1-4-Hugh_transform.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In image space, a line is plotted as x vs. y, but in 1962, Paul Hough devised a method for representing lines in parameter space, which we will call “Hough space” in his honor.\n",
    "\n",
    "In Hough space, I can represent my \"x vs. y\" line as a point in \"m vs. b\" instead. The Hough Transform is just the conversion from image space to Hough space. So, the characterization of a line in image space will be a single point at the position (m, b) in Hough space. \n",
    "\n",
    "Alright, so a line in image space corresponds to a point in Hough space. What does a point in image space correspond to in Hough space?\n",
    "\n",
    "A single point in image space has many possible lines that pass through it, but not just any lines, only those with particular combinations of the m and b parameters. Rearranging the equation of a line, we find that a single point (x,y) corresponds to the line b = y - xm.\n",
    "\n",
    "So what is the representation of a point in image space in Hough space?\n",
    "\n",
    "Alright, now we have two intersecting lines in Hough Space. How would you represent their intersection at the point (m0, b0) in image space?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f12eb519ba8>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f132e176978>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.image as mpimg\n",
    "import numpy as np\n",
    "import cv2\n",
    "\n",
    "\n",
    "# Read in and grayscale the image\n",
    "image = mpimg.imread('test_images/solidWhiteCurve.jpg')\n",
    "gray = cv2.cvtColor(image,cv2.COLOR_RGB2GRAY)\n",
    "\n",
    "# Define a kernel size and apply Gaussian smoothing\n",
    "kernel_size = 5\n",
    "blur_gray = cv2.GaussianBlur(gray,(kernel_size, kernel_size),0)\n",
    "\n",
    "# Define our parameters for Canny and apply\n",
    "low_threshold = 50\n",
    "high_threshold = 150\n",
    "edges = cv2.Canny(blur_gray, low_threshold, high_threshold)\n",
    "\n",
    "# Next we'll create a masked edges image using cv2.fillPoly()\n",
    "mask = np.zeros_like(edges)   \n",
    "ignore_mask_color = 255   \n",
    "\n",
    "# This time we are defining a four sided polygon to mask\n",
    "imshape = image.shape\n",
    "vertices = np.array([[(0,imshape[0]),(450, 300), (imshape[1]-450, 300), (imshape[1],imshape[0])]], dtype=np.int32)\n",
    "cv2.fillPoly(mask, vertices, ignore_mask_color)\n",
    "masked_edges = cv2.bitwise_and(edges, mask)\n",
    "\n",
    "# Define the Hough transform parameters\n",
    "# Make a blank the same size as our image to draw on\n",
    "rho = 2 # distance resolution in pixels of the Hough grid\n",
    "theta = np.pi/180 # angular resolution in radians of the Hough grid\n",
    "threshold = 15     # minimum number of votes (intersections in Hough grid cell)\n",
    "min_line_length = 40 #minimum number of pixels making up a line\n",
    "max_line_gap = 20   # maximum gap in pixels between connectable line segments\n",
    "line_image = np.copy(image)*0 # creating a blank to draw lines on\n",
    "\n",
    "# Run Hough on edge detected image\n",
    "# Output \"lines\" is an array containing endpoints of detected line segments\n",
    "lines = cv2.HoughLinesP(masked_edges, rho, theta, threshold, np.array([]),\n",
    "                            min_line_length, max_line_gap)\n",
    "\n",
    "# Iterate over the output \"lines\" and draw lines on a blank image\n",
    "for line in lines:\n",
    "    for x1,y1,x2,y2 in line:\n",
    "        cv2.line(line_image,(x1,y1),(x2,y2),(255,0,0),10)\n",
    "\n",
    "# Create a \"color\" binary image to combine with line image\n",
    "color_edges = np.dstack((edges, edges, edges)) \n",
    "\n",
    "# Draw the lines on the edge image\n",
    "lines_edges = cv2.addWeighted(color_edges, 0.8, line_image, 1, 0) \n",
    "plt.imshow(lines_edges)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
   "name": "python3"
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