% projections.m

%% This MATLAB function takes an image matrix and vector of angles and then 
%% finds the 1D projection (Radon transform) at each of the angles.  It returns
%% a matrix whose columns are the projections at each angle.
%%
%% Written by : Justin K. Romberg

function PR = projections(IMG, THETA)

% pad the image with zeros so we don't lose anything when we rotate.
[iLength, iWidth] = size(IMG);
iDiag = sqrt(iLength^2 + iWidth^2);
LengthPad = ceil(iDiag - iLength) + 2;
WidthPad = ceil(iDiag - iWidth) + 2;
padIMG = zeros(iLength+LengthPad, iWidth+WidthPad);
padIMG(ceil(LengthPad/2):(ceil(LengthPad/2)+iLength-1), ...
       ceil(WidthPad/2):(ceil(WidthPad/2)+iWidth-1)) = IMG;

% loop over the number of angles, rotate 90-theta (because we can easily sum
% if we look at stuff from the top), and then add up.  Don't perform any
% interpolation on the rotating.
n = length(THETA);
PR = zeros(size(padIMG,2), n);
for i = 1:n
   tic
   tmpimg = imrotate(padIMG, 90-THETA(i), 'bilinear', 'crop');
   PR(:,i) = (sum(tmpimg))';
   THETA(i)
   toc
end