





from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve






def   lowerCamelCase_		(       _UpperCamelCase				,       _UpperCamelCase				,       _UpperCamelCase				)	->		np.ndarray:






    """simple docstring"""


    snake_case_		:					List[str]			    =						np.stack((horizontal_flow, vertical_flow)				,       2				)

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

    # Find the locations outside of the original image
    snake_case_		:					Tuple			    =						(grid < 0) | (grid >= np.array([image.shape[1], image.shape[0]]				))
    snake_case_		:					str			    =						0

    snake_case_		:					str			    =						image[grid[:, :, 1], grid[:, :, 0]]

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

    return warped






def   lowerCamelCase_		(       _UpperCamelCase				,       _UpperCamelCase				,       _UpperCamelCase				,       _UpperCamelCase = None				,       )	->		tuple[np.ndarray, np.ndarray]:






    """simple docstring"""


    if alpha is None:
        snake_case_		:					Optional[Any]			    =						0.1

    # Initialize flow
    snake_case_		:					Dict			    =						np.zeros_like(_UpperCamelCase				)
    snake_case_		:					Any			    =						np.zeros_like(_UpperCamelCase				)

    # Prepare kernels for the calculation of the derivatives and the average velocity
    snake_case_		:					str			    =						np.array([[-1, 1], [-1, 1]]				) * 0.25
    snake_case_		:					Union[str, Any]			    =						np.array([[-1, -1], [1, 1]]				) * 0.25
    snake_case_		:					Tuple			    =						np.array([[1, 1], [1, 1]]				) * 0.25
    snake_case_		:					int			    =						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(_UpperCamelCase				):
        snake_case_		:					Optional[int]			    =						warp(_UpperCamelCase				,       _UpperCamelCase				,       _UpperCamelCase				)
        snake_case_		:					Union[str, Any]			    =						convolve(_UpperCamelCase				,       _UpperCamelCase				) + convolve(_UpperCamelCase				,       _UpperCamelCase				)
        snake_case_		:					Optional[Any]			    =						convolve(_UpperCamelCase				,       _UpperCamelCase				) + convolve(_UpperCamelCase				,       _UpperCamelCase				)
        snake_case_		:					List[str]			    =						convolve(_UpperCamelCase				,       _UpperCamelCase				) + convolve(_UpperCamelCase				,       -kernel_t				)

        snake_case_		:					Dict			    =						convolve(_UpperCamelCase				,       _UpperCamelCase				)
        snake_case_		:					Optional[int]			    =						convolve(_UpperCamelCase				,       _UpperCamelCase				)

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

        snake_case_		:					Union[str, Any]			    =						avg_horizontal_velocity - derivative_x * update
        snake_case_		:					Tuple			    =						avg_vertical_velocity - derivative_y * update

    return horizontal_flow, vertical_flow


if __name__ == "__main__":
 import doctest

 doctest.testmod()







class       __lowerCAmelCase :






			def __init__(self					)  ->     Dict:


							'''simple docstring'''



							snake_case_		:					Union[str, Any]			    =						[]
							snake_case_		:					Any			    =						0
							snake_case_		:					Optional[int]			    =						0






			def __str__(self					)  ->     Dict:


							'''simple docstring'''



							snake_case_		:					int			    =						'''<''' + str(self.entries					)[1:-1] + '''>'''
							return printed






			def     lowerCamelCase						(self      ,							__magic_name__					)  ->     Dict:


							'''simple docstring'''



							self.entries.append(__magic_name__					)
							snake_case_		:					List[str]			    =						self.length + 1






			def     lowerCamelCase						(self					)  ->     Tuple:


							'''simple docstring'''



							snake_case_		:					Union[str, Any]			    =						self.length - 1
							snake_case_		:					Dict			    =						self.entries[self.front]
							# self.front-=1
							# self.entries = self.entries[self.front:]
							snake_case_		:					List[str]			    =						self.entries[1:]
							return dequeued






			def     lowerCamelCase						(self      ,							__magic_name__					)  ->     Optional[Any]:


							'''simple docstring'''



							for _ in range(__magic_name__					):
											self.put(self.get()					)






			def     lowerCamelCase						(self					)  ->     Optional[Any]:


							'''simple docstring'''



							return self.entries[0]






			def     lowerCamelCase						(self					)  ->     Union[str, Any]:


							'''simple docstring'''



							return self.length
