function [flow,labels] = maxflow(A,T)
%MAXFLOW Max-flow/min-cut calculation using the
% Boykov-Kolmogorov's algorithm. Let G=(V,E) be
% a directed graph with |V| vertices and |E| edges.
% w:(i,j)-->R, (i,j) in E, a weight function on the graph's
% edges.
%
% A (smoothness term) - a sparse matrix of size |V|x|V| containing, where
% A(i,j) = w(i,j). Typically, for a grid graph, the node
% indices would be taken in column-major order, but it is not assumed.
% T (data term) - a sparse matrix of size |V|x|L|, where |L| is the number
% of labels (The library currently supports |L|=2 only).
% T(i,j) = the cost of assigning label j to node i.
%
% flow - the calculated maximum flow value
% labels - a vector of size |V|, where labels(i) is 0 or 1 if
% node i belongs to S (source) or T (sink) respectively.
%
% Also refer to the following link for tips on creating large
% sparse matrices efficiently.
% In case of a dense adjacency matrix B, simply wrap it in a
% sparse structure before passing it to this function:
% A = sparse(B);
% [flow,labels] = maxflow(A,T);
%
% This library can be used for reseatch purposes only, and is
% supplied with no guarantees.
%
% (c) 2008 Michael Rubinstein, WDI R&D and IDC
% $Revision: 140 $
% $Date: 2008-09-15 15:35:01 -0700 (Mon, 15 Sep 2008) $
%
[flow,labels] = maxflowmex(A,T);
% release the dll
clear maxflowmex
end
