How can we perform cumulative sums along a particular directions in matrices?

Hi all,

I'm actually trying to perform cumulative sums along arbitrary directions in images. For sure a simple sum can be done with the radon() function, however I need to keep track of an integral, thus requiring a cumsum(). I've tried to use imrotate() and then cumsum() but initial and final images don't have the same dimensions anymore, causing another problem.

Any help would be really appreciated!

Regards,

Simon

[the cyclist]

It might be helpful to give a small example or two of inputs and expected outputs.

Answer 1

[Image Analyst]

I pretty sure there's nothing built in to MATLAB or the Image Processing Toolbox to do that. You'd have to program it up yourself. Sorry, but it's just such a unique requirement that there's no code yet to do that as far as I know. It can be done though. You might find improfile() helpful as you scan across, at one pixel spacings or whatever you require, getting profiles and calling cumsum().

[Simon]

Alright, this is what I thought. I came up recently with something that seems to be a pretty good approximation of what I need. It looks like the following lines:

% Creating Image

A=phantom();

% Rotating frame at angle phi

B=imrotate(A,-phi);

% Performing cumulative sum

B=cumsum(B,1);

% Returning back to reference frame

B=imrotate(A,phi);

Then I crop the final image B with imcrop() since two calls of imrotate() doubles image dimensions. It can be extended to image stacks by simply operating a for-loop on imcrop().

It seems to work well, but if anyone has a better idea, please let me know!

Thanks for the proposal,

Simon

[Image Analyst]

Sounds reasonable to me. If it works well, as you say, then use it.

Answer 2

[the cyclist]

Direct from the documentation:

B = cumsum(A,dim) returns the cumulative sum of the elements along dimension dim.

Does that help?

So,

A = magic(5);

B_down   = cumsum(A,1); % Cumulative sum down columns (the default)
B_across = cumsum(A,2); % Cumulative sum across the rows

[Simon]

No, it is not that simple, I think there is a misunderstanding about the question.

I want to do a cumsum at an arbitrary projection angle. The radon() does exactly that, but is not cumulative. I need something of the form:

A=phantom(); B=cumsum_dir(A,phi);

Where the cumsum() is executed at angle phi from the reference frame.

I hope this is clearer.

Thanks for the answer,

Simon