Edge detection using Local Variance

Local statistics can determine the gradient of the image. The local variance can be used to generate an edge map.

Steps to be performed:

1.       Read a grayscale image

2.       Define a window size (For eg: 3x3,5x5,7x7)

3.       Find the local variance

4.       Find the global mean of the local variance

5.       Set local variance to zero if it is less than the global mean else set it to one

MATLAB code:

%Boundary Detection - Local Variance

%Read an image

I = imread('rice.png');

figure,imagesc(I);colormap(gray);

I = double(I);

Explanation:

A grayscale image is taken as input for edge detection. If the input image is RGB then convert it to gray scaleusing ‘rgb2gray’.

MATLAB code:

%Define the window size

sz=3;

window = ones(sz)/sz.^2;

%Find the local mean

mu = conv2(I,window,'same');

%Find the local Variance

II = conv2(I.^2,window,'same');

Lvar = II-mu.^2;

figure,imagesc(Lvar);colormap(gray);title('Local Variance of the image');

Explanation:

A window size of 3 by 3 is defined and local variance is computed. Check ‘local variance- matlab code’ to understand how local variance is estimated.

MATLAB CODE:

%Define a Threshold

meanL = mean(Lvar(:));

%Set the pixel values based on threshold

Boundary = zeros(size(Lvar));

Boundary(Lvar < meanL)=1;

Boundary(Lvar >= meanL) = 0;

figure,imagesc(Boundary);colormap(gray);title('Boundary Extracted Image');

Explanation:

 The mean of the local variance is obtained and using the mean value as threshold, the boundary is defined for the image.  The mean value of the given image is 239.3638.

The threshold value can also be set randomly by the user. For instance, set the threshold value to 500.