194 lines
6.1 KiB
C++
194 lines
6.1 KiB
C++
/****************************************************************************
|
|
* VCGLib o o *
|
|
* Visual and Computer Graphics Library o o *
|
|
* _ O _ *
|
|
* Copyright(C) 2004-2016 \/)\/ *
|
|
* Visual Computing Lab /\/| *
|
|
* ISTI - Italian National Research Council | *
|
|
* \ *
|
|
* All rights reserved. *
|
|
* *
|
|
* This program 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. *
|
|
* *
|
|
* This program 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 (http://www.gnu.org/licenses/gpl.txt) *
|
|
* for more details. *
|
|
* *
|
|
****************************************************************************/
|
|
|
|
#ifndef _VCG_MATH_POINTMATCHING_H
|
|
#define _VCG_MATH_POINTMATCHING_H
|
|
|
|
#include <vcg/math/quaternion.h>
|
|
#include <vcg/math/matrix44.h>
|
|
|
|
#include <Eigen/Dense>
|
|
#include <Eigen/Eigenvalues>
|
|
#include <iostream>
|
|
|
|
namespace vcg
|
|
{
|
|
|
|
/*! \brief Compute cross covariance
|
|
|
|
It computes the cross covariance matrix of two set of 3D points P and X;
|
|
it returns also the barycenters of P and X.
|
|
Ref:
|
|
|
|
Besl, McKay
|
|
A method for registration of 3d Shapes
|
|
IEEE TPAMI Vol 14, No 2 1992
|
|
|
|
*/
|
|
template <class S >
|
|
void ComputeCrossCovarianceMatrix(const std::vector<Point3<S> > &spVec, Point3<S> &spBarycenter,
|
|
const std::vector<Point3<S> > &tpVec, Point3<S> &tpBarycenter,
|
|
Eigen::Matrix3d &m)
|
|
{
|
|
assert(spVec.size()==tpVec.size());
|
|
m.setZero();
|
|
spBarycenter.SetZero();
|
|
tpBarycenter.SetZero();
|
|
Eigen::Vector3d spe;
|
|
Eigen::Vector3d tpe;
|
|
typename std::vector <Point3<S> >::const_iterator si,ti;
|
|
for(si=spVec.begin(),ti=tpVec.begin();si!=spVec.end();++si,++ti){
|
|
spBarycenter+=*si;
|
|
tpBarycenter+=*ti;
|
|
si->ToEigenVector(spe);
|
|
ti->ToEigenVector(tpe);
|
|
m+=spe*tpe.transpose();
|
|
}
|
|
spBarycenter/=spVec.size();
|
|
tpBarycenter/=tpVec.size();
|
|
spBarycenter.ToEigenVector(spe);
|
|
tpBarycenter.ToEigenVector(tpe);
|
|
m/=spVec.size();
|
|
m-=spe*tpe.transpose();
|
|
}
|
|
|
|
/*! \brief Compute the roto-translation that applied to PMov bring them onto Pfix
|
|
* Rotation is computed as a quaternion.
|
|
*
|
|
* E.g. it find a matrix such that:
|
|
*
|
|
* Pfix[i] = res * Pmov[i]
|
|
*
|
|
* Ref:
|
|
* Besl, McKay
|
|
* A method for registration of 3d Shapes
|
|
* IEEE TPAMI Vol 14, No 2 1992
|
|
*/
|
|
|
|
template < class S >
|
|
void ComputeRigidMatchMatrix(std::vector<Point3<S> > &Pfix,
|
|
std::vector<Point3<S> > &Pmov,
|
|
Quaternion<S> &q,
|
|
Point3<S> &tr)
|
|
{
|
|
Eigen::Matrix3d ccm;
|
|
Point3<S> bfix,bmov; // baricenter of src e trg
|
|
|
|
ComputeCrossCovarianceMatrix(Pmov,bmov,Pfix,bfix,ccm);
|
|
|
|
Eigen::Matrix3d cyc; // the cyclic components of the cross covariance matrix.
