vmquantc.m

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%%%     if wi
%%%         varg(vind) = (M1i * M1i') / wi;
%%%     end
%%%        M1diff = M1box - M1i;
%%%     wdiff = wbox - wi;
%%%     if wdiff
%%%         varg(vind) = varg(vind) + (M1diff * M1diff') / wdiff;
%%%     end
%%%    end % for i (green)
%%%    if isempty(varg)
%%%     varg = -1;
%%%    end
%%% 
%%%%       Find point of minimum variance in b dimension of box.
%%% 
%%%    M0base = sum( M0( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%        [boxur(box,2) boxll(box,2)], [boxll(box,3) boxll(box,3)] ) ) - ...
%%%        M0( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%        [boxll(box,2) boxur(box,2)], [boxll(box,3) boxll(box,3)] ) ) );
%%%    M1base = [sum( M1r( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%            [boxur(box,2) boxll(box,2)], [boxll(box,3) boxll(box,3)] ) ) - ...
%%%            M1r( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxur(box,2)], [boxll(box,3) boxll(box,3)] ) ) ) ...
%%%        sum( M1g( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%            [boxur(box,2) boxll(box,2)], [boxll(box,3) boxll(box,3)] ) ) - ...
%%%            M1g( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxur(box,2)], [boxll(box,3) boxll(box,3)] ) ) ) ...
%%%        sum( M1b( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%            [boxur(box,2) boxll(box,2)], [boxll(box,3) boxll(box,3)] ) ) - ...
%%%            M1b( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxur(box,2)], [boxll(box,3) boxll(box,3)] ) ) )];
%%% 
%%%    varb = zeros(1,boxur(box,3)-boxll(box,3)-1); % Allocate space for the array.
%%%    for i=boxll(box,3)+1:boxur(box,3)-1
%%%        wi = M0base + ...
%%%         sum( M0( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxur(box,2)], [i i] ) ) - ...
%%%            M0( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%            [boxur(box,2) boxll(box,2)], [i i] ) ) );
%%%        M1i = M1base + ...
%%%         [sum( M1r( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxur(box,2)], [i i] ) ) - ...
%%%            M1r( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%            [boxur(box,2) boxll(box,2)], [i i] ) ) ) ...
%%%            sum( M1g( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxur(box,2)], [i i] ) ) - ...
%%%            M1g( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%            [boxur(box,2) boxll(box,2)], [i i] ) ) ) ...
%%%            sum( M1b( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxur(box,2)], [i i] ) ) - ...
%%%            M1b( elem3d( rgbsize, [boxll(box,1) boxur(box,1)], ...
%%%            [boxur(box,2) boxll(box,2)], [i i] ) ) )];
%%%     vind = i - boxll(box,3);        % Inefficient.
%%%     if wi
%%%         varb(vind) = (M1i * M1i') / wi;
%%%     end
%%%        M1diff = M1box - M1i;
%%%     wdiff = wbox - wi;
%%%     if wdiff
%%%         varb(vind) = varb(vind) + (M1diff * M1diff') / wdiff;
%%%     end
%%%    end % for i (blue)
%%%    if isempty(varb)
%%%     varb = -1;
%%%    end
%%% 
%%%%    Find the partition point with the minimum variance.
%%%
%%%    [minvarr minindr] = max(varr);
%%%    [minvarg minindg] = max(varg);
%%%    [minvarb minindb] = max(varb);
%%%    [minvar mindim] = max([minvarr minvarg minvarb]);
%%%
%%%    boxr = size( boxll, 1 );
%%%    if mindim == 1   % Cut in red dimension.
%%%     minindr = minindr + boxll(box,1);
%%%        if box == boxr
%%%            boxll = [boxll(1:box,:); minindr boxll(box,2) boxll(box,3)];
%%%     else
%%%         boxll = [boxll(1:box,:); minindr boxll(box,2) boxll(box,3); ...
