



def 	_UpperCAmelCase       (   snake_case    ):





					"""simple docstring"""

					_lowerCAmelCase      			=					[True for i in range(n + 1    )]
					_lowerCAmelCase      			=					[i - 1 for i in range(n + 1    )]
					_lowerCAmelCase      			=					[]
					for i in range(2			,		n + 1    ):
										if is_prime[i]:
															primes.append(snake_case    )
										for j in range(0			,		len(snake_case    )    ):
															if i * primes[j] >= n:
																				break
															_lowerCAmelCase      			=					False

															if i % primes[j] == 0:
																				_lowerCAmelCase      			=					totients[i] * primes[j]
																				break

															_lowerCAmelCase      			=					totients[i] * (primes[j] - 1)

					return totients


if __name__ == "__main__":
	import doctest

	doctest.testmod()








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

A__			   = 1_80


def 	_UpperCAmelCase       (   snake_case			,		snake_case    ):





					"""simple docstring"""

					_lowerCAmelCase      			=					k_size // 2
					_lowerCAmelCase			,			_lowerCAmelCase      			=					np.mgrid[0 - center : k_size - center, 0 - center : k_size - center]
					_lowerCAmelCase      			=					(
					    1
					    / (2 * np.pi * sigma)
					    * np.exp(-(np.square(snake_case    ) + np.square(snake_case    )) / (2 * np.square(snake_case    ))    )
					)
					return g


def 	_UpperCAmelCase       (   snake_case			,		snake_case			,		snake_case    ):





					"""simple docstring"""

					_lowerCAmelCase      			=					np.zeros(snake_case    )

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

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

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

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

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

					return destination


def 	_UpperCAmelCase       (   snake_case			,		snake_case			,		snake_case			,		snake_case			,		snake_case			,		snake_case    ):





					"""simple docstring"""

					for row in range(1			,		image_shape[0] - 1    ):
										for col in range(1			,		image_shape[1] - 1    ):
															if destination[row, col] >= threshold_high:
																				_lowerCAmelCase      			=					strong
															elif destination[row, col] <= threshold_low:
																				_lowerCAmelCase      			=					0
															else:
																				_lowerCAmelCase      			=					weak


def 	_UpperCAmelCase       (   snake_case			,		snake_case			,		snake_case			,		snake_case    ):





					"""simple docstring"""

					for row in range(1			,		image_shape[0]    ):
										for col in range(1			,		image_shape[1]    ):
															if destination[row, col] == weak:
																				if 2_55 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],
																				):
																									_lowerCAmelCase      			=					strong
																				else:
																									_lowerCAmelCase      			=					0


def 	_UpperCAmelCase       (   snake_case			,		snake_case=15			,		snake_case=30			,		snake_case=1_28			,		snake_case=2_55    ):





					"""simple docstring"""

					_lowerCAmelCase      			=					img_convolve(snake_case			,		gen_gaussian_kernel(9			,		sigma=1.4    )    )
					# get the gradient and degree by sobel_filter
					_lowerCAmelCase			,			_lowerCAmelCase      			=					sobel_filter(snake_case    )
					_lowerCAmelCase      			=					PI + np.radadeg(snake_case    )

					_lowerCAmelCase      			=					suppress_non_maximum(image.shape			,		snake_case			,		snake_case    )

					detect_high_low_threshold(
					    image.shape			,		snake_case			,		snake_case			,		snake_case			,		snake_case			,		snake_case    )

					track_edge(image.shape			,		snake_case			,		snake_case			,		snake_case    )

					return destination


if __name__ == "__main__":
	# read original image in gray mode
	A__			   = cva.imread(R"""../image_data/lena.jpg""", 0)
	# canny edge detection
	A__			   = canny(lena)
	cva.imshow("""canny""", canny_destination)
	cva.waitKey(0)



