function predictedLaplaceDepthMap = applyLaplacianSmoothing(d_naive, nImages)
% This function would not make sense by itself.
% It is just to give a better idea of what Q matrix is in the IJCV paper at:
% http://ai.stanford.edu/~asaxena/learningdepth/
% In a simplified example: If d = [d_1 d_2 d_3] gives the depth of a 3x1 image, for example.
% Then if Q = [1 -1 0; 0 1 -1],
% then Q d = [d_1 - d_2;   d_2 - d_3 ]
% then || Q d ||_1 = |d_1-d_2| + |d_2-d_3|
% therefore you get differences in depth of neighboring patches.
%
% (This does not uses learned variances for inference.)
% Author = Ashutosh Saxena; however do not bug him about the code.

% This code is copyrighted by Ashutosh Saxena, Stanford University
% It is available for non-commercial use only. For commericial use, please
% contact the authors.
% Any publication or report resulting from Use of this code, should cite:
% Learning Depth from Single Monocular Images, Ashutosh Saxena, Sung H. Chung, Andrew Y. Ng, NIPS 2005.
% 3-D Depth Reconstruction from a Single Still Image, Ashutosh Saxena, Sung H. Chung, Andrew Y. Ng, To appear in IJCV 2007.
% For more info, visit: http://ai.stanford.edu/~asaxena/learningdepth/

global nGridRow nGridCol
configurationFile;

d_naive_img = reshape(permute( reshape( d_naive, [nGridCol, nImages, nGridRow]), [3 1 2]), ...
    [nGridRow*nGridCol nImages]);
clear d_naive;

totalnDepths = nGridRow*nGridCol;
I = sparse(eye(totalnDepths));
I_minus_Py = sparse(I - I([(nGridCol+1):end (end-nGridCol+1):end],:) );                     %== ERROR ... ERROR

XShiftIndices = [];
for r = 0:(nGridRow-1)
    XShiftIndices = [XShiftIndices r*nGridCol + [2:nGridCol, nGridCol] ];
end

I_minus_Px = sparse(I - I(XShiftIndices,:) );  

% first try without variance
for n= 1:nImages
    %boundary case not properly taken care of
    if mod(n,10) == 0,     disp(num2str(n));    end
    tmp = linprog(  [ repmat(0,totalnDepths,1); repmat(1,3*totalnDepths,1)], ...
                    [ speye(totalnDepths),    -speye(totalnDepths),     0*speye(totalnDepths), 0*speye(totalnDepths); ...
                      -speye(totalnDepths),   -speye(totalnDepths),     0*speye(totalnDepths), 0*speye(totalnDepths); ...
                      I_minus_Px,           0*speye(totalnDepths),    -speye(totalnDepths),  0*speye(totalnDepths); ...
                      -I_minux_Px,          0*speye(totalnDepths),    -speye(totalnDepths),  0*speye(totalnDepths); ...
                      I_minus_Py,           0*speye(totalnDepths),    0*speye(totalnDepths), -speye(totalnDepths);  ...
                      -I_minus_Py,          0*speye(totalnDepths),    0*speye(totalnDepths), -speye(totalnDepths)  ], ...
                    [d_naive_img(:,n);  d_naive_img(:,n);   repmat(0,totalnDepths*4,1)] );

    laplaceDepthVector(:,n) = tmp(1:totalnDepths);
end

predictedLaplaceDepthMap = reshape(laplaceDepthVector, [nGridRow nGridCol nImages]);