%%%             boxll(box+1:boxr,:)];
%%%         E(box+2:boxr+1) = E(box+1:boxr);    % Make space in E.
%%%     end % if box == boxr
%%%     boxur = [boxur(1:box-1,:); minindr boxur(box,2) boxur(box,3); ...
%%%         boxur(box:boxr,:)];
%%%    elseif mindim == 2       % Cut in green dimension.
%%%     minindg = minindg + boxll(box,2);
%%%     if box == boxr
%%%         boxll = [boxll(1:box,:); boxll(box,1) minindg boxll(box,3)];
%%%     else
%%%         boxll = [boxll(1:box,:); boxll(box,1) minindg boxll(box,3); ...
%%%             boxll(box+1:boxr,:)];
%%%         E(box+2:boxr+1) = E(box+1:boxr);    % Make space in E.
%%%     end % if box == boxr
%%%     boxur = [boxur(1:box-1,:); boxur(box,1) minindg boxur(box,3); ...
%%%         boxur(box:boxr,:)];
%%%    else             % Cut in blue dimension.
%%%     minindb = minindb + boxll(box,3);
%%%     if box == boxr
%%%         boxll = [boxll(1:box,:); boxll(box,1) boxll(box,2) minindb];
%%%     else
%%%         boxll = [boxll(1:box,:); boxll(box,1) boxll(box,2) minindb; ...
%%%             boxll(box+1:boxr,:)];
%%%         E(box+2:boxr+1) = E(box+1:boxr);    % Make space in E.
%%%     end % if box == boxr
%%%     boxur = [boxur(1:box-1,:); boxur(box,1) boxur(box,2) minindb; ...
%%%         boxur(box:boxr,:)];
%%%    end % if mindim
%%%
%%%%       Compute variance of two new boxes.
%%%
%%%    boxr = box;
%%%    for box=boxr:boxr+1
%%%      if sum(boxur(box,:)-boxll(box,:)) > 3     % Box can be subdivided.
%%%        E(box) = sum( M2( elem3d( rgbsize, ...
%%%            [boxll(box,1) boxll(box,1) boxur(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxur(box,2) boxll(box,2) boxur(box,2)], ...
%%%            [boxur(box,3) boxll(box,3) boxll(box,3) boxur(box,3)] ) ) - ...
%%%            M2( elem3d( rgbsize, ...
%%%            [boxll(box,1) boxll(box,1) boxur(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxur(box,2) boxll(box,2) boxur(box,2)], ...
%%%            [boxll(box,3) boxur(box,3) boxur(box,3) boxll(box,3)] ) ) );
%%%        wbox = sum( M0( elem3d( rgbsize, ...
%%%            [boxll(box,1) boxll(box,1) boxur(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxur(box,2) boxll(box,2) boxur(box,2)], ...
%%%            [boxur(box,3) boxll(box,3) boxll(box,3) boxur(box,3)] ) ) - ...
%%%            M0( elem3d( rgbsize, ...
%%%            [boxll(box,1) boxur(box,1) boxll(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxll(box,2) boxur(box,2) boxur(box,2)], ...
%%%            [boxll(box,3) boxur(box,3) boxur(box,3) boxll(box,3)] ) ) );
%%%        if wbox
%%%            M1box = [sum( M1r( elem3d( rgbsize, ...
%%%                [boxll(box,1) boxur(box,1) boxll(box,1) boxur(box,1)], ...
%%%                [boxur(box,2) boxll(box,2) boxll(box,2) boxur(box,2)], ...
%%%                [boxll(box,3) boxll(box,3) boxur(box,3) boxur(box,3)] ) ) - ...
%%%                M1r( elem3d( rgbsize, ...
%%%                [boxll(box,1) boxur(box,1) boxll(box,1) boxur(box,1)], ...
%%%                [boxll(box,2) boxur(box,2) boxur(box,2) boxll(box,2)], ...
%%%                [boxll(box,3) boxll(box,3) boxur(box,3) boxur(box,3)] ) ) ) ...
