I need help for creating a point with 2x2 pixels , a line of 2x200 pixels and 256x256 solid square to produce a sinogram by using sinogram function.

Hello! I need help for creating a point with 2x2 pixels , a line of 2x200 pixels and 256x256 solid square to produce a sinogram by using sinogram function. I wrote the code for square down below:

%Creating the square image of 256x256 pixels

Image_sqr = zeros(256,256);

Image_sqr(128:129, 128:129) = 1;

imshow(Image_sqr);

title('Square Image')

%Radon transform for producing sinogram

theta=0:180;

imagesc(theta, 1:size(p,1), p);

%Sinogram

figure;

imagesc(theta, q, p);

title('Sinogram of a Square');

xlabel('Projection Angle Theta');

ylabel('Position');

colormap(hot);

colorbar;

I could not get a triangular sinusoidal image. I could not figure out what I am doing wrong and in addition to taht I don't know how to do this process with a point and a line. Could you please help me?

Answer 1

[Tushar Sharma]

Hi Fatma,

Your code for creating a square and attempting to generate its sinogram is close, but it seems like you missed the actual Radon transform step. Here's the corrected complete code:

% Creating the square image of 256x256 pixels
Image_sqr = zeros(256,256);
Image_sqr(128:129, 128:129) = 1; % This creates a 2x2 square in the center
imshow(Image_sqr); 
title('Square Image');

% Radon transform for producing sinogram
theta = 0:179; % 180 is unnecessary as 0 and 180 are the same due to symmetry
[R, xp] = radon(Image_sqr, theta);

% Displaying the sinogram
figure; 
imagesc(theta, xp, R); 
title('Sinogram of a Square');
xlabel('Projection Angle Theta'); 
ylabel('Position');
colormap(hot);
colorbar;

Similarly, a point can be represented by setting a single pixel to 1 in an otherwise zero matrix.

Also, a line can be created by setting a row or a column (or any arbitrary set of pixels) to 1.

Please refer to the below code for generating a sinogram for a line -

% Creating a line image of 256x256 pixels
Image_line = zeros(256,256);
Image_line(:,128:129) = 1; % This creates a vertical line of 2x200 pixels
imshow(Image_line); 
title('Line Image');

% Radon transform for producing sinogram
[R_line, xp] = radon(Image_line, theta);

% Displaying the sinogram
figure; 
imagesc(theta, xp, R_line); 
title('Sinogram of a Line');
xlabel('Projection Angle Theta'); 
ylabel('Position');
colormap(hot);
colorbar;

The sinogram of a point will look like a sinusoidal line due to its projection at different angles, while the line and square will have different patterns based on their shapes and the angles of projection.

Hope it helps!

[Fatma Beyza]

Thank you so much for your help!