code: 
  
  
  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_    :					Any             =180
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						a_					=		k_size // 2
  						a_			,   a_					=		np.mgrid[0 - center : k_size - center, 0 - center : k_size - center]
  						a_					=		(
  						    1
  						    / (2 * np.pi * sigma)
  						    * np.exp(-(np.square(UpperCAmelCase__      ) + np.square(UpperCAmelCase__      )) / (2 * np.square(UpperCAmelCase__      ))      )
  						)
  						return g
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						a_					=		np.zeros(UpperCAmelCase__      )
  
  						for row in range(1       ,    image_shape[0] - 1      ):
  												for col in range(1       ,    image_shape[1] - 1      ):
  																		a_					=		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_					=		sobel_grad[row, col - 1]
  																								a_					=		sobel_grad[row, col + 1]
  																								if sobel_grad[row, col] >= w and sobel_grad[row, col] >= e:
  																														a_					=		sobel_grad[row, col]
  
  																		elif (
  																		    PI / 8 <= direction < 3 * PI / 8
  																		    or 9 * PI / 8 <= direction < 11 * PI / 8
  																		):
  																								a_					=		sobel_grad[row + 1, col - 1]
  																								a_					=		sobel_grad[row - 1, col + 1]
  																								if sobel_grad[row, col] >= sw and sobel_grad[row, col] >= ne:
  																														a_					=		sobel_grad[row, col]
  
  																		elif (
  																		    3 * PI / 8 <= direction < 5 * PI / 8
  																		    or 11 * PI / 8 <= direction < 13 * PI / 8
  																		):
  																								a_					=		sobel_grad[row - 1, col]
  																								a_					=		sobel_grad[row + 1, col]
  																								if sobel_grad[row, col] >= n and sobel_grad[row, col] >= s:
  																														a_					=		sobel_grad[row, col]
  
  																		elif (
  																		    5 * PI / 8 <= direction < 7 * PI / 8
  																		    or 13 * PI / 8 <= direction < 15 * PI / 8
  																		):
  																								a_					=		sobel_grad[row - 1, col - 1]
  																								a_					=		sobel_grad[row + 1, col + 1]
  																								if sobel_grad[row, col] >= nw and sobel_grad[row, col] >= se:
  																														a_					=		sobel_grad[row, col]
  
  						return destination
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""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:
  																								a_					=		strong
  																		elif destination[row, col] <= threshold_low:
  																								a_					=		0
  																		else:
  																								a_					=		weak
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						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_					=		strong
  																								else:
  																														a_					=		0
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__=15       ,    UpperCAmelCase__=30       ,    UpperCAmelCase__=128       ,    UpperCAmelCase__=255      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						a_					=		img_convolve(UpperCAmelCase__       ,    gen_gaussian_kernel(9       ,    sigma=1.4      )      )
  						# get the gradient and degree by sobel_filter
  						a_			,   a_					=		sobel_filter(UpperCAmelCase__      )
  						a_					=		PI + np.radadeg(UpperCAmelCase__      )
  
  						a_					=		suppress_non_maximum(image.shape       ,    UpperCAmelCase__       ,    UpperCAmelCase__      )
  
  						detect_high_low_threshold(
  						    image.shape       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__      )
  
  						track_edge(image.shape       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__      )
  
  						return destination
  
  
  if __name__ == "__main__":
  	# read original image in gray mode
  	A_    :					Optional[Any]             =cva.imread(r"""../image_data/lena.jpg""", 0)
  	# canny edge detection
  	A_    :					int             =canny(lena)
  	cva.imshow("""canny""", canny_destination)
  	cva.waitKey(0)
style_context: 
  
  
  from collections.abc import Callable
  from math import log
  from os import name, system
  from random import gauss, seed
  from typing import TypeVar
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						seed(1      )
  						return [gauss(UpperCAmelCase__       ,    UpperCAmelCase__      ) for _ in range(UpperCAmelCase__      )]
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						return [k for k in range(UpperCAmelCase__      ) for _ in range(instance_count[k]      )]
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						return sum(UpperCAmelCase__      ) / instance_count
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						return instance_count / total_count
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						a_					=		[]  # An empty list to store all squared differences
  						# iterate over number of elements in items
  						for i in range(len(UpperCAmelCase__      )      ):
  												# for loop iterates over number of elements in inner layer of items
  												for j in range(len(items[i]      )      ):
  																		# appending squared differences to 'squared_diff' list
  																		squared_diff.append((items[i][j] - means[i]) ** 2      )
  
