HomographyNet.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# HomographyNet Implementation in Keras / TensorFlow\n",
    "** by Richard Guinto **\n",
    "*<richard.guinto@gmail.com>*\n",
    "\n",
    "## Description\n",
    "\n",
    "Deep Image Homography Estimation a.k.a. HomographyNet is a Deep Convulation Neural Network which directly produces the Homography relating two images.  The paper is fully described from this link:  https://arxiv.org/pdf/1606.03798.pdf\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"files/HomographyNet%20Layers.png\">\n",
    "<img src=\"files/Loss.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dataset\n",
    "The dataset was generated using images from the COCO 2017 Test Images as described in the paper.\n",
    "Samples are bundled together in NumPy archives (.npz), with 9216 samples per archive.\n",
    "I used 40 archives during the training, and 3 archives for the evaluation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each archive is ~289MiB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Volume in drive C has no label.\n",
      " Volume Serial Number is 4A9E-AED8\n",
      "\n",
      " Directory of C:\\Users\\Richard Guinto\\msee\\dataset\\test\n",
      "\n",
      "10/22/2017  07:14 PM    <DIR>          .\n",
      "10/22/2017  07:14 PM    <DIR>          ..\n",
      "10/22/2017  07:14 PM             6,148 .DS_Store\n",
      "10/22/2017  07:14 PM       302,580,104 f7823b11-901a-457a-89a2-8c37dc4fef60.npz\n",
      "10/22/2017  07:14 PM       302,580,104 fa6716a8-218c-42b1-a6aa-3fd014eb0f64.npz\n",
      "10/22/2017  07:14 PM       302,580,104 faf48514-698b-45e3-ae58-60c9189e0426.npz\n",
      "               4 File(s)    907,746,460 bytes\n",
      "               2 Dir(s)  681,769,811,968 bytes free\n"
     ]
    }
   ],
   "source": [
    "%ls \"dataset\\\\test\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "path: C:\\Users\\Richard Guinto\\msee\\dataset\\test\\f7823b11-901a-457a-89a2-8c37dc4fef60.npz\n",
      "keys: ['images', 'offsets']\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import os.path\n",
    "import glob\n",
    "\n",
    "path = \"dataset/test/f7823b11-901a-457a-89a2-8c37dc4fef60.npz\"\n",
    "print('path:', os.path.abspath(path))\n",
    "\n",
    "archive = np.load(os.path.abspath(path))\n",
    "print('keys:', archive.files)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "images.shape:  (9216, 128, 128, 2)\n",
      "offsets.shape:  (9216, 8)\n"
     ]
    }
   ],
   "source": [
    "images = archive['images']\n",
    "offsets = archive['offsets']\n",
    "\n",
    "print('images.shape: ', images.shape)\n",
    "print('offsets.shape: ', offsets.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x153ecb70>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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1HijWE7Rp0irpuKK3Wq1CPDxQlNAEV2X1xxNa1NOSaDp+lYxehCK/ZyXj6upqKVZ+MBiU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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15366080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_image = np.split(images[0], 2, axis=-1)\n",
    "plt.imshow(sample_image[0].squeeze(), cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x16472780>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nLnnReNFUy3il76XRaGTSh5lyS7vSZqvVCn2Sj4GrDVtRl3ox2Xq9nlpCTo7X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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x154412e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(sample_image[1].squeeze(), cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample offset:  [ -4  -6 -29 -12  -3 -23  -2  24]\n"
