeleton.copy", "kind": "function", "doc": "

    Return copy of the skeleton.

    \n", "signature": "(self):", "funcdef": "def"}, "skeletor.Skeleton.get_graph": {"fullname": "skeletor.Skeleton.get_graph", "modulename": "skeletor", "qualname": "Skeleton.get_graph", "kind": "function", "doc": "

    Generate networkX representation of the skeletons.

    \n\n

    Distance between nodes will be used as edge weights.

    \n\n
    Returns
    \n\n
      \n
    • networkx.DiGraph
      • \n
    \n", "signature": "(self):", "funcdef": "def"}, "skeletor.Skeleton.get_segments": {"fullname": "skeletor.Skeleton.get_segments", "modulename": "skeletor", "qualname": "Skeleton.get_segments", "kind": "function", "doc": "

    Generate a list of linear segments while maximizing segment lengths.

    \n\n
    Parameters
    \n\n
      \n
    • weight ('weight' | None, optional):\nIf \"weight\" use physical, geodesic length to determine\nsegment length. If None use number of nodes (faster).
      • \n
    • return_lengths (bool):\nIf True, also return lengths of segments according to weight.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • segments (list):\nSegments as list of lists containing node IDs. List is\nsorted by segment lengths.
      • \n
    • lengths (list):\nLength for each segment according to weight. Only provided\nif return_lengths is True.
      • \n
    \n", "signature": "(self, weight='weight', return_lengths=False):", "funcdef": "def"}, "skeletor.Skeleton.save_swc": {"fullname": "skeletor.Skeleton.save_swc", "modulename": "skeletor", "qualname": "Skeleton.save_swc", "kind": "function", "doc": "

    Save skeleton in SWC format.

    \n\n
    Parameters
    \n\n
      \n
    • filepath (path-like):\nFilepath to save SWC to.
      • \n
    \n", "signature": "(self, filepath):", "funcdef": "def"}, "skeletor.Skeleton.scene": {"fullname": "skeletor.Skeleton.scene", "modulename": "skeletor", "qualname": "Skeleton.scene", "kind": "function", "doc": "

    Return a Scene object containing the skeleton.

    \n\n
    Returns
    \n\n
      \n
    • scene (trimesh.scene.scene.Scene):\nContains the skeleton and optionally the mesh.
      • \n
    \n", "signature": "(self, mesh=False, **kwargs):", "funcdef": "def"}, "skeletor.Skeleton.show": {"fullname": "skeletor.Skeleton.show", "modulename": "skeletor", "qualname": "Skeleton.show", "kind": "function", "doc": "

    Render the skeleton in an opengl window. Requires pyglet.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (bool):\nIf True, will render transparent mesh on top of the\nskeleton.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • scene (trimesh.scene.Scene):\nScene with skeleton in it.
      • \n
    \n", "signature": "(self, mesh=False, **kwargs):", "funcdef": "def"}, "skeletor.example_mesh": {"fullname": "skeletor.example_mesh", "modulename": "skeletor", "qualname": "example_mesh", "kind": "function", "doc": "

    Load and return example mesh.

    \n\n

    The example mesh is a fruit fly neuron (an olfactory projection neuron of\nthe DA1 glomerulus) segmented from an EM image data set. It is part of the\nJanelia hemibrain data set (see here) [1].

    \n\n
    References
    \n\n

    [1] Louis K. Scheffer et al., eLife. 2020. doi: 10.7554/eLife.57443\nA connectome and analysis of the adult Drosophila central brain

    \n\n
    Returns
    \n\n
      \n
    • trimesh.Trimesh
      • \n
    \n\n
    Examples
    \n\n
    \n
    >>> import skeletor as sk\n>>> # Load this example mesh\n>>> mesh = sk.example_mesh()\n
    \n
    \n", "signature": "():", "funcdef": "def"}, "skeletor.post": {"fullname": "skeletor.post", "modulename": "skeletor.post", "kind": "module", "doc": "

    The skeletor.post module contains functions to post-process skeletons after\nskeletonization.

    \n\n

    Fixing issues with skeletons

    \n\n

    Depending on your mesh, pre-processing and the parameters you chose for\nskeletonization, chances are that your skeleton will not come out perfectly.

    \n\n

    skeletor.post.clean_up can help you solve some potential issues:

    \n\n
      \n
    • skeleton nodes (vertices) that outside or right on the surface instead of\ncentered inside the mesh
      • \n
    • superfluous \"hairs\" on otherwise straight bits
      • \n
    \n\n

    skeletor.post.smooth will smooth out the skeleton.

    \n\n

    skeletor.post.despike can help you remove spikes in the skeleton where\nsingle nodes are out of aligment.

    \n\n

    skeletor.post.remove_bristles will remove bristles from the skeleton.

    \n\n

    Computing radius information

    \n\n

    Only skeletor.skeletonize.by_wavefront() provides radii off the bat. For all\nother methods, you might want to run skeletor.post.radii can help you\n(re-)generate radius information for the skeletons.

    \n"}, "skeletor.post.radii": {"fullname": "skeletor.post.radii", "modulename": "skeletor.post", "qualname": "radii", "kind": "function", "doc": "

    Extract radii for given skeleton table.

    \n\n
    Important
    \n\n

    This function really only produces useful radii if the skeleton is centered\ninside the mesh. by_wavefront does that by default whereas all other\nskeletonization methods don't. Your best bet to get centered skeletons is\nto contract the mesh first (sk.pre.contract).

