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 np
import matplotlib.pyplot as plt
# Harris corner detection
def 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 image
img = cv.imread("../qiqiao.jpg").astype(np.float32)
# Harris corner detection
out = 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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