energy.h
/* energy.h */
/* Vladimir Kolmogorov (vnk@cs.cornell.edu), 2003. */
/*
This software implements an energy minimization technique described in
What Energy Functions can be Minimized via Graph Cuts?
Vladimir Kolmogorov and Ramin Zabih.
To appear in IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI).
Earlier version appeared in European Conference on Computer Vision (ECCV), May 2002.
More specifically, it computes the global minimum of a function E of binary
variables x_1, ..., x_n which can be written as a sum of terms involving
at most three variables at a time:
E(x_1, ..., x_n) = \sum_{i} E^{i} (x_i)
+ \sum_{i,j} E^{i,j} (x_i, x_j)
+ \sum_{i,j,k} E^{i,j,k}(x_i, x_j, x_k)
The method works only if each term is "regular". Definitions of regularity
for terms E^{i}, E^{i,j}, E^{i,j,k} are given below as comments to functions
add_term1(), add_term2(), add_term3().
This software can be used only for research purposes. IF YOU USE THIS SOFTWARE,
YOU SHOULD CITE THE AFOREMENTIONED PAPER IN ANY RESULTING PUBLICATION.
In order to use it, you will also need a MAXFLOW software which can be
obtained from http://www.cs.cornell.edu/People/vnk/software.html
Example usage
(Minimizes the following function of 3 binary variables:
E(x, y, z) = x - 2*y + 3*(1-z) - 4*x*y + 5*|y-z|):
///////////////////////////////////////////////////
#include <stdio.h>
#include "energy.h"
void main()
{
// Minimize the following function of 3 binary variables:
// E(x, y, z) = x - 2*y + 3*(1-z) - 4*x*y + 5*|y-z|
Energy::Var varx, vary, varz;
Energy *e = new Energy();
varx = e -> add_variable();
vary = e -> add_variable();
varz = e -> add_variable();
e -> add_term1(varx, 0, 1); // add term x
e -> add_term1(vary, 0, -2); // add term -2*y
e -> add_term1(varz, 3, 0); // add term 3*(1-z)
e -> add_term2(x, y, 0, 0, 0, -4); // add term -4*x*y
e -> add_term2(y, z, 0, 5, 5, 0); // add term 5*|y-z|
Energy::TotalValue Emin = e -> minimize();
printf("Minimum = %d\n", Emin);
printf("Optimal solution:\n");
printf("x = %d\n", e->get_var(varx));
printf("y = %d\n", e->get_var(vary));
printf("z = %d\n", e->get_var(varz));
delete e;
}
///////////////////////////////////////////////////
*/
#ifndef __ENERGY_H__
#define __ENERGY_H__
#include <assert.h>
#include "graph.h"
template <typename captype, typename tcaptype, typename flowtype> class Energy: public Graph<captype,tcaptype,flowtype>
{
typedef Graph<captype,tcaptype,flowtype> GraphT;
public:
typedef typename GraphT::node_id Var;
/* Types of energy values.
Value is a type of a value in a single term
TotalValue is a type of a value of the total energy.
By default Value = short, TotalValue = int.
To change it, change the corresponding types in graph.h */
typedef captype Value;
typedef flowtype TotalValue;
/* interface functions */
/* Constructor. Optional argument is the pointer to the
function which will be called if an error occurs;
an error message is passed to this function. If this
argument is omitted, exit(1) will be called. */
Energy(int var_num_max, int edge_num_max, void (*err_function)(char *) = NULL);
/* Destructor */
~Energy();
/* Adds a new binary variable */
Var add_variable(int num=1);
/* Adds a constant E to the energy function */
void add_constant(Value E);
/* Adds a new term E(x) of one binary variable
to the energy function, where
E(0) = E0, E(1) = E1
E0 and E1 can be arbitrary */
void add_term1(Var x,
Value E0, Value E1);
/* Adds a new term E(x,y) of two binary variables
to the energy function, where
E(0,0) = E00, E(0,1) = E01
E(1,0) = E10, E(1,1) = E11
The term must be regular, i.e. E00 + E11 <= E01 + E10 */
void add_term2(Var x, Var y,
Value E00, Value E01,
Value E10, Value E11);
/* Adds a new term E(x,y,z) of three binary variables
to the energy function, where
E(0,0,0) = E000, E(0,0,1) = E001
E(0,1,0) = E010, E(0,1,1) = E011
E(1,0,0) = E100, E(1,0,1) = E101
E(1,1,0) = E110, E(1,1,1) = E111
The term must be regular. It means that if one
of the variables is fixed (for example, y=1), then
the resulting function of two variables must be regular.
Since there are 6 ways to fix one variable
(3 variables times 2 binary values - 0 and 1),
this is equivalent to 6 inequalities */
void add_term3(Var x, Var y, Var z,
Value E000, Value E001,
Value E010, Value E011,
Value E100, Value E101,
Value E110, Value E111);
/* After the energy function has been constructed,
call this function to minimize it.
Returns the minimum of the function */
TotalValue minimize();
/* After 'minimize' has been called, this function
can be used to determine the value of variable 'x'
in the optimal solution.