%%%                sum( M1g( elem3d( rgbsize, ...
%%%                [boxll(box,1) boxur(box,1) boxll(box,1) boxur(box,1)], ...
%%%                [boxur(box,2) boxll(box,2) boxll(box,2) boxur(box,2)], ...
%%%                [boxll(box,3) boxll(box,3) boxur(box,3) boxur(box,3)] ) ) - ...
%%%                M1g( elem3d( rgbsize, ...
%%%                [boxll(box,1) boxur(box,1) boxll(box,1) boxur(box,1)], ...
%%%                [boxll(box,2) boxur(box,2) boxur(box,2) boxll(box,2)], ...
%%%                [boxll(box,3) boxll(box,3) boxur(box,3) boxur(box,3)] ) ) ) ...
%%%                sum( M1b( elem3d( rgbsize, ...
%%%                [boxll(box,1) boxur(box,1) boxll(box,1) boxur(box,1)], ...
%%%                [boxur(box,2) boxll(box,2) boxll(box,2) boxur(box,2)], ...
%%%                [boxll(box,3) boxll(box,3) boxur(box,3) boxur(box,3)] ) ) - ...
%%%                M1b( elem3d( rgbsize, ...
%%%                [boxll(box,1) boxur(box,1) boxll(box,1) boxur(box,1)], ...
%%%                [boxll(box,2) boxur(box,2) boxur(box,2) boxll(box,2)], ...
%%%                [boxll(box,3) boxll(box,3) boxur(box,3) boxur(box,3)] ) ) )];
%%%            E(box) = E(box) - (M1box * M1box') / wbox;
%%%        else
%%%         disp(['Warning(2): Box with no population was created.']);
%%%         E(box) = 0;
%%%     end
%%%      else      % Box cannot be subdivided.
%%%        E(box) = 0;
%%%      end
%%%    end    % for box
%%%    waitbar( .1 + .6 * color / (k-1) );
%%%end  % for color
%%%
%%%%    Place each point in image into proper box.
%%%
%%%%    Build map of color values on top of M2.
%%%%        and
%%%%    Build matrix mapping rgb combo into boxes.
%%%
%%%boxr = size( boxll, 1 );
%%%map = zeros( boxr, 3 );
%%%for box=1:boxr
%%%  if ~realmap
%%%    map(box,:) = [sum( M1r( elem3d( rgbsize, ...
%%%         [boxll(box,1) boxur(box,1) boxll(box,1) boxur(box,1)], ...
%%%            [boxur(box,2) boxll(box,2) boxll(box,2) boxur(box,2)], ...
%%%         [boxll(box,3) boxll(box,3) boxur(box,3) boxur(box,3)] ) ) - ...
%%%            M1r( elem3d( rgbsize, ...
%%%         [boxll(box,1) boxur(box,1) boxll(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxur(box,2) boxur(box,2) boxll(box,2)], ...
%%%         [boxll(box,3) boxll(box,3) boxur(box,3) boxur(box,3)] ) ) ) ...
%%%        sum( M1g( elem3d( rgbsize, ...
%%%         [boxll(box,1) boxur(box,1) boxll(box,1) boxur(box,1)], ...
%%%            [boxur(box,2) boxll(box,2) boxll(box,2) boxur(box,2)], ...
%%%         [boxll(box,3) boxll(box,3) boxur(box,3) boxur(box,3)] ) ) - ...
%%%            M1g( elem3d( rgbsize, ...
%%%         [boxll(box,1) boxur(box,1) boxll(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxur(box,2) boxur(box,2) boxll(box,2)], ...
%%%         [boxll(box,3) boxll(box,3) boxur(box,3) boxur(box,3)] ) ) ) ...
%%%        sum( M1b( elem3d( rgbsize, ...
%%%         [boxll(box,1) boxur(box,1) boxll(box,1) boxur(box,1)], ...
%%%            [boxur(box,2) boxll(box,2) boxll(box,2) boxur(box,2)], ...
