Canny 邊緣檢測算法

Steps:

高斯濾波平滑

計算梯度大小和方向

非極大值抑制

雙閾值檢測和連接

代碼結構：

Canny Edge Detection

|Gaussian_Smoothing

||convolution.py

|||convolution()

||gaussion_smoothing.py

|||dnorm()

|||gaussian_kernel()

|||gaussian_blur()

|Sobel_Filter

||sobel.py

|||sobel_edge_detection()

|Canny.py

||non_max_suppression()

||threshold()

||hysteresis()

||main()

代碼解讀：

1. 高斯濾波平滑

創建一個高斯核(kernel_size=5)：

執行卷積和平均操作(以下均以 lenna 圖為例)

2. 計算梯度大小和方向

水平方向和豎直方向

梯度圖：

3. 非極大值抑制

4. 雙閾值檢測和連接

以下是代碼：

import numpy as np

import cv2

import argparse

from Computer_Vision.Canny_Edge_Detection.sobel import sobel_edge_detection

from Computer_Vision.Canny_Edge_Detection.gaussian_smoothing import gaussian_blur

import matplotlib.pyplot as plt

def non_max_suppression(gradient_magnitude, gradient_direction, verbose):

image_row, image_col = gradient_magnitude.shape

output = np.zeros(gradient_magnitude.shape)

PI = 180

for row in range(1, image_row - 1):

for col in range(1, image_col - 1):

direction = gradient_direction[row, col]

if (0 <= direction < PI / 8) or (15 * PI / 8 <= direction <= 2 * PI):

before_pixel = gradient_magnitude[row, col - 1]

after_pixel = gradient_magnitude[row, col + 1]

elif (PI / 8 <= direction < 3 * PI / 8) or (9 * PI / 8 <= direction < 11 * PI / 8):

before_pixel = gradient_magnitude[row + 1, col - 1]

after_pixel = gradient_magnitude[row - 1, col + 1]

elif (3 * PI / 8 <= direction < 5 * PI / 8) or (11 * PI / 8 <= direction < 13 * PI / 8):

before_pixel = gradient_magnitude[row - 1, col]

after_pixel = gradient_magnitude[row + 1, col]

else:

before_pixel = gradient_magnitude[row - 1, col - 1]

after_pixel = gradient_magnitude[row + 1, col + 1]

if gradient_magnitude[row, col] >= before_pixel and gradient_magnitude[row, col] >= after_pixel:

output[row, col] = gradient_magnitude[row, col]

if verbose:

plt.imshow(output, cmap='gray')

plt.title("Non Max Suppression")

plt.show()

return output

def threshold(image, low, high, weak, verbose=False):

output = np.zeros(image.shape)

strong = 255

strong_row, strong_col = np.where(image >= high)

weak_row, weak_col = np.where((image <= high) & (image >= low))

output[strong_row, strong_col] = strong

output[weak_row, weak_col] = weak

if verbose:

plt.imshow(output, cmap='gray')

plt.title("threshold")

plt.show()

return output

def hysteresis(image, weak):

image_row, image_col = image.shape

top_to_bottom = image.copy()

for row in range(1, image_row):

for col in range(1, image_col):

if top_to_bottom[row, col] == weak:

if top_to_bottom[row, col + 1] == 255 or top_to_bottom[row, col - 1] == 255 or top_to_bottom[row - 1, col] == 255 or top_to_bottom[

row + 1, col] == 255 or top_to_bottom[

row - 1, col - 1] == 255 or top_to_bottom[row + 1, col - 1] == 255 or top_to_bottom[row - 1, col + 1] == 255 or top_to_bottom[

row + 1, col + 1] == 255:

top_to_bottom[row, col] = 255

else:

top_to_bottom[row, col] = 0

bottom_to_top = image.copy()

for row in range(image_row - 1, 0, -1):

for col in range(image_col - 1, 0, -1):

if bottom_to_top[row, col] == weak:

if bottom_to_top[row, col + 1] == 255 or bottom_to_top[row, col - 1] == 255 or bottom_to_top[row - 1, col] == 255 or bottom_to_top[

row + 1, col] == 255 or bottom_to_top[

row - 1, col - 1] == 255 or bottom_to_top[row + 1, col - 1] == 255 or bottom_to_top[row - 1, col + 1] == 255 or bottom_to_top[

row + 1, col + 1] == 255:

bottom_to_top[row, col] = 255

else:

bottom_to_top[row, col] = 0

right_to_left = image.copy()

for row in range(1, image_row):

for col in range(image_col - 1, 0, -1):

if right_to_left[row, col] == weak:

if right_to_left[row, col + 1] == 255 or right_to_left[row, col - 1] == 255 or right_to_left[row - 1, col] == 255 or right_to_left[

row + 1, col] == 255 or right_to_left[

row - 1, col - 1] == 255 or right_to_left[row + 1, col - 1] == 255 or right_to_left[row - 1, col + 1] == 255 or right_to_left[

row + 1, col + 1] == 255:

right_to_left[row, col] = 255

else:

right_to_left[row, col] = 0

left_to_right = image.copy()

for row in range(image_row - 1, 0, -1):

for col in range(1, image_col):

if left_to_right[row, col] == weak:

if left_to_right[row, col + 1] == 255 or left_to_right[row, col - 1] == 255 or left_to_right[row - 1, col] == 255 or left_to_right[

row + 1, col] == 255 or left_to_right[

row - 1, col - 1] == 255 or left_to_right[row + 1, col - 1] == 255 or left_to_right[row - 1, col + 1] == 255 or left_to_right[

row + 1, col + 1] == 255:

left_to_right[row, col] = 255

else:

left_to_right[row, col] = 0

final_image = top_to_bottom + bottom_to_top + right_to_left + left_to_right

final_image[final_image > 255] = 255

return final_image

if __name__ == '__main__':

ap = argparse.ArgumentParser()

ap.add_argument("-i", "--image", required=True, help="Path to the image")

ap.add_argument("-v", "--verbose", type=bool, default=False, help="Path to the image")

args = vars(ap.parse_args())

image = cv2.imread(args["image"])

blurred_image = gaussian_blur(image, kernel_size=9, verbose=False)

edge_filter = np.array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]])

gradient_magnitude, gradient_direction = sobel_edge_detection(blurred_image, edge_filter, convert_to_degree=True, verbose=args["verbose"])

new_image = non_max_suppression(gradient_magnitude, gradient_direction, verbose=args["verbose"])

weak = 50

new_image = threshold(new_image, 5, 20, weak=weak, verbose=args["verbose"])

new_image = hysteresis(new_image, weak)

plt.imshow(new_image, cmap='gray')

plt.title("Canny Edge Detector")

plt.show()

References

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