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一. 总的算法流程：
① 使用高斯滤波器滤波
② 使用 Sobel 滤波器滤波获得在 x 和 y 方向上的输出，在此基础上求出边缘的强度和边缘的角度
edge 为边缘强度，tan 为边缘角度 ↑
③ 对边缘角度进行量化处理
对边缘角度进行量化处理算法 ↑
④ 根据边缘角度对边缘强度进行非极大值抑制（Non-maximum suppression），使图像边缘变得更细
非极大值抑制算法：0°时取(x,y)、(x+1,y)、(x-1,y) 中的最大值，其它角度类似 ↑
⑤ 使用滞后阈值对图像进行二值化处理，优化图像显示效果
算法如上所示 ↑
⑥ 输出图像边缘提取效果
二. 使用python手动实现 Canny 算法，完成图像边缘提取
1 # writer：[email protected]
2 # date ：2020.3.20
3 import cv2
4 import numpy as np
5 import matplotlib.pyplot as plt
6
7 def Canny(img):
8
9 # Gray scale
10 def BGR2GRAY(img):
11 b = img[:, :, 0].copy()
12 g = img[:, :, 1].copy()
13 r = img[:, :, 2].copy()
14
15 # Gray scale
16 out = 0.2126 * r + 0.7152 * g + 0.0722 * b
17 out = out.astype(np.uint8)
18
19 return out
20
21
22 # Gaussian filter for grayscale
23 def gaussian_filter(img, K_size=3, sigma=1.4):
24
25 if len(img.shape) == 3:
26 H, W, C = img.shape
27 gray = False
28 else:
29 img = np.expand_dims(img, axis=-1)
30 H, W, C = img.shape
31 gray = True
32
33 ## Zero padding
34 pad = K_size // 2
35 out = np.zeros([H + pad * 2, W + pad * 2, C], dtype=np.float)
36 out[pad : pad + H, pad : pad + W] = img.copy().astype(np.float)
37
38 ## prepare Kernel
39 K = np.zeros((K_size, K_size), dtype=np.float)
40 for x in range(-pad, -pad + K_size):
41 for y in range(-pad, -pad + K_size):
42 K[y + pad, x + pad] = np.exp( - (x ** 2 + y ** 2) / (2 * sigma * sigma))
43 #K /= (sigma * np.sqrt(2 * np.pi))
44 K /= (2 * np.pi * sigma * sigma)
45 K /= K.sum()
46
47 tmp = out.copy()
48
49 # filtering
50 for y in range(H):
51 for x in range(W):
52 for c in range(C):
53 out[pad + y, pad + x, c] = np.sum(K * tmp[y : y + K_size, x : x + K_size, c])
54
55 out = np.clip(out, 0, 255)
56 out = out[pad : pad + H, pad : pad + W]
57 out = out.astype(np.uint8)
58
59 if gray:
60 out = out[..., 0]
61
62 return out
63
64
65 # sobel filter
66 def sobel_filter(img, K_size=3):
67 if len(img.shape) == 3:
68 H, W, C = img.shape
69 else:
70 H, W = img.shape
71
72 # Zero padding
73 pad = K_size // 2
74 out = np.zeros((H + pad * 2, W + pad * 2), dtype=np.float)
75 out[pad : pad + H, pad : pad + W] = img.copy().astype(np.float)
76 tmp = out.copy()
77
78 out_v = out.copy()
79 out_h = out.copy()