     ]
    }
   ],
   "source": [
    "sample_offset = offsets[0]\n",
    "print('sample offset: ', sample_offset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The offset represents the displacement x,y with respect to the patch corner points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#data loading in Keras (credits: baudm)\n",
    "\n",
    "def data_loader(path, batch_size=64):\n",
    "    \"\"\"Generator to be used with model.fit_generator()\"\"\"\n",
    "    while True:\n",
    "        for npz in glob.glob(os.path.join(path, '*.npz')):\n",
    "            # Load pack into memory\n",
    "            archive = np.load(npz)\n",
    "            images = archive['images']\n",
    "            offsets = archive['offsets']\n",
    "            # Yield minibatch\n",
    "            for i in range(0, len(offsets), batch_size):\n",
    "                end_i = i + batch_size\n",
    "                try:\n",
    "                    batch_images = images[i:end_i]\n",
    "                    batch_offsets = offsets[i:end_i]\n",
    "                except IndexError:\n",
    "                    continue\n",
    "                # Normalize\n",
    "                batch_images = (batch_images - 127.5) / 127.5\n",
    "                batch_offsets = batch_offsets / 32.\n",
    "                yield batch_images, batch_offsets\n",
    "                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "from keras import backend as K\n",
    "\n",
    "#Loss Function using SMSE\n",
    "def euclidean_l2(y_true, y_pred):\n",
    "    return K.sqrt(K.sum(K.square(y_pred - y_true), axis=-1, keepdims=True))\n",
    "\n",
    "def mace(y_true, y_pred):\n",
    "    return K.mean(32*K.sqrt(K.sum(K.square(K.reshape(y_pred, (-1,4,2)) - K.reshape(y_true, (-1,4,2))),\\\n",
    "        axis=-1, keepdims=True)),axis=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "samples per archive:  9216\n"
     ]
    }
   ],
   "source": [
    "samples_per_archive = images.shape[0]\n",
    "print('samples per archive: ', samples_per_archive)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training\n",
    "The python script below is the training model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Activation, Dense, Dropout, Conv2D, MaxPooling2D, Flatten, BatchNormalization, InputLayer\n",
    "from keras.callbacks import ModelCheckpoint\n",
    "from keras import backend as K\n",
    "from keras import optimizers\n",
    "import tensorflow as tf\n",
    "\n",
    "# Dataset-specific\n",
    "train_data_path = 'dataset/training'\n",
    "test_data_path = 'dataset/test'\n",
    "samples_per_archive = 9216\n",
    "num_archives = 40\n",
    "# 43 archives x 9,216 samples per archive, but use just 40 and save the 3 for testing\n",
    "num_samples = num_archives * samples_per_archive\n",
    "\n",
    "\n",
    "# From the paper\n",
    "batch_size = 64\n",
    "total_iterations = 90000\n",
    "\n",
    "steps_per_epoch = num_samples / batch_size # As stated in Keras docs\n",
    "epochs = int(total_iterations / steps_per_epoch)\n",
    "\n",
    "input_shape = (128, 128, 2)\n",
    "kernel_size = 3\n",
    "pool_size = 2\n",
    "filters = 64\n",
    "dropout = 0.5\n",
    "\n",
    "\n",
    "model = Sequential()\n",
    "model.add(InputLayer(input_shape))\n",
    "model.add(Conv2D(filters=filters,\\\n",
    "        kernel_size=kernel_size, activation='relu', padding='same'))\n",
    "model.add(BatchNormalization())\n",
    "model.add(Conv2D(filters=filters,\\\n",
    "        kernel_size=kernel_size, activation='relu', padding='same'))\n",
    "model.add(BatchNormalization())\n",
    "model.add(MaxPooling2D(pool_size))\n",
    "model.add(Conv2D(filters=filters,\\\n",
    "        kernel_size=kernel_size, activation='relu', padding='same'))\n",
    "model.add(BatchNormalization())\n",
    "model.add(Conv2D(filters=filters,\\\n",
    "        kernel_size=kernel_size, activation='relu', padding='same'))\n",
    "model.add(BatchNormalization())\n",
    "model.add(MaxPooling2D(pool_size))\n",
    "model.add(Conv2D(filters=filters*2,\\\n",
    "        kernel_size=kernel_size, activation='relu', padding='same',))\n",
    "model.add(BatchNormalization())\n",
    "model.add(Conv2D(filters=filters*2,\\\n",
    "        kernel_size=kernel_size, activation='relu', padding='same',))\n",
    "model.add(BatchNormalization())\n",
    "model.add(MaxPooling2D(pool_size))\n",
    "model.add(Conv2D(filters=filters*2,\\\n",
    "        kernel_size=kernel_size, activation='relu', padding='same',))\n",
    "model.add(BatchNormalization())\n",
    "model.add(Conv2D(filters=filters*2,\\\n",
    "        kernel_size=kernel_size, activation='relu', padding='same',))\n",
    "model.add(BatchNormalization())\n",
    "model.add(Flatten())\n",
    "model.add(Dropout(dropout))\n",
    "model.add(Dense(1024, activation='relu'))\n",
    "model.add(Dropout(dropout))\n",
    "#for regression model\n",
    "model.add(Dense(8))\n",
    "#model.add(Activation('softmax'))\n",
    "model.summary()\n",
    "\n",
    "#use optimizer Stochastic Gradient Methond with a Learning Rate of 0.005 and momentum of 0.9\n",
    "#sgd = optimizers.SGD(lr=0.005, momentum=0.9, decay=0.001355)\n",
    "sgd = optimizers.SGD(lr=0.005, momentum=0.9)\n",
    "\n",
    "#compile model\n",
    "model.compile(loss=euclidean_l2,\\\n",
    "        optimizer=sgd, metrics=['mean_squared_error'])\n",
    "\n",
    "#check point\n",
    "filepath = \"checkpoints/weights-{epoch:02d}-{loss:.2f}.hdf5\"\n",
    "checkpoint = ModelCheckpoint(filepath, monitor='loss', verbose=1)\n",
    "callback_list = [checkpoint]\n",
    "\n",
    "# Train\n",
    "print('TRAINING...')\n",
    "model.fit_generator(data_loader(train_data_path, batch_size),\n",
    "                    steps_per_epoch=steps_per_epoch,\n",
    "                    epochs=epochs, callbacks=callback_list)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"files/Model%20Summary.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Below is the screenshot of the training results for 15 epochs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"files/Training%20Result.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing / Evaluation\n",
    "The training produced the record of the weights for each epoch and the last checkpoint was used to load for the model evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Volume in drive C has no label.\n",
      " Volume Serial Number is 4A9E-AED8\n",
      "\n",
      " Directory of C:\\Users\\Richard Guinto\\msee\n",
      "\n",
      "\n",
