{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import skimage.transform\n",
    "import scipy\n",
    "from scipy import ndimage\n",
    "import matplotlib.pyplot as plt\n",
    "from skimage.morphology import medial_axis, watershed\n",
    "create_dist_map = lambda img, mask=None: medial_axis(img,mask, return_distance = True)[1]\n",
    "import os\n",
    "from skimage.measure import block_reduce\n",
    "plt_settings = {'interpolation':'none'}\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Distance Maps\n",
    "Here we calculate distance maps with the ```ndimage.distance_transform_``` family of functions. Initially we focus on test images since it is easier to see what is happening with these images."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_dot_image(size = 100, cutoff = 0.15):\n",
    "    \"\"\"\n",
    "    Create a simple  synthetic image with a repeating pattern\n",
    "    Keyword arguments:\n",
    "    size -- the size of the image on one size, final size is size x size (default 100)\n",
    "    imag -- the cutoff between 0 and 1, higher means less connected objects (default 0.15)\n",
    "    \"\"\"\n",
    "    xx,yy = np.meshgrid(range(size),range(size))\n",
    "    return np.sin(6*np.pi*xx/(100)-1)+1.25*np.cos(5*np.pi*yy/(100)-2)>cutoff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x113d8bac8>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "img_bw = generate_dot_image(28,0.50)\n",
    "plt.imshow(img_bw,cmap='gray', **plt_settings)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x113e9c588>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "img_dist = ndimage.distance_transform_edt(img_bw)\n",
    "plt.imshow(img_dist, **plt_settings)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing \n",
    "There are a number of different methods for ```distance_transform``` inside the ```ndimage``` package of ```scipy``` compare the results of the different approaches for this and other images.\n",
    "- What are the main differences?\n",
    "- Quantitatively (histogram) show what situations each one might be best suited for?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Distance\\n(px)')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 2160x720 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "# calculate new distance transforms\n",
    "img_dist = ndimage.distance_transform_edt(img_bw)\n",
    "img_dist_cityblock = ndimage.distance_transform_cdt(img_bw,metric = 'taxicab')\n",
    "img_dist_chess = ndimage.distance_transform_cdt(img_bw,metric = 'chessboard')\n",
    "\n",
    "fig, (ax1,ax2,ax3,ax4) = plt.subplots(1,4, figsize = (30,10))\n",
    "ax1.imshow(img_bw,cmap = 'gray', **plt_settings)\n",
    "ax1.set_title('Mask Image')\n",
    "dmap_im = ax2.imshow(img_dist,vmax = img_dist.max(), **plt_settings)\n",
    "ax2.set_title('Euclidean')\n",
    "ax3.imshow(img_dist_cityblock,vmax = img_dist.max(), **plt_settings)\n",
    "ax3.set_title('Cityblock')\n",
    "ax4.imshow(img_dist_chess,vmax = img_dist.max(), **plt_settings)\n",
    "ax4.set_title('Chess')\n",
    "fig.subplots_adjust(right=0.8)\n",
    "cbar_ax = fig.add_axes([0.85, 0.15, 0.05, 0.7])\n",
    "cbar = fig.colorbar(dmap_im,cax=cbar_ax)\n",
    "cbar_ax.set_title('Distance\\n(px)')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More Complicated Objects\n",
    "We now make the image bigger (changing the ```size``` parameter) and connect them together (the ```cutoff``` parameter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Distance\\n(px)')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2160x720 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "# use a bigger base image\n",
    "img_bw = generate_dot_image(100,0.15)\n",
    "img_dist = ndimage.distance_transform_edt(img_bw)\n",
    "img_dist_cityblock = ndimage.distance_transform_cdt(img_bw,metric = 'taxicab')\n",
    "img_dist_chess = ndimage.distance_transform_cdt(img_bw,metric = 'chessboard')\n",
    "\n",
    "fig, (ax1,ax2,ax3,ax4) = plt.subplots(1,4, figsize = (30,10))\n",
    "ax1.imshow(img_bw,cmap = 'gray', **plt_settings)\n",
    "ax1.set_title('Mask Image')\n",
    "dmap_im = ax2.imshow(img_dist,vmax = img_dist.max(), **plt_settings)\n",
    "ax2.set_title('Euclidean')\n",
    "ax3.imshow(img_dist_cityblock,vmax = img_dist.max(), **plt_settings)\n",
    "ax3.set_title('Cityblock')\n",
    "ax4.imshow(img_dist_chess,vmax = img_dist.max(), **plt_settings)\n",
    "ax4.set_title('Chess')\n",
    "fig.subplots_adjust(right=0.8)\n",
    "cbar_ax = fig.add_axes([0.85, 0.15, 0.05, 0.7])\n",
    "cbar = fig.colorbar(dmap_im,cax=cbar_ax)\n",
    "cbar_ax.set_title('Distance\\n(px)')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Watershed\n",
    "We can use the watershed transform to segment closely connected objects. We see in the first image that the standard connected component labeling ```ndimage.label``` shows only 3 when we see 9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Connected Component Analysis')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2160x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cc_img = ndimage.label(img_bw)[0]\n",
    "\n",
    "%matplotlib inline\n",
    "fig, (ax1,ax2) = plt.subplots(1,2, figsize = (30,10))\n",
    "ax1.imshow(img_bw,cmap = 'gray', **plt_settings)\n",
    "ax1.set_title('Mask Image')\n",
    "dmap_im = ax2.imshow(cc_img, **plt_settings)\n",
    "ax2.set_title('Connected Component Analysis');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from skimage.feature import peak_local_max\n",
    "def simple_watershed(img_dist, img_bw):\n",
    "    \"\"\"\n",
    "    Calculate the watershed transform on an image and its distance map \n",
    "    by finding the troughs and expanding from these points\n",
    "    \"\"\"\n",
    "    local_maxi = peak_local_max(img_dist, labels=img_bw,\n",
    "                                footprint=np.ones((3, 3)),\n",
    "                                indices=False)\n",
    "    markers = ndimage.label(local_maxi)[0]\n",
    "    return watershed(-img_dist,markers,mask = img_bw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Applying Watershed\n",
    "We can apply watershed to the following image. \n",
    "- Why do the bottom row of objects not show up?\n",
    "- How can the results be improved"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Watershed Analysis')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2160x720 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ws_img = simple_watershed(img_dist,img_bw)\n",
    "%matplotlib inline\n",
    "fig, (ax1,ax2,ax3) = plt.subplots(1,3, figsize = (30,10))\n",
    "ax1.imshow(img_bw,cmap = 'gray', **plt_settings)\n",
    "ax1.set_title('Mask Image')\n",
    "ax2.imshow(cc_img, **plt_settings)\n",
    "ax2.set_title('Connected Component Analysis')\n",
    "ax3.imshow(ws_img, **plt_settings)\n",
    "ax3.set_title('Watershed Analysis')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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