Catalog

Abstract

First order edge detection basic operator （First Order Edge Detection）

Improved first-order edge detection

Rorberts Crossover operator

Prewitt Edge detector  

Sobel Detection operator ：

First order edge detection （First Order Edge Detection）

Abstract

The analysis based on edge detection is not easily affected by the change of overall illumination intensity , Edge detection emphasizes image contrast , That is, the difference in brightness . To detect the edge position , We can first apply first-order differential , Because the first-order differential can enhance the change ; And when the signal does not change , The first-order differential will not respond .

First order edge detection basic operator （First Order Edge Detection）

Define vertical edges ：（E yes edge Abbreviation ）

Define horizontal edges ：

Then the vertical and horizontal edges ：（ Add vertical and horizontal edges ）

It is called first-order edge detection .

A template for ：

Pseudo code ：

function edge = basic_difference(inage)

for x = 1:cols-2 
    for y = 1:rows-2
        edge(y,x)=abs(2*image(y,x)-image(y+1,x)-image(y+1,x))
    end
end

-------------------------------------------------------------------------------------------------------------------------------- 

Improved first-order edge detection

Taylor series analysis shows that the difference processing of adjacent points can be used to estimate the first derivative of points

  Therefore, the improved first-order difference template is ：

 Mx For vertical formwork ,My For horizontal formwork .

  So the improved formula is

---------------------------------------------------------------------------------------------------------------------------------

Rorberts Crossover operator

It is one of the earliest edge detection operators , It implements edge detection , Use two templates , Calculate the differential on the diagonal rather than along the coordinate axis . These two templates are ：

  Edge point Ex,y Is at the image point Px,y The larger of the two values obtained by convolution calculation of these two templates , Formula for ：

 Roberts Application of crossover operator ：

--------------------------------------------------------------------------------------------------------------------------------

Prewitt Edge detector  

Prewitt The operator template is ： 

  among Mx It's a vertical template ,My Is a horizontal template .

For vertical formwork , First （a） The middle shaded part in the figure is the pixel value we require . It is equal to the surrounding 8 Convolute the pixel values to get , That is to say Mx Make inner product with these nine pixel values , Pixels P_00 * 1 + P_01 * 0 + P_02 * (-1) + P_10 * 1 + P_11 * 0 + P_12 * (-1) + P_20 * 1 + P_21 * 0 + P_22 * (-1). obtain Mx(x,y).（ I don't understand what this symbol stands for ）

For horizontal formwork , First （b） The middle shaded part in the figure is the pixel value we require . It is equal to the surrounding 8 Convolute the pixel values to get , That is to say Mx Make inner product with these nine pixel values , Pixels P_00 * 1 + P_01 * 1 + P_02 * 1 + P_10 * 0 + P_11 * 0 + P_12 * 0 + P_20 * (-1) + P_21 * (-1) + P_22 * (-1). 

And then put Mx(x,y) , My(x,y) The square of the sum of squares of gets the value of the pixel in the center of our shadow . This is the solution of vector ,（ Similar to finding the hypotenuse of a triangle ） As shown in the following formula .

                ​​​​​​​        ​​​​​​​        ​​​​​​​        ​​​​​​​        

Edge strength M It represents the length of the vector , Edge direction θ It represents the direction of the vector .

        ​​​​​​​        ​​​​​​​        ​​​​​​​        ​​​​​​​        ​​​​​​​        ​​​​​​​        

Matlab Code

image=double(imread('lizardsmall.png'));
[rows, cols]=size(image)
edge = zeros(rows,cols)
kernelx = [1,0,-1;1,0,-1;1,0,-1]
kernely = [1,1,1;0,0,0;-1,-1,-1]
for x = 2:cols-1 
    for y = 2:rows-1
        tempx = sum(sum(image(y-1:y+1,x-1:x+1) * kernelx,1),2);
        tempy = sum(sum(image(y-1:y+1,x-1:x+1) * kernely,1),2);
        edge(y,x)=abs(sqrt(tempx*tempx+tempy*tempy));
    end
end
imshow(uint8(edge)),title('original');

Sobel Detection operator ：

Prewitt The operator template is ：

 Sobel The calculation formula of each pixel of the operator and Prewitt identical , That is, the previous coefficient has changed .

Reference books 《Feature extraction and image processing》 Mark S. Nixon and Alberto S. Aguado 

Chinese version ,《 Feature extraction and image processing 》