      # one divided by (the number of all instances - number of classes) multiplied by
      # sum of all squared differences
  						a_					=		len(UpperCAmelCase__      )  # Number of classes in dataset
  						return 1 / (total_count - n_classes) * sum(UpperCAmelCase__      )
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						a_					=		[]
  						# for loop iterates over number of elements in list
  						for i in range(len(UpperCAmelCase__      )      ):
  												# for loop iterates over number of inner items of each element
  												for j in range(len(x_items[i]      )      ):
  																		a_					=		[]  # to store all discriminant values of each item as a list
  																		# for loop iterates over number of classes we have in our dataset
  																		for k in range(len(UpperCAmelCase__      )      ):
  																								# appending values of discriminants for each class to 'temp' list
  																								temp.append(
  																								    x_items[i][j] * (means[k] / variance)
  																								    - (means[k] ** 2 / (2 * variance))
  																								    + log(probabilities[k]      )      )
  																		# appending discriminant values of each item to 'results' list
  																		results.append(UpperCAmelCase__      )
  
  						return [result.index(max(UpperCAmelCase__      )      ) for result in results]
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__      ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						a_					=		sum(1 for i, j in zip(UpperCAmelCase__       ,    UpperCAmelCase__      ) if i == j      )
  						# percentage of accuracy equals to number of correct predictions divided by number
  						# of all data and multiplied by 100
  						return (correct / len(UpperCAmelCase__      )) * 100
  
  
  A_    :					Dict             =TypeVar("""num""")
  
  
  
  
  def   lowerCamelCase_       (					UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__ = lambda UpperCAmelCase__      : True       ,    UpperCAmelCase__ = None       ,    ):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						while True:
  												try:
  																		a_					=		input_type(input(UpperCAmelCase__      ).strip() or default      )
  																		if condition(UpperCAmelCase__      ):
  																								return user_input
  																		else:
  																								print(F"{user_input}: {err_msg}"      )
  																								continue
  												except ValueError:
  																		print(
  																		    F"{user_input}: Incorrect input type, expected {input_type.__name__!r}"      )
  
  
  
  
  def   lowerCamelCase_       (					):
  
  
  
  						"""simple docstring"""
  
  
  
  
  						while True:
  												print(""" Linear Discriminant Analysis """.center(50       ,    """*"""      )      )
  												print("""*""" * 50       ,    """\n"""      )
  												print("""First of all we should specify the number of classes that"""      )
  												print("""we want to generate as training dataset"""      )
  												# Trying to get number of classes
  												a_					=		valid_input(
  												    input_type=UpperCAmelCase__       ,    condition=lambda UpperCAmelCase__      : x > 0       ,    input_msg="""Enter the number of classes (Data Groupings): """       ,    err_msg="""Number of classes should be positive!"""       ,    )
  
  												print("""-""" * 100      )
  
  												# Trying to get the value of standard deviation
  												a_					=		valid_input(
  												    input_type=UpperCAmelCase__       ,    condition=lambda UpperCAmelCase__      : x >= 0       ,    input_msg=(
  												        """Enter the value of standard deviation"""
  												        """(Default value is 1.0 for all classes): """
  												    )       ,    err_msg="""Standard deviation should not be negative!"""       ,    default="""1.0"""       ,    )
  
  												print("""-""" * 100      )
  
  												# Trying to get number of instances in classes and theirs means to generate
  												# dataset
  												a_					=		[]  # An empty list to store instance counts of classes in dataset
  												for i in range(UpperCAmelCase__      ):
  																		a_					=		valid_input(
  																		    input_type=UpperCAmelCase__       ,    condition=lambda UpperCAmelCase__      : x > 0       ,    input_msg=(F"Enter The number of instances for class_{i+1}: ")       ,    err_msg="""Number of instances should be positive!"""       ,    )
  																		counts.append(UpperCAmelCase__      )
  												print("""-""" * 100      )
  