      " Directory of C:\\Users\\Richard Guinto\\msee\\checkpoints\n",
      "\n",
      "10/23/2017  06:55 PM    <DIR>          .\n",
      "10/23/2017  06:55 PM    <DIR>          ..\n",
      "10/23/2017  06:37 AM       273,658,120 weights-01-1.08.hdf5\n",
      "10/23/2017  06:37 AM       273,658,120 weights-02-0.86.hdf5\n",
      "10/23/2017  06:38 AM       273,658,120 weights-03-0.77.hdf5\n",
      "10/23/2017  06:38 AM       273,658,120 weights-04-0.72.hdf5\n",
      "10/23/2017  06:38 AM       273,658,120 weights-05-0.68.hdf5\n",
      "10/23/2017  06:38 AM       273,658,120 weights-06-0.66.hdf5\n",
      "10/23/2017  06:39 AM       273,658,120 weights-07-0.64.hdf5\n",
      "10/23/2017  06:39 AM       273,658,120 weights-08-0.62.hdf5\n",
      "10/23/2017  06:39 AM       273,658,120 weights-09-0.61.hdf5\n",
      "10/22/2017  08:58 PM       273,658,120 weights-10-0.60.hdf5\n",
      "10/23/2017  06:40 AM       273,658,120 weights-11-0.58.hdf5\n",
      "10/23/2017  06:40 AM       273,658,120 weights-12-0.57.hdf5\n",
      "10/23/2017  06:40 AM       273,658,120 weights-13-0.57.hdf5\n",
      "10/23/2017  06:40 AM       273,658,120 weights-14-0.56.hdf5\n",
      "              14 File(s)  3,831,213,680 bytes\n",
      "               2 Dir(s)  681,763,631,104 bytes free\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "File Not Found\n"
     ]
    }
   ],
   "source": [
    "%ls -l checkpoints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The python script below is used to evaluate our trained model with the 3 test archives (3 x 9216 samples).\n",
    "I modified the metrics to use the custom function to define the Mean Average Corner Error (mace) instead of just the mean square error used in the training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.models import load_model\n",
    "from keras import optimizers\n",
    "\n",
    "#Model Checkpoint\n",
    "checkpoint = \"checkpoints/weights-14-0.56.hdf5\"\n",
    "test_data_path = \"datasets/test\"\n",
    "\n",
    "test_samples = 3 * samples_per_archive\n",
    "batch_size = 64\n",
    "steps = test_samples / batch_size\n",
    "\n",
    "# load model\n",
    "model = load_model(checkpoint, custom_objects={'euclidean_l2': euclidean_l2, 'mace': mace})\n",
    "\n",
    "#use optimizer Stochastic Gradient Methond with a Learning Rate of 0.005 and momentum of 0.9\n",
    "sgd = optimizers.SGD(lr=0.005, momentum=0.9)\n",
    "\n",
    "#compile model\n",
    "model.compile(loss=euclidean_l2,\\\n",
    "        optimizer=sgd, metrics=[mace])\n",
    "\n",
    "# Test\n",
    "score = model.evaluate_generator(data_loader(test_data_path, batch_size),\n",
    "                         steps=steps)\n",
    "\n",
    "print('Test score:', score)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing Result:\n",
    "The Mean Average Corner Error for the evaluation phase resulted to 6.30 pixels only, which is better than 9.2 pixels (the published result in the paper)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"files/Model%20Evaluation.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prediction samples\n",
    "This python code shows the prediction results with the first 10 samples of the test archive.\n",
    "The result of each prediction is a normalized value (-1 to 1).  To get the actual offset value, we multiply the result by 32 (p = 32 in the paper).\n",
    "Mean Square Error is used for our metrics, while Root Mean Square Error is used for the loss function.\n",
