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LevenbergMarquardtMinimizer.h
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LevenbergMarquardtMinimizer.h
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/***********************************************************************
LevenbergMarquardtMinimizer - Class to implement n-dimensional least-
squares minimization using a version of the modified Levenberg-Marquardt
algorithm.
Copyright (c) 2007-2010 Oliver Kreylos
This file is part of the Kinect 3D Video Capture Project (Kinect).
The Kinect 3D Video Capture Project is free software; you can
redistribute it and/or modify it under the terms of the GNU General
Public License as published by the Free Software Foundation; either
version 2 of the License, or (at your option) any later version.
The Kinect 3D Video Capture Project is distributed in the hope that it
will be useful, but WITHOUT ANY WARRANTY; without even the implied
warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See
the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along
with the Kinect 3D Video Capture Project; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA
***********************************************************************/
#ifndef LEVENBERGMARQUARDTMINIMIZER_INCLUDED
#define LEVENBERGMARQUARDTMINIMIZER_INCLUDED
#include <Math/Math.h>
#include <Geometry/ComponentArray.h>
#include <Geometry/Matrix.h>
template <class FitterFunctor>
class LevenbergMarquardtMinimizer
{
/* Embedded classes: */
public:
typedef FitterFunctor Fitter; // Functor class for the fitting geometry
typedef typename FitterFunctor::Scalar Scalar; // Scalar type
static const int dimension=Fitter::dimension; // Dimension of the optimization space
typedef typename FitterFunctor::Derivative Derivative; // Type for distance function derivatives
typedef Geometry::Matrix<Scalar,dimension,dimension> Matrix; // Type for matrices
typedef Geometry::ComponentArray<Scalar,dimension> Vector; // Type for vectors (in the matrix sense)
/* Methods: */
static Scalar minimize(Fitter& fitter); // Minimizes the target function by manipulating the given fitter
};
/********************************************
Methods of class LevenbergMarquardtMinimizer:
********************************************/
template <class FitterParam>
inline
typename LevenbergMarquardtMinimizer<FitterParam>::Scalar
LevenbergMarquardtMinimizer<FitterParam>::minimize(
typename LevenbergMarquardtMinimizer<FitterParam>::Fitter& fitter)
{
/* Initialize the optimizer: */
Scalar tau=Scalar(1.0e-3);
Scalar epsilon1=Scalar(1.0e-20);
Scalar epsilon2=Scalar(1.0e-20);
int maxNumIterations=1000;
/* Compute the Jacobian matrix, the error vector, and the initial target function value: */
Matrix A;
Vector g;
for(int i=0;i<dimension;++i)
{
for(int j=0;j<dimension;++j)
A(i,j)=Scalar(0);
g[i]=Scalar(0);
}
Scalar F(0);
for(size_t index=0;index<fitter.getNumPoints();++index)
{
Derivative dp=fitter.calcDistanceDerivative(index);
Scalar d=fitter.calcDistance(index);
for(int i=0;i<dimension;++i)
{
for(int j=0;j<dimension;++j)
A(i,j)+=dp[i]*dp[j];
g[i]+=dp[i]*d;
}
F+=Math::sqr(d);
}
F*=Scalar(0.5);
/* Compute the initial damping factor: */
Scalar maxA=A(0,0);
for(int i=1;i<dimension;++i)
if(maxA<A(i,i))
maxA=A(i,i);
Scalar mu=tau*maxA;
Scalar nu=Scalar(2);
/* Check for convergence: */
bool found=true;
for(int i=0;i<dimension;++i)
if(Math::abs(g[i])>epsilon1)
found=false;
int iteration;
for(iteration=0;!found&&iteration<maxNumIterations;++iteration)
{
/* Calculate step direction: */
Matrix H=A;
for(int i=0;i<dimension;++i)
H(i,i)+=mu;
Vector h=g/H; // h is actually the negative of hlm in the pseudo-code
/* Check for convergence: */
if(Geometry::mag(h)<=epsilon2*(fitter.calcMag()+epsilon2))
break;
/* Try updating the current state: */
fitter.save();
fitter.increment(h); // Subtracts h instead of adding (h is negative, see above)
fitter.normalize();
/* Calculate the new target function value: */
Scalar newF(0);
for(size_t index=0;index<fitter.getNumPoints();++index)
newF+=Math::sqr(fitter.calcDistance(index));
newF*=Scalar(0.5);
/* Calculate the gain value: */
Scalar denom(0);
for(int i=0;i<dimension;++i)
denom+=h[i]*(mu*h[i]+g[i]); // Adds g instead of subtracting (h is negative, see above)
denom*=Scalar(0.5);
Scalar rho=(F-newF)/denom;
/* Accept or deny the step: */
if(rho>Scalar(0))
{
/* Compute the new Jacobian matrix and the new error vector: */
for(int i=0;i<dimension;++i)
{
for(int j=0;j<dimension;++j)
A(i,j)=Scalar(0);
g[i]=Scalar(0);
}
for(size_t index=0;index<fitter.getNumPoints();++index)
{
Derivative dp=fitter.calcDistanceDerivative(index);
Scalar d=fitter.calcDistance(index);
for(int i=0;i<dimension;++i)
{
for(int j=0;j<dimension;++j)
A(i,j)+=dp[i]*dp[j];
g[i]+=dp[i]*d;
}
}
/* Update the target function value: */
F=newF;
/* Check for convergence: */
found=true;
for(int i=0;i<dimension;++i)
if(Math::abs(g[i])>epsilon1)
found=false;
/* Update the damping factor: */
Scalar rhof=Scalar(2)*rho-Scalar(1);
Scalar factor=Scalar(1)-rhof*rhof*rhof;
if(factor<Scalar(1)/Scalar(3))
factor=Scalar(1)/Scalar(3);
mu*=factor;
nu=Scalar(2);
}
else
{
/* Deny the step: */
fitter.restore();
/* Update the damping factor: */
mu*=nu;
nu*=Scalar(2);
}
}
return F;
}
#endif