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/****************************************************************************
* 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 /= double(spVec.size());
tpBarycenter /= double(tpVec.size());
spBarycenter.ToEigenVector(spe);
tpBarycenter.ToEigenVector(tpe);
m /= double(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;
}
/*! \brief Computes the best fitting rigid transformations to align two sets of corresponding points
*
* Ref:
* Olga Sorkine-Hornung and Michael Rabinovich
* Least-Squares Rigid Motion Using SVD
*/
template <class S>
Matrix44<S> ComputeLeastSquaresRigidMotion(std::vector<Point3<S> > &pFix,
std::vector<Point3<S> > &pMov)
{
if (pFix.size() != pMov.size() || pFix.size() < 3)
return Matrix44<S>::Identity();
Eigen::Matrix3Xd p(3, pMov.size()); // moving
Eigen::MatrixX3d q(pFix.size(), 3); // fixed
for (size_t i=0; i<pMov.size(); i++)
{
Eigen::Vector3d v;
pMov[i].ToEigenVector(v);
p.col(i) = v;
}
Eigen::Vector3d avgP = p.rowwise().mean();
p.colwise() -= avgP;
for (size_t i=0; i<pFix.size(); i++)
{
Eigen::Vector3d v;
pFix[i].ToEigenVector(v);
q.row(i) = v;
}
Eigen::Vector3d avgQ = q.colwise().mean();
q.rowwise() -= avgQ.transpose();
Eigen::Matrix3d cov = p * q;
Eigen::JacobiSVD<Eigen::Matrix3d> svd;
svd.compute(cov, Eigen::ComputeFullU | Eigen::ComputeFullV);
Eigen::Matrix3d d = Eigen::Matrix3d::Identity();
d(2,2) = (svd.matrixV() * svd.matrixU().transpose()).determinant() > 0 ? 1 : -1;
Eigen::Matrix3d R = (svd.matrixV() * d * svd.matrixU().transpose());
Eigen::Vector3d t = avgQ - R * avgP;
Eigen::Matrix4d res = Eigen::Matrix4d::Identity();
res.block<3,3>(0,0) = R;
res.block<3,1>(0,3) = t;
Matrix44<S> ret;
ret.FromEigenMatrix(res);
return ret;
}
/*
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
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