  												# An empty list to store values of user-entered means of classes
  												a_					=		[]
  												for a in range(UpperCAmelCase__      ):
  																		a_					=		valid_input(
  																		    input_type=UpperCAmelCase__       ,    input_msg=(F"Enter the value of mean for class_{a+1}: ")       ,    err_msg="""This is an invalid value."""       ,    )
  																		user_means.append(UpperCAmelCase__      )
  												print("""-""" * 100      )
  
  												print("""Standard deviation: """       ,    UpperCAmelCase__      )
  												# print out the number of instances in classes in separated line
  												for i, count in enumerate(UpperCAmelCase__       ,    1      ):
  																		print(F"Number of instances in class_{i} is: {count}"      )
  												print("""-""" * 100      )
  
  												# print out mean values of classes separated line
  												for i, user_mean in enumerate(UpperCAmelCase__       ,    1      ):
  																		print(F"Mean of class_{i} is: {user_mean}"      )
  												print("""-""" * 100      )
  
  												# Generating training dataset drawn from gaussian distribution
  												a_					=		[
  												    gaussian_distribution(user_means[j]       ,    UpperCAmelCase__       ,    counts[j]      )
  												    for j in range(UpperCAmelCase__      )
  												]
  												print("""Generated Normal Distribution: \n"""       ,    UpperCAmelCase__      )
  												print("""-""" * 100      )
  
  												# Generating Ys to detecting corresponding classes
  												a_					=		y_generator(UpperCAmelCase__       ,    UpperCAmelCase__      )
  												print("""Generated Corresponding Ys: \n"""       ,    UpperCAmelCase__      )
  												print("""-""" * 100      )
  
  												# Calculating the value of actual mean for each class
  												a_					=		[calculate_mean(counts[k]       ,    x[k]      ) for k in range(UpperCAmelCase__      )]
  												# for loop iterates over number of elements in 'actual_means' list and print
  												# out them in separated line
  												for i, actual_mean in enumerate(UpperCAmelCase__       ,    1      ):
  																		print(F"Actual(Real) mean of class_{i} is: {actual_mean}"      )
  												print("""-""" * 100      )
  
  												# Calculating the value of probabilities for each class
  												a_					=		[
  												    calculate_probabilities(counts[i]       ,    sum(UpperCAmelCase__      )      ) for i in range(UpperCAmelCase__      )
  												]
  
  												# for loop iterates over number of elements in 'probabilities' list and print
  												# out them in separated line
  												for i, probability in enumerate(UpperCAmelCase__       ,    1      ):
  																		print(F"Probability of class_{i} is: {probability}"      )
  												print("""-""" * 100      )
  
  												# Calculating the values of variance for each class
  												a_					=		calculate_variance(UpperCAmelCase__       ,    UpperCAmelCase__       ,    sum(UpperCAmelCase__      )      )
  												print("""Variance: """       ,    UpperCAmelCase__      )
  												print("""-""" * 100      )
  
  												# Predicting Y values
  												# storing predicted Y values in 'pre_indexes' variable
  												a_					=		predict_y_values(UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__       ,    UpperCAmelCase__      )
  												print("""-""" * 100      )
  
  												# Calculating Accuracy of the model
  												print(F"Accuracy: {accuracy(UpperCAmelCase__       ,    UpperCAmelCase__      )}"      )
  												print("""-""" * 100      )
  												print(""" DONE """.center(100       ,    """+"""      )      )
  
  												if input("""Press any key to restart or 'q' for quit: """      ).strip().lower() == "q":
  																		print("""\n""" + """GoodBye!""".center(100       ,    """-"""      ) + """\n"""      )
  																		break
  												system("""cls""" if name == """nt""" else """clear"""      )  # noqa: S605
  
  
  if __name__ == "__main__":
  	main()