


'''simple docstring'''



import cva
import numpy as np

from digital_image_processing.filters.convolve import img_convolve
from digital_image_processing.filters.sobel_filter import sobel_filter

__lowercase			:		Union[str, Any] =			1_80






def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     List[str]		,   _SCREAMING_SNAKE_CASE   :     Union[str, Any]     ):
					__a    : str      					=						k_size // 2
					__a    : str      					=						np.mgrid[0 - center : k_size - center, 0 - center : k_size - center]
					__a    : Any      					=						(
					    1
					    / (2 * np.pi * sigma)
					    * np.exp(-(np.square(_SCREAMING_SNAKE_CASE     ) + np.square(_SCREAMING_SNAKE_CASE     )) / (2 * np.square(_SCREAMING_SNAKE_CASE     ))     )
					)
					return g






def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     Optional[int]		,   _SCREAMING_SNAKE_CASE   :     List[str]		,   _SCREAMING_SNAKE_CASE   :     Any     ):
					__a    : List[Any]      					=						np.zeros(_SCREAMING_SNAKE_CASE     )

					for row in range(1		,   image_shape[0] - 1     ):
										for col in range(1		,   image_shape[1] - 1     ):
															__a    : int      					=						gradient_direction[row, col]

															if (
															    0 <= direction < PI / 8
															    or 15 * PI / 8 <= direction <= 2 * PI
															    or 7 * PI / 8 <= direction <= 9 * PI / 8
															):
																				__a    : int      					=						sobel_grad[row, col - 1]
																				__a    : int      					=						sobel_grad[row, col + 1]
																				if sobel_grad[row, col] >= w and sobel_grad[row, col] >= e:
																									__a    : List[str]      					=						sobel_grad[row, col]

															elif (
															    PI / 8 <= direction < 3 * PI / 8
															    or 9 * PI / 8 <= direction < 11 * PI / 8
															):
																				__a    : Optional[int]      					=						sobel_grad[row + 1, col - 1]
																				__a    : Optional[int]      					=						sobel_grad[row - 1, col + 1]
																				if sobel_grad[row, col] >= sw and sobel_grad[row, col] >= ne:
																									__a    : int      					=						sobel_grad[row, col]

															elif (
															    3 * PI / 8 <= direction < 5 * PI / 8
															    or 11 * PI / 8 <= direction < 13 * PI / 8
															):
																				__a    : List[str]      					=						sobel_grad[row - 1, col]
																				__a    : str      					=						sobel_grad[row + 1, col]
																				if sobel_grad[row, col] >= n and sobel_grad[row, col] >= s:
																									__a    : Optional[Any]      					=						sobel_grad[row, col]

															elif (
															    5 * PI / 8 <= direction < 7 * PI / 8
															    or 13 * PI / 8 <= direction < 15 * PI / 8
															):
																				__a    : Dict      					=						sobel_grad[row - 1, col - 1]
																				__a    : str      					=						sobel_grad[row + 1, col + 1]
																				if sobel_grad[row, col] >= nw and sobel_grad[row, col] >= se:
																									__a    : List[str]      					=						sobel_grad[row, col]

					return destination






def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     int		,   _SCREAMING_SNAKE_CASE   :     Dict		,   _SCREAMING_SNAKE_CASE   :     Tuple		,   _SCREAMING_SNAKE_CASE   :     Dict		,   _SCREAMING_SNAKE_CASE   :     Dict		,   _SCREAMING_SNAKE_CASE   :     Any     ):
					for row in range(1		,   image_shape[0] - 1     ):
										for col in range(1		,   image_shape[1] - 1     ):
															if destination[row, col] >= threshold_high:
																				__a    : Tuple      					=						strong
															elif destination[row, col] <= threshold_low:
																				__a    : Optional[Any]      					=						0
															else:
																				__a    : int      					=						weak






def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     Union[str, Any]		,   _SCREAMING_SNAKE_CASE   :     Union[str, Any]		,   _SCREAMING_SNAKE_CASE   :     Optional[int]		,   _SCREAMING_SNAKE_CASE   :     str     ):
					for row in range(1		,   image_shape[0]     ):
										for col in range(1		,   image_shape[1]     ):
															if destination[row, col] == weak:
																				if 255 in (
																				    destination[row, col + 1],
																				    destination[row, col - 1],
																				    destination[row - 1, col],
																				    destination[row + 1, col],
																				    destination[row - 1, col - 1],
																				    destination[row + 1, col - 1],
																				    destination[row - 1, col + 1],
																				    destination[row + 1, col + 1],
																				):
																									__a    : List[Any]      					=						strong
																				else:
																									__a    : Optional[Any]      					=						0






def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     Optional[int]		,   _SCREAMING_SNAKE_CASE   :     List[Any]=15		,   _SCREAMING_SNAKE_CASE   :     List[Any]=30		,   _SCREAMING_SNAKE_CASE   :     List[str]=128		,   _SCREAMING_SNAKE_CASE   :     str=255     ):
					# gaussian_filter
					__a    : List[str]      					=						img_convolve(_SCREAMING_SNAKE_CASE		,   gen_gaussian_kernel(9		,   sigma=1.4     )     )
					# get the gradient and degree by sobel_filter
					__a    : Union[str, Any]      					=						sobel_filter(_SCREAMING_SNAKE_CASE     )
					__a    : Tuple      					=						PI + np.radadeg(_SCREAMING_SNAKE_CASE     )

					__a    : Tuple      					=						suppress_non_maximum(image.shape		,   _SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE     )

					detect_high_low_threshold(
					    image.shape		,   _SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE     )

					track_edge(image.shape		,   _SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE     )

					return destination


if __name__ == "__main__":
							# read original image in gray mode
							__lowercase			:		List[str] =			cva.imread(R'../image_data/lena.jpg', 0)
							# canny edge detection
							__lowercase			:		int =			canny(lena)
							cva.imshow('canny', canny_destination)
							cva.waitKey(0)







'''simple docstring'''



import itertools






def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     int = 1_000_000     ):
					__a    : str      					=						[1]

					for i in itertools.count(len(_SCREAMING_SNAKE_CASE     )     ):
										__a    : Dict      					=						0
										for j in itertools.count(1     ):
															__a    : int      					=						-1 if j % 2 == 0 else +1
															__a    : Optional[int]      					=						(j * j * 3 - j) // 2
															if index > i:
																				break
															item += partitions[i - index] * sign
															item %= number
															index += j
															if index > i:
																				break
															item += partitions[i - index] * sign
															item %= number

										if item == 0:
															return i
										partitions.append(_SCREAMING_SNAKE_CASE     )

					return 0


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	print(f'''{solution() = }''')