    \n\n
    Parameters
    \n\n
      \n
    • s (skeletor.Skeleton):\nSkeleton to clean up.
      • \n
    • mesh (trimesh.Trimesh, optional):\nOriginal mesh (e.g. before contraction). If not provided will\nuse the mesh associated with s.
      • \n

    • method (\"knn\" | \"ray\"):\nWhether and how to add radius information to each node::

      \n\n
        \n
      • \"knn\" uses k-nearest-neighbors to get radii: fast but\npotential for being very wrong
        • \n
      • \"ray\" uses ray-casting to get radii: slower but sometimes\nless wrong
        • \n
      • \n
    • aggregate (\"mean\" | \"median\" | \"max\" | \"min\" | \"percentile75\"):\nFunction used to aggregate radii over sample (i.e. across\nk nearest-neighbors or ray intersections)
      • \n
    • validate (bool):\nIf True, will try to fix potential issues with the mesh\n(e.g. infinite values, duplicate vertices, degenerate faces)\nbefore skeletonization. Note that this might make changes to\nyour mesh inplace!
      • \n
    • **kwargs: Keyword arguments are passed to the respective method:
      • \n
    \n\n

    For method \"knn\"::

    \n\n
    n :             int (default 5)\n                Radius will be the mean over n nearest-neighbors.\n
    \n\n

    For method \"ray\"::

    \n\n
    n_rays :        int (default 20)\n                Number of rays to cast for each node.\nprojection :    \"sphere\" (default) | \"tangents\"\n                Whether to cast rays in a sphere around each node or in a\n                circle orthogonally to the node's tangent vector.\nfallback :      \"knn\" (default) | None | number\n                If a point is outside or right on the surface of the mesh\n                the raycasting will return nonesense results. We can either\n                ignore those cases (``None``), assign a arbitrary number or\n                we can fall back to radii from k-nearest-neighbors (``knn``).\n
    \n\n
    Returns
    \n\n
      \n
    • None: But attaches radius to the skeleton's SWC table. Existing\nvalues are replaced!
      • \n
    \n", "signature": "(\ts,\tmesh=None,\tmethod='knn',\taggregate='mean',\tvalidate=False,\t**kwargs):", "funcdef": "def"}, "skeletor.post.clean_up": {"fullname": "skeletor.post.clean_up", "modulename": "skeletor.post", "qualname": "clean_up", "kind": "function", "doc": "

    Clean up the skeleton.

    \n\n

    This function bundles a bunch of procedures to clean up the skeleton:

    \n\n
      \n
    1. Remove twigs that are running parallel to their parent branch
      2. \n
    2. Move nodes outside the mesh back inside (or at least snap to surface)
      3. \n
    \n\n

    Note that this is not a magic bullet and some of this will not work (well)\nif the original mesh was degenerate (e.g. internal faces or not watertight)\nto begin with.

    \n\n
    Parameters
    \n\n
      \n
    • s (skeletor.Skeleton):\nSkeleton to clean up.
      • \n
    • mesh (trimesh.Trimesh, optional):\nOriginal mesh (e.g. before contraction). If not provided will\nuse the mesh associated with s.
      • \n
    • validate (bool):\nIf True, will try to fix potential issues with the mesh\n(e.g. infinite values, duplicate vertices, degenerate faces)\nbefore cleaning up. Note that this might change your mesh\ninplace!
      • \n
    • inplace (bool):\nIf False will make and return a copy of the skeleton. If True,\nwill modify the s inplace.
      • \n
    • **kwargs: Keyword arguments are passed to the bundled function.
      • \n
    \n\n

    For skeletor.postprocessing.drop_parallel_twigs::

    \n\n

    theta : float (default 0.01)\n For each twig we generate the dotproduct between the tangent\n vectors of it and its parents. If these line up perfectly the\n dotproduct will equal 1. theta determines how much that\n value can differ from 1 for us to still prune the twig: higher\n theta = more pruning.

    \n\n
    Returns
    \n\n
      \n
    • s_clean (skeletor.Skeleton):\nHopefully improved skeleton.
      • \n
    \n", "signature": "(s, mesh=None, validate=False, inplace=False, **kwargs):", "funcdef": "def"}, "skeletor.post.smooth": {"fullname": "skeletor.post.smooth", "modulename": "skeletor.post", "qualname": "smooth", "kind": "function", "doc": "

    Smooth skeleton using rolling windows.

    \n\n
    Parameters
    \n\n
      \n
    • s (skeletor.Skeleton):\nSkeleton to be processed.
      • \n
    • window (int, optional):\nSize (N observations) of the rolling window in number of\nnodes.
      • \n
    • to_smooth (list):\nColumns of the node table to smooth. Should work with any\nnumeric column (e.g. 'radius').
      • \n
    • inplace (bool):\nIf False will make and return a copy of the skeleton. If\nTrue, will modify the s inplace.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • s (skeletor.Skeleton):\nSkeleton with smoothed node table.
      • \n
    \n", "signature": "(\ts,\twindow: int = 3,\tto_smooth: list = ['x', 'y', 'z'],\tinplace: bool = False):", "funcdef": "def"}, "skeletor.post.despike": {"fullname": "skeletor.post.despike", "modulename": "skeletor.post", "qualname": "despike", "kind": "function", "doc": "

    Remove spikes in skeleton.

    \n\n

    For each node A, the euclidean distance to its next successor (parent)\nB and that node's successor C (i.e A->B->C) is computed. If\n\\( \\frac{dist(A,B)}{dist(A,C)}>sigma \\), node B is considered a spike\nand realigned between A and C.

    \n\n
    Parameters
    \n\n
      \n
    • x (skeletor.Skeleton):\nSkeleton to be processed.
      • \n
    • sigma (float | int, optional):\nThreshold for spike detection. Smaller sigma = more\naggressive spike detection.
      • \n
    • max_spike_length (int, optional):\nDetermines how long (# of nodes) a spike can be.
      • \n
    • inplace (bool, optional):\nIf False, a copy of the neuron is returned.
      • \n
    • reverse (bool, optional):\nIf True, will also walk the segments from proximal\nto distal. Use this to catch spikes on e.g. terminal\nnodes.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • s skeletor.Skeleton: Despiked neuron.
      • \n
    \n", "signature": "(s, sigma=5, max_spike_length=1, inplace=False, reverse=False):", "funcdef": "def"}, "skeletor.post.remove_bristles": {"fullname": "skeletor.post.remove_bristles", "modulename": "skeletor.post", "qualname": "remove_bristles", "kind": "function", "doc": "

    Remove \"bristles\" that sometimes occurr along the backbone.

