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PMKMP

Matlab function to create perceptual colormaps, [as submitted on the Matlab File Exchange] (http://www.mathworks.com/matlabcentral/fileexchange/28982-perceptually-improved-colormaps).

Function and supporting files and images licensed under the terms of [BSD] (https://opensource.org/licenses/BSD-2-Clause) license.

function map=pmkmp(n,scheme)

PMKMP Returns perceptually balanced colormaps with rainbow-like colors

PMKMP(N,SCHEME) returns an Nx3 colormap.

usage: map=pmkmp(n,scheme);

JUSTIFICATION: rainbow, or spectrum color schemes are considered a poor choice for scientific data display by many in the scientific community (see for example reference 1 and 2) in that they introduce artifacts that mislead the viewer. "The rainbow color map appears as if it’s separated into bands of almost constant hue, with sharp transitions between hues. Viewers perceive these sharp transitions as sharp transitions in the data, even when this is not the casein how regularly spaced (interval) data are displayed (quoted from reference 1). This submission is intended to share the results of my work to create more perceptually balanced, rainbow-like color maps. Please see output arguments section for descriptions.

arguments: (input) scheme - can be one of the following strings: 'IsoL' Lab-based isoluminant rainbow with constant luminance L*=60 For interval data displayed with external lighting

 'IsoAZ'      Lightness-Chroma-Hue based isoluminant rainbow going
              around the full Hue circle.
              For azimuthal and phase data.

 'LinearL'	  Lab-based linear lightness rainbow. 
              For interval data displayed without external lighting
              100 perceptual

 'LinLhot'	  Linear lightness modification of Matlab's hot color palette. 
              For interval data displayed without external lighting
              100 perceptual    

 'CubicYF'	   Lab-based rainbow scheme with cubic-law luminance(default)
              For interval data displayed without external lighting
              100 perceptual

 'CubicL'	   Lab-based rainbow scheme with cubic-law luminance
              For interval data displayed without external lighting
              As above but has red at high end (a modest deviation from
              100 perceptual)

 'Edge'       Diverging Black-blue-cyan-white-yellow-red-black scheme
              For ratio data (ordered, constant scale, natural zero)

n - scalar specifying number of points in the colorbar. Maximum n=256 If n is not specified, the size of the colormap is determined by the current figure. If no figure exists, MATLAB creates one.

arguments: (output) map - colormap of the chosen scheme

  • IsoL is based on work in paper 2 in the reference section. In both this paper and in several others this is indicated as the best for displaying interval data with external lighting. This is so as to allow the lighting to provide the shading to highlight the details of interest. If lighting is combined with a colormap that has its own luminance function associated - even as simple as a linear increase this will confuse the viewer. The only difference from the paper is that I changed the value of constant luminance to L*=60 to make it brighter that the authors' example.

  • IsoAZ is a Lightness-Chroma-Hue based isoluminant rainbow that goes around the full Hue circle.For azimuthal and phase data. Created with code snippet below. This is a modification from an example by Steve Eddins on his Matlab central blog (reference 15). Steve had lightness increasing while as hue changed. I hold the ligthness constant instead to make the result isoluminant. I also use the Colorspace transformations function instead of the Image Processing Toolbox for the color conversion. Here's the code:

    radius = 50; chroma theta = linspace(0, pi/2, 256)'; hue a = radius * cos(theta); b = radius * sin(theta); L = (ones(1, 256)*100)'; lightness Lab = [L, a, b]; RGB=colorspace('RGB<-Lab',(Lab));
    (needs Colorspace transformations from Matlab File Exchange) www.mathworks.com/matlabcentral/fileexchange/28790-colorspace-transformations

  • LinearL is a linear lightness modification of another palette from paper 2 in the reference. For how it was generated see my blog post: mycarta.wordpress.com/2012/12/06/the-rainbow-is-deadlong-live-the-rainbow-part-5-cie-lab-linear-l-rainbow/

  • LinLhot is a linear lightness modification of Matlab's hot color palette. For how it was generated see my blog post: mycarta.wordpress.com/2012/10/14/the-rainbow-is-deadlong-live-the-rainbow-part-4-cie-lab-heated-body/

  • CubicL too is based on some of the ideas in paper 2 in the reference section but rather than using a linearly increasing L* function such as the one used by those authors, I am using a compressive or cubic law function for the increase in L*. L* ranges between 31 and 90 in the violet to yellowish portion of the colormap, then decreases to about 80 to get to the red (please refer to figure L_a_b_PlotsCubicL.png). The choice to start at 31 was a matter of taste. I like having violet instead of black at the cold end of the colormap. The latter choice was so as to have red and not white at the warm end of the colorbar, which is also a matter of personal taste. As a result, there is an inversion in the L* trend, but I believe because it is a smooth one that this is an acceptable compromise and the resulting colormap is much of an improvement over the standard rainbow or spectrum schemes, which typically have at least 3 sharp L* inversions. Please run CompareLabPlotsUsingColorspace.m or see figures: L_plot_for_CubicL_colormap.png, L_plot_for_jet_colormap.png, and L_plot_for_spectrum_colormap.png for a demonstration

- CubicYF A fully perceptual version of the above in which I eliminated
  the red tip at the high end. The work is described in papers 12 and 13. 
  I've uploaded 2 figures. The first, spectrum vs cubicYF.png, is a comparison
  of lightness versus sample number for the spectrum (top left) and the
  new color palette (bottom left), and also a comparison of test surface
  (again the Great Pyramid of Giza)using the spectrum (top right)and 
  the new color palette (bottom right). The second figure 
  simulations color vision deficieny.png
  is a comparison of spectrum and cubicYF rainbow for all viewers. 
  Left column: full color vision – for the spectrum (top left) and for the 
  cubeYF rainbow (bottom left). Centre column: simulation of Deuternaopia
  for spectrum (top centre) and cubeYF rainbow (bottom centre).
  Right column: simulation of Tritanopia for spectrum (top right) and
  cubeYF rainbow (bottom right). For the cubeYF there are no
  confusing color pairs in these simulations. There are several in the
  spectrum. Please refer to reference 14 for vcolor vision deficiency
  terminoligy. For how it was generated see my blog post:
  http://mycarta.wordpress.com/2013/02/21/perceptual-rainbow-palette-the-method/
  • Edge is based on the Goethe Edge Colors described in the book in reference 3. In practice the colormap resembles a cold color map attached to a warm color map. But the science behind it is rigorous and the experimental work is based on is very intriguing to me: an alternative to the Newtonian spectrum. This is not perceptually balanced in a strict sense but because it does not have green it is perceptually improved in a harmonious sense (refer to paper reference 10 for a review of the concept of harmony in color visualization).

Example1: 128-color rainbow with cubic-law luminance (default) load mandrill; imagesc(X); colormap(pmkmp(128)); colorbar;

Example2: 128-color palette for azimuthal data a=0:8:360; b = repmat(a,[46 1]); imagesc(b); colormap(pmkmp(128,'IsoAZ')); colorbar;

See files examples.m, examples1.m, and example2.m for more examples See files MakeLabPlotUsingColorspace.m and CompareLabPlotsUsingColorspace.m for some demonstrations

See also: JET, HSV, GRAY, HOT, COOL, BONE, COPPER, PINK, FLAG, PRISM, COLORMAP, RGBPLOT

Other submissions of interest

 Matlab's new Parula colormap
 http://blogs.mathworks.com/steve/2014/10/13/a-new-colormap-for-matlab-part-1-introduction/

 Haxby color map
 www.mathworks.com/matlabcentral/fileexchange/25690-haxby-color-map

 Colormap and colorbar utilities
 www.mathworks.com/matlabcentral/fileexchange/24371-colormap-and-color
 bar-utilities-sep-2009

 Lutbar
 www.mathworks.com/matlabcentral/fileexchange/9137-lutbar-a-pedestrian-colormap-toolbarcontextmenu-creator

 usercolormap
 www.mathworks.com/matlabcentral/fileexchange/7144-usercolormap

 freezeColors
 www.mathworks.com/matlabcentral/fileexchange/7943


 Bipolar Colormap
 www.mathworks.com/matlabcentral/fileexchange/26026

 colorGray
 www.mathworks.com/matlabcentral/fileexchange/12804-colorgray

 mrgb2gray
 www.mathworks.com/matlabcentral/fileexchange/5855-mrgb2gray

 CMRmap
 www.mathworks.com/matlabcentral/fileexchange/2662-cmrmap-m

 real2rgb & colormaps
 www.mathworks.com/matlabcentral/fileexchange/23342-real2rgb-colormaps

 ColorBrewer: Attractive and Distinctive Colormaps
 http://www.mathworks.com/matlabcentral/fileexchange/45208-colorbrewer--attractive-and-distinctive-colormaps

Acknowledgements

 For input to do this research I was inspired by: 
 ColorSpiral - http://bsp.pdx.edu/Software/ColorSpiral.m
 Despite an erroneous assumption about conversion/equivalence to 
 grayscale (which CMRmap achieves correctly) the main idea is ingenious
 and the code is well written. It also got me interested in perceptual
 colormaps. See reference 5 for paper
 
 For function architecture and code syntax I was inspired by:
 Light Bartlein Color Maps 
 www.mathworks.com/matlabcentral/fileexchange/17555
 (and comments posted therein)

