






"""simple docstring"""





from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve






def 							A(    snake_case_		,  snake_case_		,  snake_case_						):
       """simple docstring"""





       lowercase__:							List[Any]         =     np.stack((horizontal_flow, vertical_flow)		,  2						)

       # Create a grid of all pixel coordinates and subtract the flow to get the
       # target pixels coordinates
       lowercase__:							Union[str, Any]         =     np.stack(
           np.meshgrid(np.arange(0		,  image.shape[1]						)		,  np.arange(0		,  image.shape[0]						)						)		,  2						)
       lowercase__:							Dict         =     np.round(grid - flow						).astype(np.intaa						)

       # Find the locations outside of the original image
       lowercase__:							Optional[int]         =     (grid < 0) | (grid >= np.array([image.shape[1], image.shape[0]]						))
       lowercase__:							List[Any]         =     0

       lowercase__:							int         =     image[grid[:, :, 1], grid[:, :, 0]]

       # Set pixels at invalid locations to 0
       lowercase__:							Tuple         =     0

       return warped






def 							A(    snake_case_		,  snake_case_		,  snake_case_		,  snake_case_ = None		,  ):
       """simple docstring"""





       if alpha is None:
              lowercase__:							Optional[int]         =     0.1

       # Initialize flow
       lowercase__:							Union[str, Any]         =     np.zeros_like(snake_case_						)
       lowercase__:							List[Any]         =     np.zeros_like(snake_case_						)

       # Prepare kernels for the calculation of the derivatives and the average velocity
       lowercase__:							int         =     np.array([[-1, 1], [-1, 1]]						) * 0.25
       lowercase__:							Tuple         =     np.array([[-1, -1], [1, 1]]						) * 0.25
       lowercase__:							Dict         =     np.array([[1, 1], [1, 1]]						) * 0.25
       lowercase__:							List[str]         =     np.array(
           [[1 / 12, 1 / 6, 1 / 12], [1 / 6, 0, 1 / 6], [1 / 12, 1 / 6, 1 / 12]]						)

       # Iteratively refine the flow
       for _ in range(snake_case_						):
              lowercase__:							Any         =     warp(snake_case_		,  snake_case_		,  snake_case_						)
              lowercase__:							Dict         =     convolve(snake_case_		,  snake_case_						) + convolve(snake_case_		,  snake_case_						)
              lowercase__:							Any         =     convolve(snake_case_		,  snake_case_						) + convolve(snake_case_		,  snake_case_						)
              lowercase__:							Dict         =     convolve(snake_case_		,  snake_case_						) + convolve(snake_case_		,  -kernel_t						)

              lowercase__:							str         =     convolve(snake_case_		,  snake_case_						)
              lowercase__:							List[Any]         =     convolve(snake_case_		,  snake_case_						)

              # This updates the flow as proposed in the paper (Step 12)
              lowercase__:							Optional[Any]         =     (
                  derivative_x * avg_horizontal_velocity
                  + derivative_y * avg_vertical_velocity
                  + derivative_t
              )
              lowercase__:							Any         =     update / (alpha**2 + derivative_x**2 + derivative_y**2)

              lowercase__:							Optional[int]         =     avg_horizontal_velocity - derivative_x * update
              lowercase__:							List[str]         =     avg_vertical_velocity - derivative_y * update

       return horizontal_flow, vertical_flow


if __name__ == "__main__":
  import doctest

  doctest.testmod()














"""simple docstring"""





from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import divide, inta, multiply, ravel, sort, zeros_like






def 							A(    snake_case_		,  snake_case_=3						):
       """simple docstring"""





       lowercase__:							Tuple         =     int(mask / 2						)
       # copy image size
       lowercase__:							str         =     zeros_like(snake_case_						)
       for i in range(snake_case_		,  gray_img.shape[0] - bd						):
              for j in range(snake_case_		,  gray_img.shape[1] - bd						):
                     # get mask according with mask
                     lowercase__:							Optional[int]         =     ravel(gray_img[i - bd : i + bd + 1, j - bd : j + bd + 1]						)
                     # calculate mask median
                     lowercase__:							Union[str, Any]         =     sort(snake_case_						)[inta(divide((multiply(snake_case_		,  snake_case_						))		,  2						) + 1						)]
                     lowercase__:							Optional[Any]         =     median
       return median_img


if __name__ == "__main__":
  # read original image
  UpperCamelCase					=     imread("""../image_data/lena.jpg""")
  # turn image in gray scale value
  UpperCamelCase					=     cvtColor(img, COLOR_BGR2GRAY)

  # get values with two different mask size
  UpperCamelCase					=     median_filter(gray, 3)
  UpperCamelCase					=     median_filter(gray, 5)

  # show result images
  imshow("""median filter with 3x3 mask""", medianaxa)
  imshow("""median filter with 5x5 mask""", medianaxa)
  waitKey(0)






