
from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)							->						List[str]:
			lowerCAmelCase__ : Optional[int]   =						np.stack((horizontal_flow, vertical_flow)			,				2	)

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

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

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

			# Set pixels at invalid locations to 0
			lowerCAmelCase__ : Union[str, Any]   =						0

			return warped
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_ = None			,				)							->						Optional[int]:
			if alpha is None:
						lowerCAmelCase__ : Optional[int]   =						0.1

			# Initialize flow
			lowerCAmelCase__ : Optional[Any]   =						np.zeros_like(UpperCAmelCase_	)
			lowerCAmelCase__ : List[str]   =						np.zeros_like(UpperCAmelCase_	)

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

						lowerCAmelCase__ : List[str]   =						convolve(UpperCAmelCase_			,				UpperCAmelCase_	)
						lowerCAmelCase__ : Dict   =						convolve(UpperCAmelCase_			,				UpperCAmelCase_	)

						# This updates the flow as proposed in the paper (Step 12)
						lowerCAmelCase__ : str   =						(
						    derivative_x * avg_horizontal_velocity
						    + derivative_y * avg_vertical_velocity
						    + derivative_t
						)
						lowerCAmelCase__ : Tuple   =						update / (alpha**2 + derivative_x**2 + derivative_y**2)

						lowerCAmelCase__ : Any   =						avg_horizontal_velocity - derivative_x * update
						lowerCAmelCase__ : Tuple   =						avg_vertical_velocity - derivative_y * update

			return horizontal_flow, vertical_flow


if __name__ == "__main__":
					import doctest

					doctest.testmod()





from __future__ import annotations

from typing import Generic, TypeVar

SCREAMING_SNAKE_CASE_    :       List[str]       =							TypeVar('''T''')







class 		__UpperCAmelCase(		lowercase__			):





     """simple docstring"""



     pass







class 		__UpperCAmelCase(		lowercase__			):





     """simple docstring"""



     pass







class 		__UpperCAmelCase(		Generic[T]			):





     """simple docstring"""



     def __init__(   self			:							str    ,					A			:							int = 10     )      ->      str:






         """simple docstring"""
         a__  			=							[]
         a__  			=							limit

     def __bool__(   self			:							Dict     )      ->      bool:






         """simple docstring"""
         return bool(self.stack     )

     def __str__(   self			:							str     )      ->      str:






         """simple docstring"""
         return str(self.stack     )

     def 					__SCREAMING_SNAKE_CASE		(   self			:							List[str]    ,					A			:							T     )      ->      None:






         """simple docstring"""
         if len(self.stack     ) >= self.limit:
             raise StackOverflowError
         self.stack.append(A     )

     def 					__SCREAMING_SNAKE_CASE		(   self			:							Any     )      ->      T:






         """simple docstring"""
         if not self.stack:
             raise StackUnderflowError
         return self.stack.pop()

     def 					__SCREAMING_SNAKE_CASE		(   self			:							Optional[int]     )      ->      T:






         """simple docstring"""
         if not self.stack:
             raise StackUnderflowError
         return self.stack[-1]

     def 					__SCREAMING_SNAKE_CASE		(   self			:							str     )      ->      bool:






         """simple docstring"""
         return not bool(self.stack     )

     def 					__SCREAMING_SNAKE_CASE		(   self			:							Dict     )      ->      bool:






         """simple docstring"""
         return self.size() == self.limit

     def 					__SCREAMING_SNAKE_CASE		(   self			:							int     )      ->      int:






         """simple docstring"""
         return len(self.stack     )






     def __contains__(   self			:							int    ,					A			:							T     )      ->      bool:






         """simple docstring"""
         return item in self.stack






def 							__lowerCAmelCase			():
    a__  			=							Stack(10		)
    assert bool(UpperCAmelCase_		) is False
    assert stack.is_empty() is True
    assert stack.is_full() is False
    assert str(UpperCAmelCase_		) == "[]"

    try:
        a__  			=							stack.pop()
        raise AssertionError  # This should not happen
    except StackUnderflowError:
        assert True  # This should happen

    try:
        a__  			=							stack.peek()
        raise AssertionError  # This should not happen
    except StackUnderflowError:
        assert True  # This should happen

    for i in range(10		):
        assert stack.size() == i
        stack.push(UpperCAmelCase_		)

    assert bool(UpperCAmelCase_		)
    assert not stack.is_empty()
    assert stack.is_full()
    assert str(UpperCAmelCase_		) == str(list(range(10		)		)		)
    assert stack.pop() == 9
    assert stack.peek() == 8

    stack.push(100		)
    assert str(UpperCAmelCase_		) == str([0, 1, 2, 3, 4, 5, 6, 7, 8, 100]		)

    try:
        stack.push(200		)
        raise AssertionError  # This should not happen
    except StackOverflowError:
        assert True  # This should happen

    assert not stack.is_empty()
    assert stack.size() == 10

    assert 5 in stack
    assert 55 not in stack


if __name__ == "__main__":
 test_stack()






