How Can I simulate non uniform background illumination?

I would like to add non uniform background illumination to some images to test some thresholding algorithms.

Answer 1

[Bruno Pop-Stefanov]

If I understand your question correctly you would like to generate images with non-uniform background illumination in order to test thresholding algorithms.

You could try to find a test set of images which already have a non-uniformly illuminated background. For example, rice.png is an image shipped with Image Processing Toolbox with non-uniform illumination. Take a look at that example to see how you could use it:

Correcting Nonuniform Illumination

It's hard to add non-uniform background illumination to images. That would be hard even with Adobe Photoshop. It's easier to create a non-uniform background and then add the foreground. So, why not create images from the ground up using basic functions in MATLAB?

Here's a code snippet that creates a grayscale image with a non-uniform background made of a sinc wave:

    % Size of our image: N-by-N
    N = 500;

    % The xy limits of the sinc function
    % we want N points in each direction
    x = linspace(-50,50,N);
    y = linspace(-50,50,N);

    % Transform these xy coordinates into a grid pattern
    [X,Y] = meshgrid(x,y);

    % The input to the sinc function is the radius from the center
    r = sqrt(X.^2 + Y.^2);

    % Create the background as the output of sinc
    background = sin(r)./r;

    % Now we need to scale the matrix so that it is a valid image
    mmin = min(background(:));
    mmax = max(background(:));

    % Subtract the min, divide by the range, multiply by 255 -> values are in [0,255]
    background = 255*(background-mmin)/(mmax-mmin);

    % Round and cast into uint8 so that it is a valid grayscale image
    background = uint8(round(background));

    % Now display the result
    figure
    imshow(background)

    % Add objects in the foreground
    img = background;
    img(100:200,100:200) = 255;
    img(150:450,150:350) = 128;

    % Display the final image
    imshow(img)

You could also do a gradient across the image. For example:

    % Create a vector of linearly varying values in x from 100 to 200
    x = linspace(100,200,N);
    y = 1:N;

    % Transform into a grid
    [X,Y] = meshgrid(x,y);

    % Define the background
    background = uint8(round(X));

    % Display
    imshow(background)

    % Add objects in foreground
    ...

[Jay]

The best way is to form the bivariate polynomials.

 I = ones(300);
 %creating a bias profile using polynomial modeling
 [x,y] = meshgrid(1:size(I,1),1:size(I,2));

 profile = -7.5.*x.^3 - 8.5.* y.^3 + 01.25 .*(x.* y.^2) - 0.3*( x.^2 .* y ) - 0.5.* x .* y - x + y  - 2.5*( x.^2) - y.^2 + 0.5 .* x .*y + 1;

Basically you just take the combination of different order of the x and y products, with the manual pick of constants as I did here.

Although it is 3rd order polynomial, you can create shading of any polynomial you wish.