80
81 ## Sobel vertical
82 Kv = [[1., 2., 1.],[0., 0., 0.], [-1., -2., -1.]]
83 ## Sobel horizontal
84 Kh = [[1., 0., -1.],[2., 0., -2.],[1., 0., -1.]]
85
86 # filtering
87 for y in range(H):
88 for x in range(W):
89 out_v[pad + y, pad + x] = np.sum(Kv * (tmp[y : y + K_size, x : x + K_size]))
90 out_h[pad + y, pad + x] = np.sum(Kh * (tmp[y : y + K_size, x : x + K_size]))
91
92 out_v = np.clip(out_v, 0, 255)
93 out_h = np.clip(out_h, 0, 255)
94
95 out_v = out_v[pad : pad + H, pad : pad + W]
96 out_v = out_v.astype(np.uint8)
97 out_h = out_h[pad : pad + H, pad : pad + W]
98 out_h = out_h.astype(np.uint8)
99
100 return out_v, out_h
101
102
103 # get edge strength and edge angle
104 def get_edge_angle(fx, fy):
105 # get edge strength
106 edge = np.sqrt(np.power(fx.astype(np.float32), 2) + np.power(fy.astype(np.float32), 2))
107 edge = np.clip(edge, 0, 255)
108
109 # make sure the denominator is not 0
110 fx = np.maximum(fx, 1e-10)
111 #fx[np.abs(fx) <= 1e-5] = 1e-5
112
113 # get edge angle
114 angle = np.arctan(fy / fx)
115
116 return edge, angle
117
118
119 # 将角度量化为0°、45°、90°、135°
120 def angle_quantization(angle):
121 angle = angle / np.pi * 180
122 angle[angle < -22.5] = 180 + angle[angle < -22.5]
123 _angle = np.zeros_like(angle, dtype=np.uint8)
124 _angle[np.where(angle <= 22.5)] = 0
125 _angle[np.where((angle > 22.5) & (angle <= 67.5))] = 45
126 _angle[np.where((angle > 67.5) & (angle <= 112.5))] = 90
127 _angle[np.where((angle > 112.5) & (angle <= 157.5))] = 135
128
129 return _angle
130
131
132 def non_maximum_suppression(angle, edge):
133 H, W = angle.shape
134 _edge = edge.copy()
135
136 for y in range(H):
137 for x in range(W):
138 if angle[y, x] == 0:
139 dx1, dy1, dx2, dy2 = -1, 0, 1, 0
140 elif angle[y, x] == 45:
141 dx1, dy1, dx2, dy2 = -1, 1, 1, -1
142 elif angle[y, x] == 90:
143 dx1, dy1, dx2, dy2 = 0, -1, 0, 1
144 elif angle[y, x] == 135:
145 dx1, dy1, dx2, dy2 = -1, -1, 1, 1
146 # 边界处理
147 if x == 0:
148 dx1 = max(dx1, 0)
149 dx2 = max(dx2, 0)
150 if x == W-1:
151 dx1 = min(dx1, 0)
152 dx2 = min(dx2, 0)
153 if y == 0:
154 dy1 = max(dy1, 0)
155 dy2 = max(dy2, 0)
156 if y == H-1:
157 dy1 = min(dy1, 0)
158 dy2 = min(dy2, 0)
159 # 如果不是最大值，则将这个位置像素值置为0
160 if max(max(edge[y, x], edge[y + dy1, x + dx1]), edge[y + dy2, x + dx2]) != edge[y, x]:
161 _edge[y, x] = 0
162
163 return _edge
164
165
166 # 滞后阈值处理二值化图像
167 # > HT 的设为255，< LT 的设置0，介于它们两个中间的值，使用8邻域判断法
168 def hysterisis(edge, HT=100, LT=30):
169 H, W = edge.shape
170
171 # Histeresis threshold
172 edge[edge >= HT] = 255
173 edge[edge <= LT] = 0
174
175 _edge = np.zeros((H + 2, W + 2), dtype=np.float32)
176 _edge[1 : H + 1, 1 : W + 1] = edge
177
178 ## 8 - Nearest neighbor
179 nn = np.array(((1., 1., 1.), (1., 0., 1.), (1., 1., 1.)), dtype=np.float32)
180
181 for y in range(1, H+2):
182 for x in range(1, W+2):
183 if _edge[y, x] < LT or _edge[y, x] > HT:
184 continue
185 if np.max(_edge[y-1:y+2, x-1:x+2] * nn) >= HT:
186 _edge[y, x] = 255
187 else:
188 _edge[y, x] = 0
189
190 edge = _edge[1:H+1, 1:W+1]
191
192 return edge
193
194 # grayscale
195 gray = BGR2GRAY(img)
196
197 # gaussian filtering
198 gaussian = gaussian_filter(gray, K_size=5, sigma=1.4)
199
200 # sobel filtering
201 fy, fx = sobel_filter(gaussian, K_size=3)
202
203 # get edge strength, angle
204 edge, angle = get_edge_angle(fx, fy)
205
206 # angle quantization
207 angle = angle_quantization(angle)
208
209 # non maximum suppression
210 edge = non_maximum_suppression(angle, edge)
211
212 # hysterisis threshold
213 out = hysterisis(edge, 80, 20)
214
215 return out
216
217
218 if __name__ == ‘__main__‘:
219 # Read image
220 img = cv2.imread("../paojie.jpg").astype(np.float32)
221
222 # Canny
223 edge = Canny(img)
224
225 out = edge.astype(np.uint8)
226
227 # Save result
228 cv2.imwrite("out.jpg", out)
229 cv2.imshow("result", out)
230 cv2.waitKey(0)
231 cv2.destroyAllWindows()
三. 实验结果：
原图 ↑
Canny 算法 提取图像边缘结果 ↑
可以看到，我的代码如愿以偿地提取了图像边缘，而且效果很好！
四. 参考内容：
https://www.jianshu.com/p/ff4c1a6a68d8
五. 版权声明：
未经作者允许，请勿随意转载抄袭，抄袭情节严重者，作者将考虑追究其法律责任，创作不易，感谢您的理解和配合！
原文地址：https://www.cnblogs.com/wojianxin/p/12533526.html
时间： 2024-08-30 15:18:08