3dpcp/.svn/pristine/2c/2ce7b870e535af9d29b8722847264faf29930fbb.svn-base

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2012-09-16 12:33:11 +00:00
/*
* icp6Ddual implementation
*
* Copyright (C) Andreas Nuechter, Alexandru-Eugen Ichim
*
* Released under the GPL version 3.
*
*/
/** @file
* @brief Implementation of the ICP error function minimization
* via dual quaternions
*
* @author Andreas Nuechter. Jacobs University Bremen gGmbH, Germany
* @author Alexandru-Eugen Ichim. Jacobs University Bremen gGmbH, Germany
*
*/
#include "slam6d/icp6Ddual.h"
#include "slam6d/globals.icc"
#include <iomanip>
using std::ios;
using std::resetiosflags;
using std::setiosflags;
#include "newmat/newmat.h"
#include "newmat/newmatap.h"
using namespace NEWMAT;
/**
* computes the rotation matrix consisting
* of a rotation and translation that
* minimizes the root-mean-square error of the
* point pairs using dual quaternions
* @param pairs Vector of point pairs (pairs of corresponding points)
* @param *alignfx The resulting transformation matrix
* @return Error estimation of the matching (rms)
*/
double icp6D_DUAL::Point_Point_Align(const vector<PtPair>& pairs, double *alignfx,
const double centroid_m[3], const double centroid_d[3])
{
double error = 0;
double sum = 0.0;
for(unsigned int i = 0; i < pairs.size(); i++){
sum += sqr(pairs[i].p1.x - pairs[i].p2.x)
+ sqr(pairs[i].p1.y - pairs[i].p2.y)
+ sqr(pairs[i].p1.z - pairs[i].p2.z) ;
}
error = sqrt(sum / (double)pairs.size());
if (!quiet) {
cout.setf(ios::basefield);
cout << "DUALQUAT RMS point-to-point error = "
<< resetiosflags(ios::adjustfield) << setiosflags(ios::internal)
<< resetiosflags(ios::floatfield) << setiosflags(ios::fixed)
<< std::setw(10) << std::setprecision(7)
<< error
<< " using " << std::setw(6) << (int)pairs.size() << " points" << endl;
}
/////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////
Matrix C1(4, 4); C1 = 0.0;
Matrix C2(4, 4); C2 = 0.0;
/// build up matrices C1 and C2
for(unsigned int i = 0; i < pairs.size(); ++i) {
ColumnVector m(3), d(3);
m << pairs[i].p1.x << pairs[i].p1.y << pairs[i].p1.z;
d << pairs[i].p2.x << pairs[i].p2.y << pairs[i].p2.z;
Matrix Cm(3, 3); Cm << 0 << -m(3) << m(2) << m(3) << 0 << -m(1) << -m(2) << m(1) << 0;
Matrix Cd(3, 3); Cd << 0 << -d(3) << d(2) << d(3) << 0 << -d(1) << -d(2) << d(1) << 0;
C1.SubMatrix(1, 1, 1, 1) += m.t()*d;
C1.SubMatrix(1, 1, 2, 4) += -m.t()*Cd;
C1.SubMatrix(2, 4, 1, 1) += -Cm*d;
C1.SubMatrix(2, 4, 2, 4) += m*d.t() + Cm*Cd;
C2.SubMatrix(1, 1, 2, 4) += -d.t() + m.t();
C2.SubMatrix(2, 4, 1, 1) += d - m;
C2.SubMatrix(2, 4, 2, 4) += -Cd - Cm;
}
/// the sums need to be multiplied by a scalar
C1 = C1 * (-2);
C2 = C2 * 2;
/// matrix A from C1 and C2
Matrix A = (C2.t()*C2 * 1.0/(2*pairs.size()) - C1 - C1.t()) * 0.5;
/// the quaternion qdot is the eigenvector of matrix A corresponding to the largest eigenvalue,
/// which is always found in the first column of matrix U
Matrix U(4, 4); DiagonalMatrix D(4);
SVD(A, D, U);
ColumnVector qdot = U.Column(1);
ColumnVector q(3); q << qdot(2) << qdot(3) << qdot(4);
Matrix Cq(3, 3); Cq << 0 << -q(3) << q(2) << q(3) << 0 << -q(1) << -q(2) << q(1) << 0;
ColumnVector s = C2*qdot * (-1.0)/(2*pairs.size());
Matrix Q(4, 4);
Q(1, 1) = qdot(1);
Q.SubMatrix(1, 1, 2, 4) = q.t();
Q.SubMatrix(2, 4, 1, 1) = -q;
Q.SubMatrix(2, 4, 2, 4) = IdentityMatrix(3)*qdot(1) + Cq;
/// get the translation from the double quaternion
ColumnVector p = Q*s;
ColumnVector translation(3); translation << p(2) << p(3) << p(4);
/// compute the rotation matrix from the quaternion
ColumnVector qtqx = q.t()*q;
Matrix R = IdentityMatrix(3) * (qdot(1)*qdot(1) - qtqx(1)) + q*q.t()*2 + Cq*qdot(1)*2;
/// create the final transformation matrix (OpenGL column-wise ordering)
alignfx[0] = R(1, 1);
alignfx[1] = R(2, 1);
alignfx[2] = R(3, 1);
alignfx[3] = 0.0;
alignfx[4] = R(1, 2);
alignfx[5] = R(2, 2);
alignfx[6] = R(3, 2);
alignfx[7] = 0.0;
alignfx[8] = R(1, 3);
alignfx[9] = R(2, 3);
alignfx[10]= R(3, 3);
alignfx[11]= 0.0;
alignfx[12]= translation(1);
alignfx[13]= translation(2);
alignfx[14]= translation(3);
alignfx[15]= 1.0;
/////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////
return error;
}