算法流程：

将图像转换为灰度图像

利用Sobel滤波器求出 海森矩阵 (Hessian matrix) :

• 将高斯滤波器分别作用于Ix²、Iy²、IxIy
• 计算每个像素的 R= det(H) - k(trace(H))²。det(H)表示矩阵H的行列式，trace表示矩阵H的迹。通常k的取值范围为[0.04,0.16]。
• 满足 R>=max(R) * th 的像素点即为角点。th常取0.1。

Harris算法实现：

import cv2 as cv import numpy as npimport matplotlib.pyplot as plt# Harris corner detectiondef Harris_corner(img): ## Grayscale def BGR2GRAY(img): gray = 0.2126 * img[..., 2] + 0.7152 * img[..., 1] + 0.0722 * img[..., 0] gray = gray.astype(np.uint8) return gray ## Sobel def Sobel_filtering(gray): # get shape H, W = gray.shape # sobel kernel sobely = np.array(((1, 2, 1), (0, 0, 0), (-1, -2, -1)), dtype=np.float32) sobelx = np.array(((1, 0, -1), (2, 0, -2), (1, 0, -1)), dtype=np.float32) # padding tmp = np.pad(gray, (1, 1), 'edge') # prepare Ix = np.zeros_like(gray, dtype=np.float32) Iy = np.zeros_like(gray, dtype=np.float32) # get differential for y in range(H): for x in range(W): Ix[y, x] = np.mean(tmp[y : y + 3, x : x + 3] * sobelx) Iy[y, x] = np.mean(tmp[y : y + 3, x : x + 3] * sobely) Ix2 = Ix ** 2 Iy2 = Iy ** 2 Ixy = Ix * Iy return Ix2, Iy2, Ixy # gaussian filtering def gaussian_filtering(I, K_size=3, sigma=3): # get shape H, W = I.shape ## gaussian I_t = np.pad(I, (K_size // 2, K_size // 2), 'edge') # gaussian kernel K = np.zeros((K_size, K_size), dtype=np.float) for x in range(K_size): for y in range(K_size): _x = x - K_size // 2 _y = y - K_size // 2 K[y, x] = np.exp( -(_x ** 2 + _y ** 2) / (2 * (sigma ** 2))) K /= (sigma * np.sqrt(2 * np.pi)) K /= K.sum() # filtering for y in range(H): for x in range(W): I[y,x] = np.sum(I_t[y : y + K_size, x : x + K_size] * K) return I # corner detect def corner_detect(gray, Ix2, Iy2, Ixy, k=0.04, th=0.1): # prepare output image out = np.array((gray, gray, gray)) out = np.transpose(out, (1,2,0)) # get R R = (Ix2 * Iy2 - Ixy ** 2) - k * ((Ix2 + Iy2) ** 2) # detect corner out[R >= np.max(R) * th] = [255, 0, 0] out = out.astype(np.uint8) return out # 1. grayscale gray = BGR2GRAY(img) # 2. get difference image Ix2, Iy2, Ixy = Sobel_filtering(gray) # 3. gaussian filtering Ix2 = gaussian_filtering(Ix2, K_size=3, sigma=3) Iy2 = gaussian_filtering(Iy2, K_size=3, sigma=3) Ixy = gaussian_filtering(Ixy, K_size=3, sigma=3) # 4. corner detect out = corner_detect(gray, Ix2, Iy2, Ixy) return out# Read imageimg = cv.imread("../qiqiao.jpg").astype(np.float32)# Harris corner detectionout = Harris_corner(img)cv.imwrite("out.jpg", out)cv.imshow("result", out)cv.waitKey(0)cv.destroyAllWindows()

实验结果：

原图：

Harris角点检测算法检测结果：

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