% make a demo of circle in square shadow 
   [x,y]=meshgrid(1:32);x=x-16;y=y-16;
   circIm=x.^2+y.^2<8^2;
   

% create 2*fnum+1 images of the same scene with different illumination.
% specifically, create a square shadow and move it along the image
% according to the index of the iamge.


% bigIm1 is an array of input images.
% Here we produce these images from the base image by applying different
% illuminations.
   
   fnum=1;
   bigIm1=zeros(32,32,2*fnum+1);
   
   for i=-fnum:fnum
     im1=zeros(32);
     im1(i+16-10:i+16+10,i+16-10:i+16+10)=0.6;  % this puts shadow
     im1=im1+circIm;
     bigIm1(:,:,i+fnum+1)=im1;
   end
   
   % and now get albedo
 
   % to debug
   bigIm1=bigIm1+1;
   
   % for boundary conditions we assume the boundary of the image
   % is set to zero
   bigIm1=zeroB(bigIm1,2);


% Albedo is computed using the Intrinsic Images decomposition algorithm
% (i.e. taking the median of the partial derivatives).
% This is actually the heart of the program.
% Images are created ahead as log images, and passed to getAlbedo
% as such.

   [imR,dxs,dys,dx,dy]=getAlbedo(bigIm1);
   
   figure(1);
   show(bigIm1(:,:,1));
   title('frame 1');
   figure(2);
   show(imR);
   title('reflectance');
   % to get lighting we subtract median lighting from the gradient
   % and reconstruct
   
   figure(3);
   %light1=reconsEdge3(dxs(:,:,1)-dx,dys(:,:,1)-dy);%,invKhat);
   light1 = solvePoisson(dxs(:,:,1)-dx,dys(:,:,1)-dy);
   show(light1);
   title('lighting frame 1');