notebooks/visualize_geometric_features.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import cv2\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.ndimage import binary_fill_holes\n",
    "from scipy.special import ellipe\n",
    "from PIL import Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Specify path to nucleus segmentation mask\n",
    "nucleus_seg_path = \"/deep/group/aihc-bootcamp-winter2020/dlbcl/DLBCL-Morph/Cells/13901/1064/14.npy\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load and visualize nucleus segmentation mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = np.load(nucleus_seg_path)\n",
    "#zero padding for clarity of visualization. The features in Cells/cell_shapes.csv are computed\n",
    "#without zero-padding, so you can comment out the next line of code to reproduce those numbers\n",
    "img = np.pad(img, 5) \n",
    "img = binary_fill_holes(img) #fill holes that sometimes appear inside the segmentation mask\n",
    "\n",
    "mask = img.copy()\n",
    "img = img.astype(np.uint8)\n",
    "img[mask] = 255\n",
    "plt.imshow(img, cmap='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ret, thresh = cv2.threshold(img,127,255,0)\n",
    "contours, hierarchy = cv2.findContours(thresh, 1, 2)\n",
    "cnt = contours[0]\n",
    "\n",
    "plt.imshow(thresh, cmap='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit rectangle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rectangle center: (23.749998092651367, 22.25)\n",
      "Rectangle width: 37.314869, height: 31.306545\n",
      "Rectangle rotation angle: -18.43494987487793\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rect = cv2.minAreaRect(cnt)\n",
    "(rectCoord1, rectCoord2, rotate_angle) = rect\n",
    "box = cv2.boxPoints(rect)\n",
    "box = np.int0(box)\n",
    "\n",
    "rgb_img = cv2.cvtColor(img, cv2.COLOR_GRAY2RGB)\n",
    "cv2.drawContours(rgb_img,[box],0,(0,0,255),1)\n",
    "plt.imshow(rgb_img)\n",
    "\n",
    "print(\"Rectangle center:\", rect[0])\n",
    "print(\"Rectangle width: %.6f, height: %.6f\" % (rect[1][0], rect[1][1]))\n",
    "print(\"Rectangle rotation angle:\", rect[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit ellipse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7faa455f3150>"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rgb_img = cv2.cvtColor(img, cv2.COLOR_GRAY2RGB)\n",
    "\n",
    "ellipse = cv2.fitEllipseDirect(cnt)  #(x, y), (major, minor), angle                                                            \n",
    "ell = cv2.ellipse(rgb_img,ellipse,(0,255,0),1)\n",
    "(ellpCtr_x, ellpCtr_y), (shortAxis, longAxis), angle = ellipse\n",
    "plt.imshow(rgb_img)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "# perimeter and area of ellipse                                                                                                            \n",
    "a = longAxis / 2\n",
    "b = shortAxis / 2\n",
    "e = np.sqrt(1 - b**2 / a**2)  # eccentricity                                                                                       \n",
    "perimt = 4 * a * ellipe(e*e)\n",
    "area = np.pi * a * b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ellipse centroid: (24.271310806274414, 21.33393669128418)\n",
      "Major axis (longAxis) length: 37.061234\n",
      "Minor axis (shortAxis) length: 30.641516\n",
      "Ellipse parimeter: 106.586413\n",
      "Ellipse area: 891.907870\n"
     ]
    }
   ],
   "source": [
    "print(\"Ellipse centroid:\", (ellpCtr_x, ellpCtr_y))\n",
    "print(\"Major axis (longAxis) length: %.6f\" % longAxis)\n",
    "print(\"Minor axis (shortAxis) length: %.6f\" % shortAxis)\n",
    "print(\"Ellipse parimeter: %.6f\" % perimt)\n",
    "print(\"Ellipse area: %.6f\" % area)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Convex hull area"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Convex hull area: 922.000000\n"
     ]
    }
   ],
   "source": [
    "hull = cv2.convexHull(cnt)\n",
    "hull_area = cv2.contourArea(hull)\n",
    "print(\"Convex hull area: %.6f\" % hull_area)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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