Continuous monochrome image sampling

How can I sample a continuous monochrome image (f(x, y) = x(1 − y) + y(1 − x), 0 ≤ x ≤ 1, 0 ≤ y ≤ 1) to a discrete image with with 5 x 7 pixels by letting the lower left pixel be a sample from point (0,0) and the upper right from (1,1)?

How it could be quantify the discrete image with 32 different gray levels from 0 to 31??

Answer 1

[Walter Roberson]

xvec = linspace(0,1,7);  %x is columns
yvec = linspace(0,1,5);  %y is rows
[X, Y] = meshgrid(xvec, yvec);
F = X.*(1-Y) + Y.*(1-X);

imagesc(F); colormap(gray)

[Ahmad Alosta]

Thanks, it was really helpful. But how it could be quantify with 32 different gray levels from 0 to 31??

[Image Analyst]

You'd need to adjust the first 2 lines so that you have an array of 32, like

xvec = linspace(0,1,8);  %x is columns
yvec = linspace(0,1,4);  %y is rows
[X, Y] = meshgrid(xvec, yvec);
F = 32 * (X.*(1-Y) + Y.*(1-X)); % Gray levels range fromm 0 to 32.
imagesc(F); 
colormap(gray);

%impixelinfo; % Uncomment in your own code (can't be used online).

[Walter Roberson]

For the case where what you care about is 32 gray levels

xvec = linspace(0,1,7);  %x is columns
yvec = linspace(0,1,5);  %y is rows
[X, Y] = meshgrid(xvec, yvec);
F = X.*(1-Y) + Y.*(1-X);

imagesc(F); colormap(gray(32))

For the case where you do care about the array being represented as 0 to 31

xvec = linspace(0,1,7);  %x is columns
yvec = linspace(0,1,5);  %y is rows
[X, Y] = meshgrid(xvec, yvec);
F = X.*(1-Y) + Y.*(1-X);

Fq = floor(rescale(F,0,32*(1-eps)));
imagesc(Fq); colormap(gray(32))

[Ahmad Alosta]

Thanks a lot :)