
'''simple docstring'''

from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve







def 						snake_case__	(      UpperCamelCase			,UpperCamelCase			,UpperCamelCase	) ->      np.ndarray:
		_UpperCamelCase       : Dict    =      np.stack((horizontal_flow, vertical_flow)			,2	)

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

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

		_UpperCamelCase       : Union[str, Any]    =      image[grid[:, :, 1], grid[:, :, 0]]

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

		return warped







def 						snake_case__	(      UpperCamelCase			,UpperCamelCase			,UpperCamelCase			,UpperCamelCase = None			,) ->      tuple[np.ndarray, np.ndarray]:
		if alpha is None:
				_UpperCamelCase       : Optional[int]    =      0.1

		# Initialize flow
		_UpperCamelCase       : Tuple    =      np.zeros_like(UpperCamelCase	)
		_UpperCamelCase       : Union[str, Any]    =      np.zeros_like(UpperCamelCase	)

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

				_UpperCamelCase       : int    =      convolve(UpperCamelCase			,UpperCamelCase	)
				_UpperCamelCase       : str    =      convolve(UpperCamelCase			,UpperCamelCase	)

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

				_UpperCamelCase       : int    =      avg_horizontal_velocity - derivative_x * update
				_UpperCamelCase       : int    =      avg_vertical_velocity - derivative_y * update

		return horizontal_flow, vertical_flow


if __name__ == "__main__":
	import doctest

	doctest.testmod()







'''simple docstring'''

from __future__ import annotations

from collections.abc import Iterable
from dataclasses import dataclass
from typing import Any

class 			UpperCAmelCase				:





		"""simple docstring"""





		A__  :   List[str]          =    ('_front', '_back', '_len')

		@dataclass
		class 			UpperCAmelCase				:





				"""simple docstring"""





				A__  :   Any          =    None
				A__  :   Deque._Node | None          =    None
				A__  :   Deque._Node | None          =    None







		class 			UpperCAmelCase				:





				"""simple docstring"""





				A__  :   Any          =    ('_cur',)
				def __init__(    self  ,					_snake_case     )				->    None:
						_UpperCamelCase       : Any    =      cur
				def __iter__(    self     )				->    Deque._Iterator:
						return self




				def _lowercase  (    self     )				->    Any:
						if self._cur is None:
								# finished iterating
								raise StopIteration
						_UpperCamelCase       : List[Any]    =      self._cur.val
						_UpperCamelCase       : List[Any]    =      self._cur.next_node

						return val







		def __init__(    self  ,					_snake_case = None     )				->    None:
				_UpperCamelCase       : Any    =      None
				_UpperCamelCase       : Any    =      None
				_UpperCamelCase       : int    =      0

				if iterable is not None:
						# append every value to the deque
						for val in iterable:
								self.append(_snake_case     )
		def _lowercase  (    self  ,					_snake_case     )				->    None:
				_UpperCamelCase       : List[str]    =      self._Node(_snake_case  ,					_snake_case  ,					_snake_case     )
				if self.is_empty():
						# front = back
						_UpperCamelCase       : Union[str, Any]    =      node
						_UpperCamelCase       : Tuple    =      1
				else:
						# connect nodes
						_UpperCamelCase       : Union[str, Any]    =      node
						_UpperCamelCase       : int    =      self._back
						_UpperCamelCase       : List[Any]    =      node  # assign new back to the new node

						self._len += 1

						# make sure there were no errors
						assert not self.is_empty(), "Error on appending value."
		def _lowercase  (    self  ,					_snake_case     )				->    None:
				_UpperCamelCase       : Optional[Any]    =      self._Node(_snake_case  ,					_snake_case  ,					_snake_case     )
				if self.is_empty():
						# front = back
						_UpperCamelCase       : Union[str, Any]    =      node
						_UpperCamelCase       : Optional[int]    =      1
				else:
						# connect nodes
						_UpperCamelCase       : Tuple    =      self._front
						_UpperCamelCase       : Optional[int]    =      node
						_UpperCamelCase       : List[str]    =      node  # assign new front to the new node

						self._len += 1

						# make sure there were no errors
						assert not self.is_empty(), "Error on appending value."
		def _lowercase  (    self  ,					_snake_case     )				->    None:
				for val in iterable:
						self.append(_snake_case     )
		def _lowercase  (    self  ,					_snake_case     )				->    None:
				for val in iterable:
						self.appendleft(_snake_case     )
		def _lowercase  (    self     )				->    Any:
				assert not self.is_empty(), "Deque is empty."

				_UpperCamelCase       : int    =      self._back
				_UpperCamelCase       : List[Any]    =      self._back.prev_node  # set new back
				# drop the last node - python will deallocate memory automatically
				_UpperCamelCase       : Union[str, Any]    =      None

				self._len -= 1

				return topop.val
		def _lowercase  (    self     )				->    Any:
				assert not self.is_empty(), "Deque is empty."

				_UpperCamelCase       : List[Any]    =      self._front
				_UpperCamelCase       : str    =      self._front.next_node  # set new front and drop the first node
				_UpperCamelCase       : Union[str, Any]    =      None

				self._len -= 1

				return topop.val
		def _lowercase  (    self     )				->    bool:
				return self._front is None
		def __len__(    self     )				->    int:
				return self._len
		def __eq__(    self  ,					_snake_case     )				->    bool:

				if not isinstance(_snake_case  ,					_snake_case     ):
						return NotImplemented

				_UpperCamelCase       : Optional[int]    =      self._front
				_UpperCamelCase       : List[Any]    =      other._front

				# if the length of the dequeues are not the same, they are not equal
				if len(self     ) != len(_snake_case     ):
						return False

				while me is not None and oth is not None:
						# compare every value
						if me.val != oth.val:
								return False
						_UpperCamelCase       : str    =      me.next_node
						_UpperCamelCase       : List[str]    =      oth.next_node

				return True
		def __iter__(    self     )				->    Deque._Iterator:
				return Deque._Iterator(self._front     )




		def __repr__(    self     )				->    str:
				_UpperCamelCase       : str    =      []
				_UpperCamelCase       : Tuple    =      self._front
				while aux is not None:
						# append the values in a list to display
						values_list.append(aux.val     )
						_UpperCamelCase       : List[str]    =      aux.next_node

				return F'''[{', '.join(repr(_snake_case     ) for val in values_list     )}]'''


if __name__ == "__main__":
	import doctest

	doctest.testmod()





