Given an image , how to efficiently (vectorization) make all the elements to zero except the one with information?

The image is scaled color version of absolute value of the matrix.

Answer 1

[Image Analyst]

This will do it:

clc;    % Clear the command window.
clearvars;
close all;  % Close all figures (except those of imtool.)
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;fontSize = 22;

s = load('image_data.mat')
D = s.D;
realD = abs(real(D));
imagD = abs(imag(D));

subplot(2, 3, 1);
imshow(realD, []);
axis square
title('Real Image', 'FontSize', fontSize);
impixelinfo();

subplot(2, 3, 2);
histogram(realD);
grid on;
title('Histogram of Real Image', 'FontSize', fontSize);

subplot(2, 3, 4);
imshow(imagD, []);
axis square
title('Imaginary Image', 'FontSize', fontSize);
impixelinfo();

subplot(2, 3, 5);
histogram(imagD);
grid on;
title('Histogram of Imaginary Image', 'FontSize', fontSize);

backgroundValueR = 5e8;
backgroundValueI = 3e8;
binaryImageR = realD > backgroundValueR;
binaryImageI = imagD > backgroundValueI;
subplot(2, 3, 3);
imshow(binaryImageR, []);
axis square
impixelinfo();
title('Real Image, binarized', 'FontSize', fontSize);

subplot(2, 3, 6);
imshow(binaryImageI, []);
axis square
impixelinfo();
title('Imaginary Image, binarized', 'FontSize', fontSize);

% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);

% Apply the mask
% Mask the image using bsxfun() function to multiply the mask by each channel individually.
maskedRealImage = bsxfun(@times, realD, cast(binaryImageR, 'like', realD));
maskedImagImage = bsxfun(@times, imagD, cast(binaryImageI, 'like', imagD));

figure;
subplot(2, 1, 1);
imshow(maskedRealImage, []);
axis square
impixelinfo();
title('Masked Real Image, binarized', 'FontSize', fontSize);

subplot(2, 1, 2);
imshow(maskedImagImage, []);
axis square
impixelinfo();
title('Masked Imaginary Image, binarized', 'FontSize', fontSize);

[D_coder]

what does '.D' do? How did you select the background value for real part and imaginary part? Is there any automatic way of doing that? If the image is inside a loop and everytime it changes little by little I want to automatically adapt the mask by automatically selecting background value. How do I convert real and imaginary binarized images back to their original form. Since I need to multiply them with another matrix. Here is my pseudo code to make you understand better

My pseudo

if true
  This is my pseudo code
 for numberofiterations
     maskedimage = maskedimage.*Anotherimage OR (realmasked +i*imaginarymasked).*Anotherimage

end

[Image Analyst]

load() returns a structure, which I call s. The members/fields of the structure are the variable names you used. So I called D=s.D to take the "D" field of the "s" structure and put it into a simpler variable called D.

You can inspect the histogram and use that to find a threshold. It really depends on what your images look like in general. Like do they vary in intensity? Does that thing change its size dramatically?

[D_coder]

is there any automatic way of selecting the threshold without any intervention.Since my image is inside the loop . How do I convert binarized image to the original form keeping the information and making everything else zero

[Image Analyst]

What if you just take the peak of the histogram and run down from the peak until you hit a certain percentage of its height?

[D_coder]

How do I convert binarized image to the original form keeping the information and making everything else zero

[Image Analyst]

If you want a complex image again, but masked by the binary image, simply combine the real and imaginary masked images:

complexImage = complex(maskedRealImage, maskedImagImage);

[D_coder]

backgroundValueR = 5e8; backgroundValueI = 3e8; HOW TO GET THESE AUTOMATICALLY WITHOUT INTERVENTION INSIDE A LOOP

[Image Analyst]

I gave two comments above telling you how to do that. You inspect the histogram. It's a judgement call - there are lots of values you could use so just decide where in the histogram you want to threshold it.

[D_coder]

got it thanks

Answer 2

[Image Analyst]

Probably thresholding and masking.

mask = theImage ~= backgroundValue; % Threshold.
theImage(mask) = 0; % Mask

Attach your data in a .mat file if you want more help.