    \n\n

    Works by finding terminal twigs that consist of only a single node.

    \n\n
    Parameters
    \n\n
      \n
    • s (skeletor.Skeleton):\nSkeleton to clean up.
      • \n
    • mesh (trimesh.Trimesh, optional):\nOriginal mesh (e.g. before contraction). If not provided will\nuse the mesh associated with s.
      • \n
    • los_only (bool):\nIf True, will only remove bristles that are in line of sight of\ntheir parent. If False, will remove all single-node bristles.
      • \n
    • inplace (bool):\nIf False will make and return a copy of the skeleton. If True,\nwill modify the s inplace.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • s (skeletor.Skeleton):\nSkeleton with single-node twigs removed.
      • \n
    \n", "signature": "(s, mesh=None, los_only=False, inplace=False):", "funcdef": "def"}, "skeletor.pre": {"fullname": "skeletor.pre", "modulename": "skeletor.pre", "kind": "module", "doc": "

    The skeletor.pre module contains functions to pre-process meshes before\nskeletonization.

    \n\n

    Fixing faulty meshes

    \n\n

    Some skeletonization methods are susceptible to faulty meshes (degenerate faces,\nwrong normals, etc.). If your skeleton looks off, it might be worth a shot\ntrying to fix the mesh using skeletor.pre.fix_mesh().

    \n\n

    Mesh contraction

    \n\n

    As a rule of thumb: the more your mesh looks like a skeleton, the easier it is\nto extract one (duh). Mesh contraction using skeletor.pre.contract() [1] can\nhelp you to get your mesh \"in shape\".

    \n\n
    References
    \n\n

    [1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh\n contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.

    \n"}, "skeletor.pre.fix_mesh": {"fullname": "skeletor.pre.fix_mesh", "modulename": "skeletor.pre", "qualname": "fix_mesh", "kind": "function", "doc": "

    Try to fix some common problems with mesh.

    \n\n
      \n
    1. Remove infinite values
      2. \n
    2. Merge duplicate vertices
      3. \n
    3. Remove duplicate and degenerate faces
      4. \n
    4. Remove unreference vertices
      5. \n
    5. Drop winglets (faces that have only one adjacent face)
      6. \n
    6. Fix normals (Optional)
      7. \n
    7. Remove disconnected fragments (Optional)
      8. \n
    \n\n
    Parameters
    \n\n
      \n
    • mesh (mesh-like object):\nMesh to fix. Must have .vertices and .faces\nproperties.
      • \n
    • remove_disconnected (False | int):\nIf a number is given, will iterate over the mesh's\nconnected components and remove those consisting of\nless than the given number of vertices. For example,\nremove_disconnected=5 will drop parts of the\nmesh that consist of five or less connected\nvertices.
      • \n
    • inplace (bool):\nIf True, will perform fixes on the input mesh.\nIf False, will make a copy first. This is silently\nignored if mesh is not already a trimesh.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • fixed mesh (trimesh.Trimesh):
      • \n
    \n", "signature": "(\tmesh,\tremote_infinite=True,\tmerge_duplicate_verts=True,\tremove_degenerate_faces=True,\tremove_unreferenced_verts=True,\tdrop_winglets=True,\tfix_normals=False,\tremove_disconnected=False,\tinplace=False):", "funcdef": "def"}, "skeletor.pre.simplify": {"fullname": "skeletor.pre.simplify", "modulename": "skeletor.pre", "qualname": "simplify", "kind": "function", "doc": "

    Simplify mesh using Blender 3D.

    \n\n

    Uses Blender's \"decimate\" modifier in \"collapse\" mode.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (trimesh.Trimesh):\nMesh to simplify.
      • \n
    • ratio (float):\nFactor to which to reduce faces. For example, a ratio of 0.5 will\nreduce the number of faces to 50%.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • trimesh.Trimesh: Simplified mesh.
      • \n
    \n", "signature": "(mesh, ratio):", "funcdef": "def"}, "skeletor.pre.remesh": {"fullname": "skeletor.pre.remesh", "modulename": "skeletor.pre", "qualname": "remesh", "kind": "function", "doc": "

    Remesh mesh using Blender 3D.

    \n\n

    Uses Blender's \"remesh\" modifier in \"voxel\" mode.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (trimesh.Trimesh):\nMesh to remesh.
      • \n
    • voxel_size (float):\nSize of individual voxels (edge length).
      • \n
    • adaptivity (float):\nReduces final face count where detail is not important.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • trimesh.Trimesh: Remeshed mesh.
      • \n
    \n", "signature": "(mesh, voxel_size=50, adaptivity=5):", "funcdef": "def"}, "skeletor.pre.contract": {"fullname": "skeletor.pre.contract", "modulename": "skeletor.pre", "qualname": "contract", "kind": "function", "doc": "

    Contract mesh.

    \n\n

    In a nutshell: this function contracts the mesh by applying rounds of\n_constraint_ Laplacian smoothing. This function can be fairly expensive\nand I highly recommend you play around with SL to contract the\nmesh in as few steps as possible. The contraction doesn't have to be perfect\nfor good skeletonization results (<10%, i.e. epsilon<0.1).

    \n\n

    Also: parameterization matters a lot! Default parameters will get you there\nbut playing around with SL and WH0 might speed things up by an order of\nmagnitude.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (mesh obj):\nThe mesh to be contracted. Can be any object (e.g.\na trimesh.Trimesh) that has .vertices and .faces\nproperties or a tuple (vertices, faces) or a dictionary\n{'vertices': vertices, 'faces': faces}.\nVertices and faces must be (N, 3) numpy arrays.
      • \n
    • epsilon (float (0-1), optional):\nTarget contraction rate as measured by the sum of all face\nareas in the contracted versus the original mesh. Algorithm\nwill stop once mesh is contracted below this threshold.\nDepending on your mesh (number of faces, shape) reaching a\nstrong contraction can be extremely costly with comparatively\nlittle benefit for the subsequent skeletonization. Note that\nthe algorithm might stop short of this target if iter_lim\nor time_lim is reached first or if the sum of face areas\nis increasing from one iteration to the next instead of\ndecreasing.
      • \n
    • iter_lim (int (>1), optional):\nMaximum rounds of contractions.
      • \n
    • time_lim (int, optional):\nMaximum run time in seconds. Note that this limit is not\nchecked during but after each round of contraction. Hence,\nthe actual total time will likely overshoot time_lim.
      • \n
    • precision (float, optional):\nSets the precision for finding the least-square solution.\nThis is the main determinant for speed vs quality: lower\nvalues will take (much) longer but will get you closer to an\noptimally contracted mesh. Higher values will be faster but\nthe iterative contractions might stop early.
      • \n
    • SL (float, optional):\nFactor by which the contraction matrix is multiplied for\neach iteration. Higher values = quicker contraction, lower\nvalues = more likely to get you an optimal contraction.
      • \n
    • WH0 (float, optional):\nInitial weight factor for the attraction constraints.\nThe ratio of the initial weights WL0 and WH0\ncontrols the smoothness and the degree of contraction of the\nfirst iteration result, thus it determines the amount of\ndetails retained in subsequent and final contracted meshes:\nhigher WH0 = more details retained.
      • \n
    • WL0 (\"auto\" | float):\nInitial weight factor for the contraction constraints. By\ndefault (\"auto\"), this will be set to 1e-3 * sqrt(A)\nwith A being the average face area. This ensures that\ncontraction forces scale with the coarseness of the mesh.
      • \n

    • operator (\"cotangent\" | \"umbrella\"):\nWhich Laplacian operator to use:

      \n\n
        \n
      • The \"cotangent\" operator (default) takes both topology\nand geometry of the mesh into account and is hence a\nbetter descriptor of the curvature flow. This is the\noperator used in the original paper.
        • \n
      • The \"umbrella\" operator (aka \"uniform weighting\") uses\nonly topological features of the mesh. This also makes\nit more robust against flaws in the mesh! Use it when\nthe cotangent operator produces oddly contracted meshes.
        • \n
      • \n
    • progress (bool):\nWhether or not to show a progress bar.
      • \n
    • validate (bool):\nIf True, will try to fix potential issues with the mesh\n(e.g. infinite values, duplicate vertices, degenerate faces)\nbefore collapsing. Degenerate meshes can lead to effectively\ninfinite runtime for this function!
      • \n
    \n\n
    Returns
    \n\n
      \n
    • trimesh.Trimesh: Contracted copy of original mesh. The final contraction rate\nis attached to the mesh as .epsilon property.
      • \n
    \n\n
    References
    \n\n

    [1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh\n contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.

    \n", "signature": "(\tmesh,\tepsilon=1e-06,\titer_lim=100,\ttime_lim=None,\tprecision=1e-07,\tSL=2,\tWH0=1,\tWL0='auto',\toperator='cotangent',\tprogress=True,\tvalidate=True):", "funcdef": "def"}, "skeletor.skeletonize": {"fullname": "skeletor.skeletonize", "modulename": "skeletor.skeletonize", "kind": "module", "doc": "

    The skeletor.skeletonize module contains functions to for skeletonization\nof meshes.

    \n\n

    There are several approaches to skeletonizing a mesh. Which one to pick depends\n(among other things) on the shape of your mesh and the skeleton quality you want\nto get out of it. In general, unless you mesh already looks like a tube I\nrecommend looking into mesh contraction 4.

    \n\n

    Please see the documentation of the individual functions for details but here\nis a quick summary:

    \n\n\n\n\n \n \n \n \n \n \n\n\n\n\n \n \n \n \n \n \n\n\n \n \n \n \n \n \n\n\n \n \n \n \n \n \n\n\n \n \n \n \n \n \n\n\n \n \n \n \n \n \n\n\n
    functionspeedrobustradii 1mesh map 2description
    skeletor.skeletonize.by_wavefront()+++++yesyesworks well for tubular meshes
    skeletor.skeletonize.by_vertex_clusters()+++noyesbest with contracted meshes 3
    skeletor.skeletonize.by_teasar()+++noyesworks on mesh surface
    skeletor.skeletonize.by_tangent_ball()++0yesyesworks with mesh normals
    skeletor.skeletonize.by_edge_collapse()-0nonopublished with [1] - never got this to work well
    \n\n

    References

    \n\n

    [1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.

    \n\n
    \n
    \n
      \n
    1. \n

      radii can also be added in postprocessing with skeletor.post.radii() ↩

      \n
      2. \n\n
    2. \n

      a mapping from the meshes vertices to skeleton nodes ↩

      \n
      3. \n\n
    3. \n

      use skeletor.pre.contract() ↩

      \n
      4. \n\n
    4. \n

      use skeletor.pre.contract() ↩

      \n
      5. \n
    \n
    \n"}, "skeletor.skeletonize.by_teasar": {"fullname": "skeletor.skeletonize.by_teasar", "modulename": "skeletor.skeletonize", "qualname": "by_teasar", "kind": "function", "doc": "

    Skeletonize a mesh mesh using the TEASAR algorithm [1].

    \n\n

    This algorithm finds the longest path from a root vertex, invalidates all\nvertices that are within inv_dist. Then picks the second longest (and\nstill valid) path and does the same. Rinse & repeat until all vertices have\nbeen invalidated. It's fast + works very well with tubular meshes, and with\ninv_dist you have control over the level of detail. Note that by its\nnature the skeleton will be exactly on the surface of the mesh.

    \n\n

    Based on the implementation by Sven Dorkenwald, Casey Schneider-Mizell and\nForrest Collman in meshparty (https://github.com/sdorkenw/MeshParty).

    \n\n
    Parameters
    \n\n
      \n
    • mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}.
      • \n
    • inv_dist (int | float):\nDistance along the mesh used for invalidation of vertices.\nThis controls how detailed (or noisy) the skeleton will be.
      • \n
    • min_length (float, optional):\nIf provided, will skip any branch that is shorter than\nmin_length. Use this to get rid of noise but note that\nit will lead to vertices not being mapped to skeleton nodes.\nSuch vertices will show up with index -1 in\nSkeleton.mesh_map.
      • \n
    • root (int, optional):\nVertex ID of a root. If not provided will use 0.
      • \n
    • progress (bool, optional):\nIf True, will show progress bar.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
      • \n
    \n\n
    References
    \n\n

    [1] Sato, M., Bitter, I., Bender, M. A., Kaufman, A. E., & Nakajima, M.\n (n.d.). TEASAR: tree-structure extraction algorithm for accurate and\n robust skeletons. In Proceedings the Eighth Pacific Conference on\n Computer Graphics and Applications. IEEE Comput. Soc.\n https://doi.org/10.1109/pccga.2000.883951

    \n", "signature": "(mesh, inv_dist, min_length=None, root=None, progress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_wavefront": {"fullname": "skeletor.skeletonize.by_wavefront", "modulename": "skeletor.skeletonize", "qualname": "by_wavefront", "kind": "function", "doc": "

    Skeletonize a mesh using wave fronts.

    \n\n

    The algorithm tries to find rings of vertices and collapse them to\ntheir center. This is done by propagating a wave across the mesh starting at\na single seed vertex. As the wave travels across the mesh we keep track of\nwhich vertices are are encountered at each step. Groups of connected\nvertices that are \"hit\" by the wave at the same time are considered rings\nand subsequently collapsed. By its nature this works best with tubular meshes.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}.
      • \n
    • waves (int):\nNumber of waves to run across the mesh. Each wave is\ninitialized at a different vertex which produces slightly\ndifferent rings. The final skeleton is produced from a mean\nacross all waves. More waves produce higher resolution\nskeletons but also introduce more noise.
      • \n
    • origins (int | list of ints, optional):\nVertex ID(s) where the wave(s) are initialized. If we run\nout of origins (either because less origins than waves\nor because no origin for one of the connected components)\nwill fall back to semi-random origin.
      • \n
    • step_size (int):\nValues greater 1 effectively lead to binning of rings. For\nexample a stepsize of 2 means that two adjacent vertex rings\nwill be collapsed to the same center. This can help reduce\nnoise in the skeleton (and as such counteracts a large\nnumber of waves).
      • \n
    • radius_agg (\"mean\" | \"median\" | \"max\" | \"min\" | \"percentile75\" | \"percentile25\"):\nFunction used to aggregate radii over sample (i.e. the\nvertices forming a ring that we collapse to its center).
      • \n
    • progress (bool):\nIf True, will show progress bar.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
      • \n
    \n", "signature": "(\tmesh,\twaves=1,\torigins=None,\tstep_size=1,\tradius_agg='mean',\tprogress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_vertex_clusters": {"fullname": "skeletor.skeletonize.by_vertex_clusters", "modulename": "skeletor.skeletonize", "qualname": "by_vertex_clusters", "kind": "function", "doc": "

    Skeletonize a (contracted) mesh by clustering vertices.

    \n\n

    The algorithm traverses the mesh graph and groups vertices together that\nare within a given distance to each other. This uses the geodesic\n(along-the-mesh) distance, not simply the Eucledian distance. Subsequently\nthese groups of vertices are collapsed and re-connected respecting the\ntopology of the input mesh.

    \n\n

    The graph traversal is fast and scales well, so this method is well suited\nfor meshes with lots of vertices. On the downside: this implementation is\nnot very clever and you might have to play around with the parameters\n(mostly sampling_dist) to get decent results.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}.
      • \n
    • sampling_dist (float | int):\nMaximal distance at which vertices are clustered. This\nparameter should be tuned based on the resolution of your\nmesh (see Examples).
      • \n

    • cluster_pos (\"median\" | \"center\"):\nHow to determine the x/y/z coordinates of the collapsed\nvertex clusters (i.e. the skeleton's nodes)::

      \n\n
        \n
      • \"median\": Use the vertex closest to cluster's center of\nmass.
        • \n
      • \"center\": Use the center of mass. This makes for smoother\nskeletons but can lead to nodes outside the mesh.
        • \n
      • \n
    • progress (bool):\nIf True, will show progress bar.
      • \n
    \n\n
    Examples
    \n\n
    \n
    >>> import skeletor as sk\n>>> mesh = sk.example_mesh()\n>>> cont = sk.pre.contract(mesh, epsilon=0.1)\n>>> skel = sk.skeletonize.vertex_cluster(cont)\n>>> skel.mesh = mesh\n
    \n
    \n\n
    Returns
    \n\n
      \n
    • skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
      • \n
    \n", "signature": "(mesh, sampling_dist, cluster_pos='median', progress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_edge_collapse": {"fullname": "skeletor.skeletonize.by_edge_collapse", "modulename": "skeletor.skeletonize", "qualname": "by_edge_collapse", "kind": "function", "doc": "

    Skeletonize a (contracted) mesh by iteratively collapsing edges.

    \n\n

    This algorithm (described in [1]) iteratively collapses edges that are part\nof a face until no more faces are left. Edges are chosen based on a cost\nfunction that penalizes collapses that would change the shape of the object\nor would introduce long edges.

    \n\n

    This is somewhat sensitive to the dimensions of the input mesh: too large\nand you might experience slow-downs or numpy OverflowErrors; too low and\nyou might get skeletons that don't quite match the mesh (e.g. too few nodes).\nIf you experience either, try down- or up-scaling your mesh, respectively.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}.
      • \n
    • shape_weight (float, optional):\nWeight for shape costs which penalize collapsing edges that\nwould drastically change the shape of the object.
      • \n
    • sample_weight (float, optional):\nWeight for sampling costs which penalize collapses that\nwould generate prohibitively long edges.
      • \n
    • progress (bool):\nIf True, will show progress bar.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
      • \n
    \n\n
    References
    \n\n

    [1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh\n contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.

    \n", "signature": "(mesh, shape_weight=1, sample_weight=0.1, progress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_tangent_ball": {"fullname": "skeletor.skeletonize.by_tangent_ball", "modulename": "skeletor.skeletonize", "qualname": "by_tangent_ball", "kind": "function", "doc": "

    Skeletonize a mesh by finding the maximal tangent ball.

    \n\n

    This algorithm casts a ray from every mesh vertex along its inverse normals\n(requires ncollpyde). It then creates a sphere that is tangent to the\nvertex and to where the ray hit the inside of a face on the opposite side.\nNext it drops spheres that overlap with another, larger sphere. Modified\nfrom [1].

    \n\n

    The method works best on smooth meshes and is rather sensitive to errors in\nthe mesh such as incorrect normals (see skeletor.pre.fix_mesh), internal\nfaces, noisy surface (try smoothing or downsampling) or holes in the mesh.

    \n\n
    Parameters
    \n\n
      \n
    • mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
      • \n
    \n\n
    Examples
    \n\n
    \n
    >>> import skeletor as sk\n>>> mesh = sk.example_mesh()\n>>> fixed = sk.pre.fix_mesh(mesh, fix_normals=True, remove_disconnected=10)\n>>> skel = sk.skeletonize.by_tangent_ball(fixed)\n
    \n
    \n\n
    References
    \n\n

    [1] Ma, J., Bae, S.W. & Choi, S. 3D medial axis point approximation using\n nearest neighbors and the normal field. Vis Comput 28, 7\u201319 (2012).\n https://doi.org/10.1007/s00371-011-0594-7

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{"tf": 1}, "skeletor.skeletonize": {"tf": 1}}, "df": 2}}}}}}}}}}, "pipeline": ["trimmer"], "_isPrebuiltIndex": true}; // mirrored in build-search-index.js (part 1) // Also split on html tags. this is a cheap heuristic, but good enough. diff --git a/docs/skeletor.html b/docs/skeletor.html index 57368e0..f8e769c 100644 --- a/docs/skeletor.html +++ b/docs/skeletor.html @@ -281,8 +281,9 @@

    Getting started

  • skeletor.pre.fix_mesh() to fix the mesh
  • skeletor.pre.simplify() to simplify the mesh
  • skeletor.pre.contract() to contract the mesh [1]
    • -
  • skeletor.skeletonize.vertex_clusters() to generate a skeleton
    • +
  • skeletor.skeletonize.by_vertex_clusters() to generate a skeleton
  • skeletor.post.clean_up() to clean up some potential issues with the skeleton
    • +
  • skeletor.post.smooth() to smooth the skeleton
  • skeletor.post.radii() to extract radii either by k-nearest neighbours or ray-casting
    • @@ -560,184 +561,185 @@

