LoG operator for image processing (Gaussian Laplacian)

LoG operator (Gaussian Laplacian operator)

The LoG operator is improved from the Laplacian operator. The Laplacian operator is a second-order derivative operator, which is a scalar quantity with linearity and displacement invariance, and the origin of its transfer function in the frequency domain space is 0. All Laplacian filtered images have zero mean grayscale. However, the disadvantage of this operator is that it is sensitive to noise, so in practical applications, it is generally necessary to smooth the image first, and then use the Laplace operator to detect the edge of the image. This is the background of the LoG operator (the final gradient expression is the convolution of the Gaussian function and the original image, and then the second-order differential operator).
Its filter function model is:

Give the square root of the frame 5*5:
$$\left[\begin{array}{ccccc}0& 0& -1& 0& 0\\ 0& -1& -2& -1& 0\\ -1& -2& 16& -2& -1\\ 0& -1& -2& -1& 0\\ 0& 0& -1& 0& 0\end{array}\right]$$
code:

import numpy as np
import  cv2
from matplotlib import pyplot as plt
import imgShow as iS

#定义掩膜
m1 = np.array([[0,0,-1,0,0],[0,-1,-2,-1,0],[-1,-2,16,-2,-1],[0,-1,-2,-1,0],[0,0,-1,0,0]]) #LoG算子模板
img = cv2.imread("./originImg/Lena.tif")
img = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
#边缘扩充

image = cv2.copyMakeBorder(img, 2, 2, 2, 2, borderType=cv2.BORDER_REPLICATE)
# image = cv2.GaussianBlur(img,(3,3),4)
rows = image.shape[0]
cols = image.shape[1]
temp = 0
image1 = np.zeros(image.shape)

for i in range(2,rows-2):
    for j in range(2,cols-2):
        temp = np.abs(
            (np.dot(np.array([1, 1, 1, 1, 1]), (m1 * image[i - 2:i + 3, j - 2:j + 3])))
                .dot(np.array([[1], [1], [1], [1], [1]])))
        image1[i,j] = int(temp)
        if image1[i, j] > 255:
            image1[i, j] = 255
        else:
            image1[i, j] = 0
iS.showImagegray(image1,img , 25, 15, 'LoG', 'origin', './LoG.jpg')
# cv2.imshow("LoG",image1)
# cv2.waitKey(0)

The test result is: