Image Gradients

By studying this article, one can understand the meaning of image gradient and role of gradient values in edge detection. The gradient of pixel represents the change of the intensity values in both X and Y directions.

Gradient of image in X – Direction

• The gradient of image in X-direction is calculated by computing change of each pixel with respect to X-direction.
• Change of each pixel in X- direction is calculated as follows

  P(x, y) = P(x, y+1) – P(x, y-1) (right pixel – left pixel)

  

% Matlab program to find X-gradient image for the given image clear all; clc; %read a color image and convert it to gray img = imread('E:images/face.jpg'); img = rgb2gray(img); %find the size of image [rows,cols] = size(img); %converting image into double for performing operations img=double(img); %initialization xgradient matrix 'xgrad' with image 'img' xgrad=img; %calculating gradient image in X-direction for i=1:rows for j=2:cols-1 xgrad(i,j) = abs(img(i,j+1) - img(i,j-1)); end end figure, imshow(uint8(img)),title('given image'); figure, imshow(uint8(xgrad+22)), title('X-gradient image');

The output of the above code is shown below:

Gradient of image in Y – Direction

• The gradient of image in Y-direction is calculated by computing change of each pixel with respect to Y-direction.
• Change of each pixel in Y-direction is calculated as follows

  P(x, y) = P(x+1, y) – P(x-1, y) (upper pixel – lower pixel)

  

% Matlab program to find Y-gradient image for the given image clear all; clc; %read a color image and convert it to gray img = imread('E:images/face.jpg'); img = rgb2gray(img); %find the size of image [rows,cols] = size(img); %converting image into double for performing operations img=double(img); %initialization ygradient matrix 'ygrad' with image 'img' ygrad=img; %calculating gradient image in X-direction for i=2:rows-1 for j=1:cols ygrad(i,j) = abs(img(i+1,j) - img(i-1,j)); end end figure, imshow(uint8(img)),title('given image'); figure, imshow(uint8(ygrad+22)), title('Y-gradient image');

The output of the above code is shown below:

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