    Top-level functions and classes

    97 1. `skeletor.pre.fix_mesh()` to fix the mesh 98 2. `skeletor.pre.simplify()` to simplify the mesh 99 3. `skeletor.pre.contract()` to contract the mesh [1] -100 4. `skeletor.skeletonize.vertex_clusters()` to generate a skeleton +100 4. `skeletor.skeletonize.by_vertex_clusters()` to generate a skeleton 101 5. `skeletor.post.clean_up()` to clean up some potential issues with the skeleton -102 6. `skeletor.post.radii()` to extract radii either by k-nearest neighbours or ray-casting -103 -104In my experience there is no one-size-fits-all. You will have to play around to -105find the right approach and parameters to get nice skeletons for your meshes. -106If you need help just open an [issue](https://github.com/navis-org/skeletor/issues). -107 -108Also check out the Gotchas below! -109 -110# Examples -111 -112First load the example mesh (a fruit fly neuron): -113 -114```Python -115>>> import skeletor as sk -116>>> mesh = sk.example_mesh() -117>>> mesh -118<trimesh.Trimesh(vertices.shape=(6582, 3), faces.shape=(13772, 3))> -119``` -120 -121Next see if there is stuff to fix in the mesh (degenerate faces, duplicate -122vertices, etc.): -123 -124```Python -125>>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False) -126>>> fixed -127<trimesh.Trimesh(vertices.shape=(6213, 3), faces.shape=(12805, 3))> -128``` -129 -130Now for tubular meshes like this neuron, the "wave front" skeletonization method -131performs really well: it works by casting waves across the mesh and collapsing -132the resulting rings into a skeleton (kinda like when you throw a stone in a -133pond and track the expanding ripples). -134 -135```Python -136>>> skel = sk.skeletonize.by_wavefront(fixed, waves=1, step_size=1) -137>>> skel -138<Skeleton(vertices=(1258, 3), edges=(1194, 2), method=wavefront)> -139``` -140 -141All skeletonization methods return a `Skeleton` object. These are just -142convenient objects to bundle the various outputs of the skeletonization. -143 -144```Python -145>>> # x/y/z location of skeleton vertices (nodes) -146>>> skel.vertices -147array([[16744, 36720, 26407], -148 ..., -149 [22076, 23217, 24472]]) -150>>> # child -> parent edges -151>>> skel.edges -152array([[ 64, 31], -153 ..., -154 [1257, 1252]]) -155>>> # Mapping for mesh to skeleton vertex indices -156>>> skel.mesh_map -157array([ 157, 158, 1062, ..., 525, 474, 547]) -158>>> # SWC table -159>>> skel.swc.head() -160 node_id parent_id x y z radius -1610 0 -1 16744.005859 36720.058594 26407.902344 0.000000 -1621 1 -1 5602.751953 22266.756510 15799.991211 7.542587 -1632 2 -1 16442.666667 14999.978516 10887.916016 5.333333 -164``` -165 -166SWC is a commonly used format for saving skeletons. `Skeleton` objects -167have a method for quickly saving a correctly formatted SWC file: -168 -169```Python -170>>> skel.save_swc('~/Documents/my_skeleton.swc') -171``` -172 -173If you installed `pyglet` (see above) you can also use `trimesh`'s plotting -174capabilities to inspect the results: -175 -176```Python -177>>> skel.show(mesh=True) -178``` -179 -180<img src="https://github.com/navis-org/skeletor/raw/master/_static/example1.png" alt="skeletor_example" width="100%"/> -181 -182That looks pretty good already but let's run some pro-forma postprocessing. -183 -184```Python -185>>> sk.post.clean_up(skel, inplace=True) -186<Skeleton(vertices=(1071, 3), edges=(1070, 2))> -187``` -188 -189So that would be a full pipeline mesh to skeleton. Don't expect your own meshes -190to produce such nice results off the bat though. Chances are you will need to -191play around to find the right recipe. If you don't know where to start, I suggest -192you try out mesh contraction + vertex clustering first: -193 -194```Python -195>>> import skeletor as sk -196>>> # Load the example mesh that ships with skeletor -197>>> mesh = sk.example_mesh() -198>>> # Alternatively use trimesh to load/construct your own mesh: -199>>> # import trimesh as tm -200>>> # mesh = tm.Trimesh(vertices, faces) -201>>> # mesh = tm.load_mesh('some/mesh.obj') -202>>> # Run some general clean-up (see docstring for details) -203>>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False) -204>>> # Contract mesh to 10% (0.1) of original volume -205>>> cont = sk.pre.contract(fixed, epsilon=0.1) -206>>> # Skeletonize -207>>> skel = sk.skeletonize.by_vertex_clusters(cont, sampling_dist=100) -208>>> # Replace contracted mesh with original for postprocessing and plotting -209>>> skel.mesh = fixed -210>>> # Add radii (vertex cluster method does not do that automatically) -211>>> sk.post.radii(skel, method='knn') -212>>> skel.show(mesh=True) -213``` -214 -215# Gotchas -216 -217- while this is a general purpose library, my personal focus is on neurons and -218 this has certainly influenced things like default parameter values and certain -219 post-processing steps -220- meshes need to be triangular (we are using `trimesh`) -221- use `sk.pre.simplify` if your mesh is very complex (half a million vertices is -222 where things start getting sluggish) -223- a good mesh contraction is often half the battle but it can be tricky to get -224 to work -225- if the mesh consists of multiple disconnected pieces the skeleton will -226 likewise be fragmented (i.e. will have multiple roots) -227- it's often a good idea to fix issues with the skeleton in postprocessing rather -228 than trying to get the skeletonization to be perfect -229 -230# Benchmarks -231 -232<img src="https://github.com/navis-org/skeletor/raw/master/benchmarks/benchmark_2.png" alt="skeletor_benchmark" width="100%"/> -233 -234[Benchmarks](https://github.com/navis-org/skeletor/blob/master/benchmarks/skeletor_benchmark.ipynb) -235were run on a 2018 MacBook Pro (2.2 GHz Core i7, 32Gb memory) with optional -236`fastremap` dependency installed. Note some of these functions (e.g. -237contraction and TEASAR/vertex cluster skeletonization) vary a lot in -238speed based on parameterization. -239 -240# What about algorithm `X`? -241 -242`skeletor` contains some algorithms that I found easy enough to implement -243and useful for my work with neurons. If you have some interesting paper/approach -244that could make a nice addition to `skeletor`, please get in touch on Github. -245Pull requests are always welcome! -246 -247# References -248 -249`[1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.