    "On Mean Average Corner Error is still less than the 9.2pixel average described in the paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading model...  checkpoints/weights-14-0.56.hdf5\n",
      "SAMPLE  0\n",
      "Sample Offset:  [ -4  -6 -29 -12  -3 -23  -2  24]\n",
      "Normalize Sample Offset:  [-0.125   -0.1875  -0.90625 -0.375   -0.09375 -0.71875 -0.0625   0.75   ]\n",
      "Predicting Offset...\n",
      "Predicted Offset(Normalize):  [[-0.14250475 -0.05554018 -0.92104042 -0.36435172 -0.11278056 -0.63863069\n",
      "  -0.19482951  0.59375417]]\n",
      "Predicted Offset:  [[ -4.56015205  -1.77728581 -29.4732933  -11.65925503  -3.60897803\n",
      "  -20.43618202  -6.23454428  19.00013351]]\n",
      "Normalize RMSE:  [[ 0.25837391]]\n",
      "Normalize MSE:  [[ 0.00834463]]\n",
      "MSE:  [[ 8.54490576]]\n",
      "Normalize MAE:  [[ 0.07032856]]\n",
      "MAE:  [[ 2.25051391]]\n",
      "Mean Ave. Corner Error:  3.50753724314\n",
      "SAMPLE  1\n",
      "Sample Offset:  [ 27 -28  -7  -6 -31 -20  -5   3]\n",
      "Normalize Sample Offset:  [ 0.84375 -0.875   -0.21875 -0.1875  -0.96875 -0.625   -0.15625  0.09375]\n",
      "Predicting Offset...\n",
      "Predicted Offset(Normalize):  [[ 0.60214853 -0.70988363 -0.21000905 -0.03854291 -0.65358949 -0.66570729\n",
      "  -0.03431126 -0.10413262]]\n",
      "Predicted Offset:  [[ 19.26875305 -22.71627617  -6.72028971  -1.23337317 -20.91486359\n",
      "  -21.30263329  -1.09796035  -3.33224392]]\n",
      "Normalize RMSE:  [[ 0.51274665]]\n",
      "Normalize MSE:  [[ 0.03286364]]\n",
      "MSE:  [[ 33.65236782]]\n",
      "Normalize MAE:  [[ 0.15501313]]\n",
      "MAE:  [[ 4.96042015]]\n",
      "Mean Ave. Corner Error:  7.93649736027\n",
      "SAMPLE  2\n",
      "Sample Offset:  [ 19 -31  -4   5 -27  -5  27  13]\n",
      "Normalize Sample Offset:  [ 0.59375 -0.96875 -0.125    0.15625 -0.84375 -0.15625  0.84375  0.40625]\n",
      "Predicting Offset...\n",
      "Predicted Offset(Normalize):  [[ 0.55748105 -0.72920072 -0.10686783  0.16751814 -0.22563538 -0.47743446\n",
      "   0.70303178  0.28376466]]\n",
      "Predicted Offset:  [[ 17.83939362 -23.33442307  -3.41977048   5.36058044  -7.22033215\n",
      "  -15.2779026   22.49701691   9.08046913]]\n",
      "Normalize RMSE:  [[ 0.76104169]]\n",
      "Normalize MSE:  [[ 0.07239806]]\n",
      "MSE:  [[ 74.13561035]]\n",
      "Normalize MAE:  [[ 0.18846515]]\n",
      "MAE:  [[ 6.03088471]]\n",
      "Mean Ave. Corner Error:  9.17414138186\n",
      "SAMPLE  3\n",
      "Sample Offset:  [ 18 -16  21  -1  17 -11 -19 -16]\n",
      "Normalize Sample Offset:  [ 0.5625  -0.5      0.65625 -0.03125  0.53125 -0.34375 -0.59375 -0.5    ]\n",
      "Predicting Offset...\n",
      "Predicted Offset(Normalize):  [[ 0.76808685 -0.46365145  0.70317274 -0.07748534  0.56381035 -0.34365073\n",
      "  -0.64307743 -0.5176217 ]]\n",
      "Predicted Offset:  [[ 24.57877922 -14.83684635  22.50152779  -2.47953081  18.04193115\n",
      "  -10.99682331 -20.57847786 -16.56389427]]\n",
      "Normalize RMSE:  [[ 0.22744346]]\n",
      "Normalize MSE:  [[ 0.00646632]]\n",
      "MSE:  [[ 6.62150741]]\n",
      "Normalize MAE:  [[ 0.05433778]]\n",
      "MAE:  [[ 1.73880893]]\n",
      "Mean Ave. Corner Error:  2.87672751712\n",
      "SAMPLE  4\n",
      "Sample Offset:  [-24  26 -14 -26 -13 -14 -10  -9]\n",