Returns either 0 or 1 */
int get_var(Var x);
/***********************************************************************/
/***********************************************************************/
/***********************************************************************/
private:
/* internal variables and functions */
TotalValue Econst;
void (*error_function)(char *); /* this function is called if a error occurs,
with a corresponding error message
(or exit(1) is called if it's NULL) */
};
/***********************************************************************/
/************************ Implementation ******************************/
/***********************************************************************/
template <typename captype, typename tcaptype, typename flowtype>
inline Energy<captype,tcaptype,flowtype>::Energy(int var_num_max, int edge_num_max, void (*err_function)(char *)) : Graph<captype,tcaptype,flowtype>(var_num_max, edge_num_max, err_function)
{
Econst = 0;
error_function = err_function;
}
template <typename captype, typename tcaptype, typename flowtype>
inline Energy<captype,tcaptype,flowtype>::~Energy() {}
template <typename captype, typename tcaptype, typename flowtype>
inline typename Energy<captype,tcaptype,flowtype>::Var Energy<captype,tcaptype,flowtype>::add_variable(int num)
{ return GraphT::add_node(num); }
template <typename captype, typename tcaptype, typename flowtype>
inline void Energy<captype,tcaptype,flowtype>::add_constant(Value A) { Econst += A; }
template <typename captype, typename tcaptype, typename flowtype>
inline void Energy<captype,tcaptype,flowtype>::add_term1(Var x,
Value A, Value B)
{
this->add_tweights(x, B, A);
}
template <typename captype, typename tcaptype, typename flowtype>
inline void Energy<captype,tcaptype,flowtype>::add_term2(Var x, Var y,
Value A, Value B,
Value C, Value D)
{
/*
E = A A + 0 B-A
D D C-D 0
Add edges for the first term
*/
this->add_tweights(x, D, A);
B -= A; C -= D;
/* now need to represent
0 B
C 0
*/
assert(B + C >= 0); /* check regularity */
if (B < 0)
{
/* Write it as
B B + -B 0 + 0 0
0 0 -B 0 B+C 0
*/
this->add_tweights(x, 0, B); /* first term */
this->add_tweights(y, 0, -B); /* second term */
this->add_edge(x, y, 0, B+C); /* third term */
}
else if (C < 0)
{
/* Write it as
-C -C + C 0 + 0 B+C
0 0 C 0 0 0
*/
this->add_tweights(x, 0, -C); /* first term */
this->add_tweights(y, 0, C); /* second term */
this->add_edge(x, y, B+C, 0); /* third term */
}
else /* B >= 0, C >= 0 */
{
this->add_edge(x, y, B, C);
}
}
template <typename captype, typename tcaptype, typename flowtype>
inline void Energy<captype,tcaptype,flowtype>::add_term3(Var x, Var y, Var z,
Value E000, Value E001,
Value E010, Value E011,
Value E100, Value E101,
Value E110, Value E111)
{
Value pi = (E000 + E011 + E101 + E110) - (E100 + E010 + E001 + E111);
Value delta;
Var u;
if (pi >= 0)
{
Econst += E111 - (E011 + E101 + E110);
add_tweights(x, E101, E001);
add_tweights(y, E110, E100);
add_tweights(z, E011, E010);
delta = (E010 + E001) - (E000 + E011); /* -pi(E[x=0]) */
assert(delta >= 0); /* check regularity */
add_edge(y, z, delta, 0);
delta = (E100 + E001) - (E000 + E101); /* -pi(E[y=0]) */
assert(delta >= 0); /* check regularity */
add_edge(z, x, delta, 0);
delta = (E100 + E010) - (E000 + E110); /* -pi(E[z=0]) */
assert(delta >= 0); /* check regularity */
add_edge(x, y, delta, 0);
if (pi > 0)
{
u = add_variable();
add_edge(x, u, pi, 0);
add_edge(y, u, pi, 0);
add_edge(z, u, pi, 0);
add_tweights(u, 0, pi);
}
}
else
{
Econst += E000 - (E100 + E010 + E001);
add_tweights(x, E110, E010);
add_tweights(y, E011, E001);
add_tweights(z, E101, E100);
delta = (E110 + E101) - (E100 + E111); /* -pi(E[x=1]) */
assert(delta >= 0); /* check regularity */
add_edge(z, y, delta, 0);
delta = (E110 + E011) - (E010 + E111); /* -pi(E[y=1]) */
assert(delta >= 0); /* check regularity */
add_edge(x, z, delta, 0);
delta = (E101 + E011) - (E001 + E111); /* -pi(E[z=1]) */
assert(delta >= 0); /* check regularity */
add_edge(y, x, delta, 0);
u = add_variable();
add_edge(u, x, -pi, 0);
add_edge(u, y, -pi, 0);
add_edge(u, z, -pi, 0);
add_tweights(u, -pi, 0);
}
}
template <typename captype, typename tcaptype, typename flowtype>
inline typename Energy<captype,tcaptype,flowtype>::TotalValue Energy<captype,tcaptype,flowtype>::minimize() {
return Econst + GraphT::maxflow(); }
template <typename captype, typename tcaptype, typename flowtype>
inline int Energy<captype,tcaptype,flowtype>::get_var(Var x) { return (int) this->what_segment(x); }
#endif