` -250 -251The abstract and the paper can be found [here](http://visgraph.cse.ust.hk/projects/skeleton/). -252Also see [this](https://www.youtube.com/watch?v=-H7n59YQCRM&feature=youtu.be) YouTube video. -253 -254Some of the code in skeletor was modified from the -255[Py_BL_MeshSkeletonization](https://github.com/aalavandhaann/Py_BL_MeshSkeletonization) -256addon created by #0K Srinivasan Ramachandran and published under GPL3. -257 -258# Top-level functions and classes -259At top-level we only expose `example_mesh()` and the `Skeleton` class (which -260you probably won't ever need to touch manually). Everything else is neatly -261tucked away into submodules (see side-bar or above table). -262 -263""" -264 -265__version__ = "1.3.0" -266__version_vector__ = (1, 3, 0) -267 -268from . import skeletonize -269from . import pre -270from . import post -271 -272from .skeletonize.base import Skeleton -273from .data import example_mesh -274 -275__docformat__ = "numpy" -276 -277__all__ = ['Skeleton', 'example_mesh', 'pre', 'post', 'skeletonize'] +102 6. `skeletor.post.smooth()` to smooth the skeleton +103 7. `skeletor.post.radii()` to extract radii either by k-nearest neighbours or ray-casting +104 +105In my experience there is no one-size-fits-all. You will have to play around to +106find the right approach and parameters to get nice skeletons for your meshes. +107If you need help just open an [issue](https://github.com/navis-org/skeletor/issues). +108 +109Also check out the Gotchas below! +110 +111# Examples +112 +113First load the example mesh (a fruit fly neuron): +114 +115```Python +116>>> import skeletor as sk +117>>> mesh = sk.example_mesh() +118>>> mesh +119<trimesh.Trimesh(vertices.shape=(6582, 3), faces.shape=(13772, 3))> +120``` +121 +122Next see if there is stuff to fix in the mesh (degenerate faces, duplicate +123vertices, etc.): +124 +125```Python +126>>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False) +127>>> fixed +128<trimesh.Trimesh(vertices.shape=(6213, 3), faces.shape=(12805, 3))> +129``` +130 +131Now for tubular meshes like this neuron, the "wave front" skeletonization method +132performs really well: it works by casting waves across the mesh and collapsing +133the resulting rings into a skeleton (kinda like when you throw a stone in a +134pond and track the expanding ripples). +135 +136```Python +137>>> skel = sk.skeletonize.by_wavefront(fixed, waves=1, step_size=1) +138>>> skel +139<Skeleton(vertices=(1258, 3), edges=(1194, 2), method=wavefront)> +140``` +141 +142All skeletonization methods return a `Skeleton` object. These are just +143convenient objects to bundle the various outputs of the skeletonization. +144 +145```Python +146>>> # x/y/z location of skeleton vertices (nodes) +147>>> skel.vertices +148array([[16744, 36720, 26407], +149 ..., +150 [22076, 23217, 24472]]) +151>>> # child -> parent edges +152>>> skel.edges +153array([[ 64, 31], +154 ..., +155 [1257, 1252]]) +156>>> # Mapping for mesh to skeleton vertex indices +157>>> skel.mesh_map +158array([ 157, 158, 1062, ..., 525, 474, 547]) +159>>> # SWC table +160>>> skel.swc.head() +161 node_id parent_id x y z radius +1620 0 -1 16744.005859 36720.058594 26407.902344 0.000000 +1631 1 -1 5602.751953 22266.756510 15799.991211 7.542587 +1642 2 -1 16442.666667 14999.978516 10887.916016 5.333333 +165``` +166 +167SWC is a commonly used format for saving skeletons. `Skeleton` objects +168have a method for quickly saving a correctly formatted SWC file: +169 +170```Python +171>>> skel.save_swc('~/Documents/my_skeleton.swc') +172``` +173 +174If you installed `pyglet` (see above) you can also use `trimesh`'s plotting +175capabilities to inspect the results: +176 +177```Python +178>>> skel.show(mesh=True) +179``` +180 +181<img src="https://github.com/navis-org/skeletor/raw/master/_static/example1.png" alt="skeletor_example" width="100%"/> +182 +183That looks pretty good already but let's run some pro-forma postprocessing. +184 +185```Python +186>>> sk.post.clean_up(skel, inplace=True) +187<Skeleton(vertices=(1071, 3), edges=(1070, 2))> +188``` +189 +190So that would be a full pipeline mesh to skeleton. Don't expect your own meshes +191to produce such nice results off the bat though. Chances are you will need to +192play around to find the right recipe. If you don't know where to start, I suggest +193you try out mesh contraction + vertex clustering first: +194 +195```Python +196>>> import skeletor as sk +197>>> # Load the example mesh that ships with skeletor +198>>> mesh = sk.example_mesh() +199>>> # Alternatively use trimesh to load/construct your own mesh: +200>>> # import trimesh as tm +201>>> # mesh = tm.Trimesh(vertices, faces) +202>>> # mesh = tm.load_mesh('some/mesh.obj') +203>>> # Run some general clean-up (see docstring for details) +204>>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False) +205>>> # Contract mesh to 10% (0.1) of original volume +206>>> cont = sk.pre.contract(fixed, epsilon=0.1) +207>>> # Skeletonize +208>>> skel = sk.skeletonize.by_vertex_clusters(cont, sampling_dist=100) +209>>> # Replace contracted mesh with original for postprocessing and plotting +210>>> skel.mesh = fixed +211>>> # Add radii (vertex cluster method does not do that automatically) +212>>> sk.post.radii(skel, method='knn') +213>>> skel.show(mesh=True) +214``` +215 +216# Gotchas +217 +218- while this is a general purpose library, my personal focus is on neurons and +219 this has certainly influenced things like default parameter values and certain +220 post-processing steps +221- meshes need to be triangular (we are using `trimesh`) +222- use `sk.pre.simplify` if your mesh is very complex (half a million vertices is +223 where things start getting sluggish) +224- a good mesh contraction is often half the battle but it can be tricky to get +225 to work +226- if the mesh consists of multiple disconnected pieces the skeleton will +227 likewise be fragmented (i.e. will have multiple roots) +228- it's often a good idea to fix issues with the skeleton in postprocessing rather +229 than trying to get the skeletonization to be perfect +230 +231# Benchmarks +232 +233<img src="https://github.com/navis-org/skeletor/raw/master/benchmarks/benchmark_2.png" alt="skeletor_benchmark" width="100%"/> +234 +235[Benchmarks](https://github.com/navis-org/skeletor/blob/master/benchmarks/skeletor_benchmark.ipynb) +236were run on a 2018 MacBook Pro (2.2 GHz Core i7, 32Gb memory) with optional +237`fastremap` dependency installed. Note some of these functions (e.g. +238contraction and TEASAR/vertex cluster skeletonization) vary a lot in +239speed based on parameterization. +240 +241# What about algorithm `X`? +242 +243`skeletor` contains some algorithms that I found easy enough to implement +244and useful for my work with neurons. If you have some interesting paper/approach +245that could make a nice addition to `skeletor`, please get in touch on Github. +246Pull requests are always welcome! +247 +248# References +249 +250`[1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.` +251 +252The abstract and the paper can be found [here](http://visgraph.cse.ust.hk/projects/skeleton/). +253Also see [this](https://www.youtube.com/watch?v=-H7n59YQCRM&feature=youtu.be) YouTube video. +254 +255Some of the code in skeletor was modified from the +256[Py_BL_MeshSkeletonization](https://github.com/aalavandhaann/Py_BL_MeshSkeletonization) +257addon created by #0K Srinivasan Ramachandran and published under GPL3. +258 +259# Top-level functions and classes +260At top-level we only expose `example_mesh()` and the `Skeleton` class (which +261you probably won't ever need to touch manually). Everything else is neatly +262tucked away into submodules (see side-bar or above table). +263 +264""" +265 +266__version__ = "1.3.0" +267__version_vector__ = (1, 3, 0) +268 +269from . import skeletonize +270from . import pre +271from . import post +272 +273from .skeletonize.base import Skeleton +274from .data import example_mesh +275 +276__docformat__ = "numpy" +277 +278__all__ = ['Skeleton', 'example_mesh', 'pre', 'post', 'skeletonize']