harris角点检测算法实现

article/2025/10/8 2:03:27

算法流程：

1、将图像转换为灰度图像；

2、利用Sobel滤波器求出海森矩阵 (Hessian matrix) :

3、将高斯滤波器分别作用于Ix²、Iy²、IxIy；

4、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]；

5、满足 R>=max(R) * th 的像素点即为角点。th常取0.1。

python代码实现：

#!/usr/bin/env python3
# coding: utf-8import cv2
import copy
import numpy as npdef bgr2gray(img):gray = 0.2126 * img[..., 2] + 0.7152 * img[..., 1] + 0.0722 * img[..., 0]gray = gray.astype(np.uint8)return graydef sobel_filtering(gray):# get shapeimg_h, img_w = gray.shape# sobel kernelsobel_y = np.array(((1, 2, 1),(0, 0, 0),(-1, -2, -1)), dtype=np.float32)sobel_x = np.array(((1, 0, -1),(2, 0, -2),(1, 0, -1)), dtype=np.float32)# paddingtmp = np.pad(gray, (1, 1), 'edge')# prepareix = np.zeros_like(gray, dtype=np.float32)iy = np.zeros_like(gray, dtype=np.float32)# get differentialfor y in range(img_h):for x in range(img_w):ix[y, x] = np.mean(tmp[y: y + 3, x: x + 3] * sobel_x)iy[y, x] = np.mean(tmp[y: y + 3, x: x + 3] * sobel_y)ix2 = ix ** 2iy2 = iy ** 2ixy = ix * iyreturn ix2, iy2, ixydef gaussian_filtering(I, k_size=3, sigma=3):# get shapeimg_h, img_w = I.shape# gaussiani_t = np.pad(I, (k_size // 2, k_size // 2), 'edge')# gaussian kernelK = np.zeros((k_size, k_size), dtype=np.float32)for x in range(k_size):for y in range(k_size):_x = x - k_size // 2_y = y - k_size // 2K[y, x] = np.exp(-(_x ** 2 + _y ** 2) / (2 * (sigma ** 2)))K /= (sigma * np.sqrt(2 * np.pi))K /= K.sum()# filteringfor y in range(img_h):for x in range(img_w):I[y, x] = np.sum(i_t[y: y + k_size, x: x + k_size] * K)return Idef corner_detect(img, ix2, iy2, ixy, k=0.04, th=0.1):# prepare output imageout = copy.deepcopy(img)# get RR = (ix2 * iy2 - ixy ** 2) - k * ((ix2 + iy2) ** 2)# detect cornerout[R >= np.max(R) * th] = [255, 0, 0]out = out.astype(np.uint8)return outdef harris_corner(img):# 1. grayscalegray = bgr2gray(img)# 2. get difference imageix2, iy2, ixy = sobel_filtering(gray)# 3. gaussian filteringix2 = 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 detectout = corner_detect(img, ix2, iy2, ixy)return outdef main():# Read imageimg = cv2.imread("test.jpg")img = cv2.resize(img, (512, 512))img = img.astype(np.float32)# Harris corner detectionout = harris_corner(img)cv2.imwrite("out.jpg", out)print("proc ok.")if __name__ == "__main__":main()

结果：

opencv python版本实现：

对于每一个像素(x,y)，在(blockSize*blockSize)邻域内，计算梯度图的协方差矩阵M(x,y) ，然后通过上面第二步中的角点响应函数得到结果图。图像中的角点可以为该结果图的局部最大值。即可以得到输出图中的局部最大值，这些值就对应图像中的角点。

Harris 角点检测函数：

cv2.cornerHarris(src, blockSize, ksize, k, dst, borderType)

src：数据类型为float32的输入图像

blockSize：角点检测中要考虑的领域大小

ksize：Sobel求导中使用的窗口大小

k：Harris 角点检测方程中的自由参数，取值参数为 [0,04，0.06].

dst：目标图像

borderType：边界类型

import cv2
import numpy as npdef test():img = cv2.imread("test.jpg")img = cv2.resize(img, (512, 512))gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)gray = np.float32(gray)# 输入图像必须是 float32，最后一个参数在 0.04 到 0.05 之间dst = cv2.cornerHarris(gray, 3, 3, 0.04)# result is dilated for marking the corners, not important# dst = cv2.dilate(dst, None)# Threshold for an optimal value, it may vary depending on the image.img[dst > 0.1 * dst.max()] = [255, 0, 0]cv2.imwrite("out2.jpg", img)print("proc ok.")

结果：