      "Normalize Sample Offset:  [-0.75     0.8125  -0.4375  -0.8125  -0.40625 -0.4375  -0.3125  -0.28125]\n",
      "Predicting Offset...\n",
      "Predicted Offset(Normalize):  [[-0.78741205  0.41173747 -0.57676262 -0.87145525 -0.46138126 -0.53484929\n",
      "  -0.69419068 -0.19469351]]\n",
      "Predicted Offset:  [[-25.19718552  13.1755991  -18.45640373 -27.88656807 -14.76420021\n",
      "  -17.11517715 -22.21410179  -6.23019218]]\n",
      "Normalize RMSE:  [[ 0.59209476]]\n",
      "Normalize MSE:  [[ 0.04382203]]\n",
      "MSE:  [[ 44.87375424]]\n",
      "Normalize MAE:  [[ 0.15714002]]\n",
      "MAE:  [[ 5.02848065]]\n",
      "Mean Ave. Corner Error:  8.45592787067\n",
      "SAMPLE  5\n",
      "Sample Offset:  [-31   3 -26  20  15  25 -14 -15]\n",
      "Normalize Sample Offset:  [-0.96875  0.09375 -0.8125   0.625    0.46875  0.78125 -0.4375  -0.46875]\n",
      "Predicting Offset...\n",
      "Predicted Offset(Normalize):  [[-0.92497671  0.12453513 -0.78725767  0.57240045  0.47227308  0.66715419\n",
      "  -0.31599027 -0.37257075]]\n",
      "Predicted Offset:  [[-29.59925461   3.98512411 -25.19224548  18.31681442  15.11273861\n",
      "   21.34893417 -10.11168861 -11.9222641 ]]\n",
      "Normalize RMSE:  [[ 0.20811785]]\n",
      "Normalize MSE:  [[ 0.00541413]]\n",
      "MSE:  [[ 5.5440692]]\n",
      "Normalize MAE:  [[ 0.06096352]]\n",
      "MAE:  [[ 1.95083266]]\n",
      "Mean Ave. Corner Error:  3.04780555406\n",
      "SAMPLE  6\n",
      "Sample Offset:  [-21 -31 -20 -24   4  -3 -20 -23]\n",
      "Normalize Sample Offset:  [-0.65625 -0.96875 -0.625   -0.75     0.125   -0.09375 -0.625   -0.71875]\n",
      "Predicting Offset...\n",
      "Predicted Offset(Normalize):  [[-0.61325133 -0.80329746 -0.52129155 -0.70986444 -0.01804418  0.05308453\n",
      "  -0.49432555 -0.64243144]]\n",
      "Predicted Offset:  [[-19.62404251 -25.70551872 -16.68132973 -22.715662    -0.57741368\n",
      "    1.69870496 -15.81841755 -20.55780602]]\n",
      "Normalize RMSE:  [[ 0.32636189]]\n",
      "Normalize MSE:  [[ 0.01331401]]\n",
      "MSE:  [[ 13.63354687]]\n",
      "Normalize MAE:  [[ 0.10614587]]\n",
      "MAE:  [[ 3.39666776]]\n",
      "Mean Ave. Corner Error:  5.10779034277\n",
      "SAMPLE  7\n",
      "Sample Offset:  [  3   3  13  27  21 -14   4   9]\n",
      "Normalize Sample Offset:  [ 0.09375  0.09375  0.40625  0.84375  0.65625 -0.4375   0.125    0.28125]\n",
      "Predicting Offset...\n",
      "Predicted Offset(Normalize):  [[ 0.13763909  0.06586245  0.53117824  0.5813545   0.699045   -0.44823477\n",
      "   0.24651718  0.35018265]]\n",
      "Predicted Offset:  [[  4.40445089   2.1075983   16.99770355  18.60334396  22.36944008\n",
      "  -14.34351254   7.8885498   11.20584488]]\n",
      "Normalize RMSE:  [[ 0.32958643]]\n",
      "Normalize MSE:  [[ 0.0135784]]\n",
      "MSE:  [[ 13.90428345]]\n",
      "Normalize MAE:  [[ 0.087885]]\n",
      "MAE:  [[ 2.81231993]]\n",
      "Mean Ave. Corner Error:  4.21156179327\n",
      "SAMPLE  8\n",
      "Sample Offset:  [-11  -8 -31 -17  27 -15 -17   5]\n",
      "Normalize Sample Offset:  [-0.34375 -0.25    -0.96875 -0.53125  0.84375 -0.46875 -0.53125  0.15625]\n",
      "Predicting Offset...\n",
      "Predicted Offset(Normalize):  [[-0.18427196 -0.10376725 -0.99645287 -0.43895617  0.73803866 -0.43310711\n",
      "  -0.43818918  0.15883529]]\n",