%%%         [boxll(box,3) boxll(box,3) boxur(box,3) boxur(box,3)] ) ) - ...
%%%            M1b( elem3d( rgbsize, ...
%%%         [boxll(box,1) boxur(box,1) boxll(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxur(box,2) boxur(box,2) boxll(box,2)], ...
%%%         [boxll(box,3) boxll(box,3) boxur(box,3) boxur(box,3)] ) ) )] / ...
%%%     sum( M0( elem3d( rgbsize, ...
%%%            [boxll(box,1) boxll(box,1) boxur(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxur(box,2) boxll(box,2) boxur(box,2)], ...
%%%            [boxur(box,3) boxll(box,3) boxll(box,3) boxur(box,3)] ) ) - ...
%%%            M0( elem3d( rgbsize, ...
%%%            [boxll(box,1) boxur(box,1) boxll(box,1) boxur(box,1)], ...
%%%            [boxll(box,2) boxll(box,2) boxur(box,2) boxur(box,2)], ...
%%%            [boxll(box,3) boxur(box,3) boxur(box,3) boxll(box,3)] ) ) );
%%%  end
%%%    indices = ndx3d( rgbsize, boxll(box,1)+1:boxur(box,1), ...
%%%        boxll(box,2)+1:boxur(box,2), boxll(box,3)+1:boxur(box,3) );
%%%    M2( indices ) =  box .* ones( size(indices) );
%%%%   for gi=boxll(box,2)+1:boxur(box,2)
%%%%    for bi=boxll(box,3)+1:boxur(box,3)
%%%%        [row col] = elem3d(rgbsize,boxll(box,1)+1:boxur(box,1),gi,bi);
%%%%        M2(row,col) = box .* ones(size(row))';
%%%%    end
%%%%   end
%%%    waitbar( .7 + .35 * box / boxr );
%%%end
%%%
%%%%    Map each rgb triple into image.
%%%
%%%if ~dith | realmap
%%%   im = M2( elem3d( rgbsize, rq, gq, bq ) );
%%%end
%%%
%%%%    Rescale color map to 0-1 or calculate means of boxes for real colormap.
%%%
%%%waitbar( 1 );
%%%
%%%if ~realmap
%%%    mapscale = rgbsize - 2;  % Map 0 onto 1 for 1d or 2d color space.
%%%    mapscale = mapscale + (mapscale == 0);   
%%%    map = (map - 2) ./ mapscale(ones(boxr,1),:);     % Map 2:Qx+1 to 0:1
%%%else
%%%    for box=1:boxr
%%%     indices = find( im == box );
%%%     map(box,1) = sum( r( indices ) ) / length( indices );
%%%     map(box,2) = sum( g( indices ) ) / length( indices );
%%%     map(box,3) = sum( b( indices ) ) / length( indices );
%%%    end % for box
%%%end
%%%
%%%if dith
%%%    im = dither( r, g, b, map, max(Q), Qe );
%%%end
%%%
%%%close( bar );

%%%function r = cumsum3d( size, matrix )
%%%%CUMSUM3D Cumulative sum of 3D matrix packed in a 2D matrix.
%%%%    B = CUMSUM3D( [M N P], A ) returns a M-by-N-by-P matrix B
%%%%    containing the cumulative sum of A, also a M-by-N-by-P matrix.
%%%%    Both B and A are stored in (M*N)-by-P matrices (see NDX3D).
%%%%    The cumulative sum is computed along all 3 axes.
%%%%
%%%
%%%%    Joseph M. Winograd 6-93
%%%%    $Revision: 5.6 $  $Date: 1997/11/24 15:56:50 $
%%%
%%%M = size(1);
%%%N = size(2);
%%%P = size(3);
%%%
%%%r = cumsum( reshape( cumsum( reshape( ...
%%%        cumsum( reshape( full(matrix), M, N*P ) )', ...
%%%        N, M*P ) )', P, M*N ) )';