 For idea on world topgraphy in examples.m I was inspired by:
 Cold color map
 www.mathworks.cn/matlabcentral/fileexchange/23865-cold-colormap

 To generate the spectrum in examples1.m I used:
 Spectral and XYZ Color Functions
 www.mathworks.com/matlabcentral/fileexchange/7021-spectral-and-xyz-color-functions
 
 For Lab=>RGB conversions I used:
 Colorspace transforamtions
 www.mathworks.com/matlabcentral/fileexchange/28790-colorspace-transformations


 For the figures in example 2 I used:
 Shaded pseudo color
 http://www.mathworks.cn/matlabcentral/fileexchange/14157-shaded-pseudo-color

 For plots in CompareLabPlotsUsingColorspace.m I used:
 cline
 http://www.mathworks.cn/matlabcentral/fileexchange/14677-cline

 For some ideas in general on working in Lab space:
 Color scale
 www.mathworks.com/matlabcentral/fileexchange/11037
 http://blogs.mathworks.com/steve/2006/05/09/a-lab-based-uniform-color-scale/

 A great way to learn more about improved colormaps and making colormaps:
 MakeColorMap
 www.mathworks.com/matlabcentral/fileexchange/17552
 blogs.mathworks.com/videos/2007/11/15/practical-example-algorithm-development-for-making-colormaps/

References

 1)  Borland, D. and Taylor, R. M. II (2007) - Rainbow Color Map (Still) 
     Considered Harmful
     IEEE Computer Graphics and Applications, Volume 27, Issue 2
     Pdf paper included in submission


 2)  Kindlmann, G. Reinhard, E. and Creem, S. Face-based Luminance Matching
     for Perceptual Colormap Generation
     IEEE - Proceedings of the conference on Visualization '02
     www.cs.utah.edu/~gk/papers/vis02/FaceLumin.pdf

 3)  Koenderink, J. J. (2010) - Color for the Sciences
     MIT press, Cambridge, Massachusset

 4)  Light, A. and Bartlein, P.J. (2004) - The end of the rainbow? 
     Color schemes for improved data graphics.
     EOS Transactions of the American Geophysical Union 85 (40)
     Reprint of Article with Comments and Reply
     http://geography.uoregon.edu/datagraphics/EOS/Light-and-Bartlein.pdf

 5)  McNames, J. (2006) An effective color scale for simultaneous color
     and gray-scale publications
     IEEE Signal Processing Magazine, Volume 23, Issue1
     http://bsp.pdx.edu/Publications/2006/SPM_McNames.pdf

 6)  Rheingans, P.L. (2000), Task-based Color Scale Design
     28th AIPR Workshop: 3D Visualization for Data Exploration and Decision Making
     www.cs.umbc.edu/~rheingan/pubs/scales.pdf.gz

 7)  Rogowitz, B.E. and  Kalvin, A.D. (2001) - The "Which Blair project":
     a quick visual method for evaluating perceptual color maps. 
     IEEE - Proceedings of the conference on Visualization ‘01
     www.research.ibm.com/visualanalysis/papers/WhichBlair-Viz01Rogowitz_Kalvin._final.pdf

 8)  Rogowitz, B.E. and  Kalvin, A.D. - Why Should Engineers and Scientists
     Be Worried About Color?
     www.research.ibm.com/people/l/lloydt/color/color.HTM

 9)  Rogowitz, B.E. and  Kalvin, A.D. - How NOT to Lie with Visualization
     www.research.ibm.com/dx/proceedings/pravda/truevis.htm

 10) Wang, L. and Mueller,K (2008) - Harmonic Colormaps for Volume Visualization
     IEEE/ EG Symposium on Volume and Point-Based Graphics
     http://www.cs.sunysb.edu/~mueller/papers/vg08_final.pdf

 11) Wyszecki, G. and Stiles W. S. (2000) - Color Science: Concepts and 
     Methods, Quantitative Data and Formulae, 2nd Edition, John Wiley and Sons

 12) Niccoli, M., (2012) - How to assess a color map - in:
     52 things you should know about Geophysics, M. Hall and E. Bianco,
     eds. 

 13) Niccoli, M., and Lynch, S. (2012, in press) - A more perceptual color
     palette for structure maps, 2012 CSEG Geoconvention extended
     abstract.

 14) Color Blind Essentials eBook
     http://www.colblindor.com/color-blind-essentials/

 15) Eddins, S. (2006) - A Lab-based uniform color scale
     http://blogs.mathworks.com/steve/2006/05/09/a-lab-based-uniform-color-scale/

Author: Matteo Niccoli e-mail address: matteo@mycarta.ca Release: 4.02 Release date: October 2014 Full research at: http://mycarta.wordpress.com/2012/05/29/the-rainbow-is-dead-long-live-the-rainbow-series-outline/