Sobel edge detection using matlab

The gradient of the image is calculated for each pixel position in the image.

The procedure and the MATLAB  code for sobel edge detection without using MATLAB built-in function:

MATLAB CODE:


A=imread('peppers.png');
B=rgb2gray(A);

C=double(B);


for i=1:size(C,1)-2
    for j=1:size(C,2)-2
        %Sobel mask for x-direction:
        Gx=((2*C(i+2,j+1)+C(i+2,j)+C(i+2,j+2))-(2*C(i,j+1)+C(i,j)+C(i,j+2)));
        %Sobel mask for y-direction:
        Gy=((2*C(i+1,j+2)+C(i,j+2)+C(i+2,j+2))-(2*C(i+1,j)+C(i,j)+C(i+2,j)));
     
        %The gradient of the image
        %B(i,j)=abs(Gx)+abs(Gy);
        B(i,j)=sqrt(Gx.^2+Gy.^2);
     
    end
end
figure,imshow(B); title('Sobel gradient');

Sobel Gradient

%Define a threshold value
Thresh=100;
B=max(B,Thresh);
B(B==round(Thresh))=0;

B=uint8(B);
figure,imshow(~B);title('Edge detected Image');

Edge detected Image

Edge detected Image(Threshold value:35)

The edge detected image can be obtained from the sobel gradient by
using a threshold value.

• If the sobel gradient values are lesser than the threshold value then replace it with the threshold value.
  if f < threshold value then
  f = threshold value.

To avoid complex computation, the gradient can also be computed using the formula:

The Image obtained from computing X-direction derivative:

The Image obtained from computing Y-direction derivative: