How to compute radon transform with invariant properties

Question

I try to work the R transformation that, according with what is written in the scientific article "Recognition of Human Home Activities via Depth Silhouettes and R Transformation for Smart Homes", is computed in this way:

where

In Matlab I get the radon transform with:

[R,xp] = radon(Silhouette,theta);

Then, according with what is written this article, I compute the R transformation by adding,for every angle (that are the columns of R), the square of radon transform values (that, setting the column, are on the rows of R). But for each column this sum is the same. Where am I wrong?

Thanks for your support.

Answer 1

With the provided evidence I can only speculate on things that might be wrong.

If you get the same values after the integration (summation) you might want to check for bad values (or provide details/examples) on i) the way you define angle theta (range, degrees or radians etc.) ii) your Silhouette data.

Using MATLAB's example for theradon function, your profile should be extracted somewhat similar to:

% input image
I = zeros(100,100); I(25:75, 25:75) = 1;

theta = 0:180;
[R,xp] = radon(I, theta);

Rt = sum(R.^2, 1);
figure; plot(theta, Rt);