      "Predicted Offset:  [[ -5.89670277  -3.32055187 -31.88649178 -14.04659748  23.61723709\n",
      "  -13.85942745 -14.02205372   5.08272934]]\n",
      "Normalize RMSE:  [[ 0.27787617]]\n",
      "Normalize MSE:  [[ 0.0096519]]\n",
      "MSE:  [[ 9.8835413]]\n",
      "Normalize MAE:  [[ 0.08283848]]\n",
      "MAE:  [[ 2.65083134]]\n",
      "Mean Ave. Corner Error:  4.13912026992\n",
      "SAMPLE  9\n",
      "Sample Offset:  [-20  26 -26 -10  16 -13  24  28]\n",
      "Normalize Sample Offset:  [-0.625    0.8125  -0.8125  -0.3125   0.5     -0.40625  0.75     0.875  ]\n",
      "Predicting Offset...\n",
      "Predicted Offset(Normalize):  [[-0.66163307  0.59332019 -0.73886538 -0.22212261  0.62033647 -0.42941627\n",
      "   0.39361817  0.69835544]]\n",
      "Predicted Offset:  [[-21.17225838  18.98624611 -23.64369202  -7.10792351  19.85076714\n",
      "  -13.74132061  12.59578133  22.34737396]]\n",
      "Normalize RMSE:  [[ 0.48600489]]\n",
      "Normalize MSE:  [[ 0.02952509]]\n",
      "MSE:  [[ 30.23369694]]\n",
      "Normalize MAE:  [[ 0.13704425]]\n",
      "MAE:  [[ 4.38541615]]\n",
      "Mean Ave. Corner Error:  6.87280602189\n"
     ]
    }
   ],
   "source": [
    "from keras.models import load_model\n",
    "\n",
    "#checkpoint\n",
    "checkpoint = \"checkpoints/weights-14-0.56.hdf5\"\n",
    "\n",
    "# load model\n",
    "print('Loading model... ', checkpoint)\n",
    "model = load_model(checkpoint, custom_objects={'euclidean_l2': euclidean_l2})\n",
    "\n",
    "for idx in range(10):\n",
    "    print('SAMPLE ', idx)\n",
    "    sample_image = images[idx];\n",
    "    sample_shape = sample_image.shape\n",
    "    sample_image = sample_image.reshape(1, 128, 128, 2)\n",
    "    sample_offset = offsets[idx];\n",
    "    print('Sample Offset: ', sample_offset)\n",
    "    norm_sample_image = (sample_image - 127.5) / 127.5\n",
    "    norm_sample_offset = sample_offset / 32.\n",
    "    print('Normalize Sample Offset: ', norm_sample_offset)\n",
    "\n",
    "    print('Predicting Offset...')\n",
    "    norm_pred_offset = model.predict(norm_sample_image)\n",
    "    print('Predicted Offset(Normalize): ', norm_pred_offset)\n",
    "    pred_offset = norm_pred_offset * 32.\n",
    "    print('Predicted Offset: ', pred_offset)\n",
    "    rmse = np.sqrt(np.sum(np.square(norm_pred_offset - norm_sample_offset),axis=-1,keepdims=True))\n",
    "    print('Normalize RMSE: ', rmse)\n",
    "    norm_mse = np.mean(np.square(norm_pred_offset - norm_sample_offset), axis=-1, keepdims=True)\n",
    "    print('Normalize MSE: ', norm_mse)\n",
    "    mse = np.mean(np.square(pred_offset - sample_offset), axis=-1, keepdims=True)\n",
    "    print('MSE: ', mse)\n",
    "    norm_mae = np.mean(np.absolute(norm_pred_offset - norm_sample_offset), axis=-1, keepdims=True)\n",
    "    print('Normalize MAE: ', norm_mae)\n",
    "    mae = np.mean(np.absolute(pred_offset - sample_offset), axis=-1, keepdims=True)\n",
    "    print('MAE: ', mae)\n",
    "    sum = 0\n",
    "    for i in range(0, len(sample_offset),2):\n",
    "        h = np.square(pred_offset[0][i] - sample_offset[i]) + np.square(pred_offset[0][i+1] - sample_offset[i+1])\n",
    "        h = np.sqrt(h)\n",
    "        #print('h: ', h)\n",
    "        sum = sum + h\n",
    "    mace = sum / (len(sample_offset) / 2)\n",
    "    print('Mean Ave. Corner Error: ', mace)\n"
   ]
  }
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