实现Canny算法 python
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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：wojianxinygcl@163.com 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！
