% function U = pargrp(M)
% Input:
%   M = mask, pixels of the same label except the minimum one
%       are constrained to group together
% Output:
%   U = partial grouping constraints, such that U'X = 0
%       specify the partial grouping info
%

% Stella X. Yu, July 12 2003.


function U = pargrp(M)

if isempty(M),
    U = [];
    return;
end

m = min(M(:)); % the minimum label is ignored
n = max(M(:));
i = [];
j = [];
v = [];
nu = 0;
for k=m+1:n,
    t = find(M==k);
    s = length(t);
    if s<2,
        continue;
    end
    i = [i; t(1:s-1); t(2:s)];
    
    z = nu+[1:s-1]';
    j = [j; z; z];
    nu = z(end);

    z = ones(s-1,1);
    v = [v; z; -z];
end
U = sparse(i,j,v,prod(size(M)),nu);