|
|
cyc=ccm-ccm.transpose();
|
|
|
|
Eigen::Matrix4d QQ;
|
|
QQ.setZero();
|
|
Eigen::Vector3d D(cyc(1,2),cyc(2,0),cyc(0,1));
|
|
|
|
Eigen::Matrix3d RM;
|
|
RM.setZero();
|
|
RM(0,0)=-ccm.trace();
|
|
RM(1,1)=-ccm.trace();
|
|
RM(2,2)=-ccm.trace();
|
|
RM += ccm + ccm.transpose();
|
|
|
|
QQ(0,0) = ccm.trace();
|
|
QQ.block<1,3> (0,1) = D.transpose();
|
|
QQ.block<3,1> (1,0) = D;
|
|
QQ.block<3,3> (1,1) = RM;
|
|
|
|
Eigen::SelfAdjointEigenSolver<Eigen::Matrix4d> eig(QQ);
|
|
Eigen::Vector4d eval = eig.eigenvalues();
|
|
Eigen::Matrix4d evec = eig.eigenvectors();
|
|
// std::cout << "EigenVectors:" << std::endl << evec << std::endl;
|
|
// std::cout << "Eigenvalues:" << std::endl << eval << std::endl;
|
|
int ind;
|
|
eval.cwiseAbs().maxCoeff(&ind);
|
|
|
|
q=Quaternion<S>(evec.col(ind)[0],evec.col(ind)[1],evec.col(ind)[2],evec.col(ind)[3]);
|
|
Matrix44<S> Rot;
|
|
q.ToMatrix(Rot);
|
|
tr= (bfix - Rot*bmov);
|
|
}
|
|
|
|
|
|
/*! \brief Compute the roto-translation that applied to PMov bring them onto Pfix
|
|
* Rotation is computed as a quaternion.
|
|
*
|
|
* E.g. it find a matrix such that:
|
|
*
|
|
* Pfix[i] = res * Pmov[i]
|
|
*
|
|
* Ref:
|
|
* Besl, McKay
|
|
* A method for registration of 3d Shapes
|
|
* IEEE TPAMI Vol 14, No 2 1992
|
|
*/
|
|
|
|
template < class S >
|
|
void ComputeRigidMatchMatrix(std::vector<Point3<S> > &Pfix,
|
|
std::vector<Point3<S> > &Pmov,
|
|
Matrix44<S> &res)
|
|
{
|
|
Quaternion<S> q;
|
|
Point3<S> tr;
|
|
ComputeRigidMatchMatrix(Pfix,Pmov,q,tr);
|
|
|
|
Matrix44<S> Rot;
|
|
q.ToMatrix(Rot);
|
|
|
|
Matrix44<S> Trn;
|
|
Trn.SetTranslate(tr);
|
|
|
|
res=Trn*Rot;
|
|
}
|
|
|
|
|
|
/*
|
|
Compute a similarity matching (rigid + uniform scaling)
|
|
simply create a temporary point set with the correct scaling factor
|
|
*/
|
|
template <class S>
|
|
void ComputeSimilarityMatchMatrix(std::vector<Point3<S> > &Pfix,
|
|
std::vector<Point3<S> > &Pmov,
|
|
Matrix44<S> &res)
|
|
{
|
|
S scalingFactor=0;
|
|
for(size_t i=0;i<( Pmov.size()-1);++i)
|
|
{
|
|
scalingFactor += Distance(Pmov[i],Pmov[i+1])/ Distance(Pfix[i],Pfix[i+1]);
|
|
}
|
|
scalingFactor/=(Pmov.size()-1);
|
|
|
|
std::vector<Point3<S> > Pnew(Pmov.size());
|
|
for(size_t i=0;i<Pmov.size();++i)
|
|
Pnew[i]=Pmov[i]/scalingFactor;
|
|
|
|
ComputeRigidMatchMatrix(Pfix,Pnew,res);
|
|
|
|
Matrix44<S> scaleM; scaleM.SetDiagonal(1.0/scalingFactor);
|
|
res = res * scaleM;
|
|
}
|
|
|
|
} // end namespace
|
|
|
|
#endif
|