text: #importing some useful packages
  import cv2
  import matplotlib
  import numpy as np
  import matplotlib.image as mpimg
  import matplotlib.pyplot as plt
  import math
  
  def grayscale(img):
      """Applies the Grayscale transform
      This will return an image with only one color channel
      but NOTE: to see the returned image as grayscale
      (assuming your grayscaled image is called 'gray')
      you should call plt.imshow(gray, cmap='gray')"""
      return cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
  
  def canny(img, low_threshold, high_threshold):
      """Applies the Canny transform"""
      return cv2.Canny(img, low_threshold, high_threshold)
  
  def gaussian_blur(img, kernel_size):
      """Applies a Gaussian Noise kernel"""
      return cv2.GaussianBlur(img, (kernel_size, kernel_size), 0)
  
  def region_of_interest(img, vertices):
      """
      Applies an image mask.
  
      Only keeps the region of the image defined by the polygon
      formed from `vertices`. The rest of the image is set to black.
      """
      #defining a blank mask to start with
      mask = np.zeros_like(img)
  
      #defining a 3 channel or 1 channel color to fill the mask with depending on the input image
      if len(img.shape) > 2:
          channel_count = img.shape[2]  # i.e. 3 or 4 depending on your image
          ignore_mask_color = (255,) * channel_count
      else:
          ignore_mask_color = 255
  
      #filling pixels inside the polygon defined by "vertices" with the fill color
      cv2.fillPoly(mask, vertices, ignore_mask_color)
  
      #returning the image only where mask pixels are nonzero
      masked_image = cv2.bitwise_and(img, mask)
      return masked_image
  
  
  def draw_lines(img, lines, color=[255, 0, 0], thickness=3):
      """
      NOTE: this is the function you might want to use as a starting point once you want to
      average/extrapolate the line segments you detect to map out the full
      extent of the lane (going from the result shown in raw-lines-example.mp4
      to that shown in P1_example.mp4).
  
      Think about things like separating line segments by their
      slope ((y2-y1)/(x2-x1)) to decide which segments are part of the left
      line vs. the right line.  Then, you can average the position of each of
      the lines and extrapolate to the top and bottom of the lane.
  
      This function draws `lines` with `color` and `thickness`.
      Lines are drawn on the image inplace (mutates the image).
      If you want to make the lines semi-transparent, think about combining
      this function with the weighted_img() function below
      """
      for line in lines:
          for x1,y1,x2,y2 in line:
              cv2.line(img, (x1, y1), (x2, y2), color, thickness)
  
  def hough_lines(img, rho, theta, threshold, min_line_len, max_line_gap):
      """
      `img` should be the output of a Canny transform.
  
      Returns an image with hough lines drawn.
      """
      lines = cv2.HoughLinesP(img, rho, theta, threshold, np.array([]), minLineLength=min_line_len, maxLineGap=max_line_gap)
      line_img = np.zeros((img.shape[0], img.shape[1], 3), dtype=np.uint8)
      draw_lines(line_img, lines)
      return line_img
  
  # Python 3 has support for cool math symbols.
  
  def weighted_img(img, initial_img, α=0.8, β=1., λ=0.):
      """
      `img` is the output of the hough_lines(), An image with lines drawn on it.
      Should be a blank image (all black) with lines drawn on it.
  
      `initial_img` should be the image before any processing.
  
      The result image is computed as follows:
  
      initial_img * α + img * β + λ
      NOTE: initial_img and img must be the same shape!
      """
      return cv2.addWeighted(initial_img, α, img, β, λ)
  