3dpcp/.svn/pristine/01/01c6e20fc458d4b3bc96dbe036d4a5d00e0637a8.svn-base

220 lines
6.1 KiB
Text
Raw Normal View History

2012-09-16 12:33:11 +00:00
/*
* icp6Dlumquat implementation
*
* Copyright (C) Andreas Nuechter, Alexandru-Eugen Ichim
*
* Released under the GPL version 3.
*
*/
/** @file
* @brief Implementation of the ICP error function minimization via
* via linearization with quaternions
*
* @author Andreas Nuechter. Jacobs University Bremen gGmbH, Germany
* @author Alexandru-Eugen Ichim. Jacobs University Bremen gGmbH, Germany
*
*/
#include "slam6d/icp6Dlumquat.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 linearization with quarernions
* @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_LUMQUAT::Point_Point_Align(const vector<PtPair>& pairs, double *alignfx,
const double centroid_m[3], const double centroid_d[3])
{
// alignfx is filled with the current pose, t is the translation, quat is the quaternion
double t[3], quat[4];
Matrix4ToQuat(alignfx, quat, t);
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 << "LUMQUAT 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;
}
/////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////
/// MZ = M^T * Z
ColumnVector MZ(7); MZ = 0.0;
/// MM = M^T * M
Matrix MM(7, 7); MM = 0.0;
double x = 0.0, y = 0.0, z = 0.0, dx = 0.0, dy = 0.0, dz = 0.0, sx = 0.0, sy = 0.0, sz = 0.0, xpy = 0.0, xpz = 0.0, ypz = 0.0, xpypz = 0.0, xy = 0.0, yz = 0.0, xz = 0.0;
for(unsigned int i = 0; i < pairs.size(); ++i) {
/// temporary values that we shall use multiple times in the subsequent computations
x = (pairs[i].p1.x + pairs[i].p1.x) / 2.0;
y = (pairs[i].p1.y + pairs[i].p2.y) / 2.0;
z = (pairs[i].p1.z + pairs[i].p2.z) / 2.0;
dx = pairs[i].p1.x - pairs[i].p2.x;
dy = pairs[i].p1.y - pairs[i].p2.y;
dz = pairs[i].p1.z - pairs[i].p2.z;
/// sums of each coordinate
sx += x;
sy += y;
sz += z;
/// sums of squares of coordinates
xpy += x*x + y*y;
xpz += x*x + z*z;
ypz += y*y + z*z;
xpypz += x*x + y*y + z*z;
/// sums of products of pairs of coordinates
xy += x*y;
xz += x*z;
yz += y*z;
/// incrementally construct matrix M^T * Z
MZ(1) += dx;
MZ(2) += dy;
MZ(3) += dz;
MZ(4) += x*dx + y*dy + z*dz;
MZ(5) += z*dy - y*dz;
MZ(6) += x*dz - z*dx;
MZ(7) += y*dx - x*dy;
}
/// construct M^ * M
MM(1,1) = MM(2,2) = MM(3,3) = pairs.size();
MM(4,4) = xpypz;
MM(5,5) = ypz;
MM(6,6) = xpz;
MM(7,7) = xpy;
MM(1,4) = MM(4,1) = sx;
MM(1,6) = MM(6,1) = -sz;
MM(1,7) = MM(7,1) = sy;
MM(2,4) = MM(4,2) = sy;
MM(2,5) = MM(5,2) = sz;
MM(2,7) = MM(7,2) = -sx;
MM(3,4) = MM(4,3) = sz;
MM(3,5) = MM(5,3) = -sy;
MM(3,6) = MM(6,3) = sx;
MM(5,6) = MM(6,5) = -xy;
MM(5,7) = MM(7,5) = -xz;
MM(6,7) = MM(7,6) = -yz;
ColumnVector Ehat = MM.i() * MZ ;
/// construct the auxiliary matrices U and T needed to build up H
double p = quat[0], q = quat[1], r = quat[2], s = quat[3];
x = t[0], y = t[1], z = t[2];
Matrix U(4, 4);
U << p << q << r << s
<< q <<-p << s <<-r
<< r <<-s <<-p << q
<< s << r <<-q <<-p;
Matrix T(3, 4);
T << p*x + s*y - r*z << q*x + r*y + s*z << r*x - q*y + p*z << s*x - p*y - q*z
<<-s*x + p*y + q*z <<-r*x + q*y - p*z << q*x + r*y + s*z << p*x + s*y - r*z
<< r*x - q*y + p*z <<-s*x + p*y + q*z <<-p*x - s*y + r*z << q*x + r*y - s*z;
/// now actually compose matrix H
Matrix H(7, 7); H = 0.0;
H.SubMatrix(1, 3, 1, 3) = IdentityMatrix(3);
H.SubMatrix(1, 3, 4, 7) = T *(-2);
H.SubMatrix(4, 7, 4, 7) = U * 2;
/// Xhat is the pose estimate for the second scan - use the pose of the first scan
ColumnVector Xhat(7); Xhat << x << y << z << p << q << r << s;
/// create a transformation matrix for the first scan with the given values
Matrix T1(4, 4); T1 = 0.0;
Matrix Cq(3, 3);
ColumnVector qvec(3); qvec << q << r << s;
Cq << 0 << -qvec(3) << qvec(2) << qvec(3) << 0 << -qvec(1) << -qvec(2) << qvec(1) << 0;
ColumnVector qtq(1); qtq = qvec.t() *qvec * (-1);
T1.SubMatrix(1, 3, 1, 3) = IdentityMatrix(3) * (p*p + qtq(1)) + qvec*qvec.t()*2 + Cq *2*p;
T1(1, 4) = x;
T1(2, 4) = y;
T1(3, 4) = z;
T1(4, 4) = 1;
/// the translation and quaternion for the second scan are computed
ColumnVector X = Xhat - H.i() * Ehat;
/// create the transformation matrix for the second scan
x = X(1), y = X(2), z = X(3);
p = X(4); q = X(5); r = X(6); s = X(7);
Matrix T2(4, 4); T2 = 0.0;
qvec = 0.0; qvec << q << r << s;
Cq = 0.0; Cq << 0 << -qvec(3) << qvec(2) << qvec(3) << 0 << -qvec(1) << -qvec(2) << qvec(1) << 0;
qtq = qvec.t() *qvec * (-1);
T2.SubMatrix(1, 3, 1, 3) = IdentityMatrix(3) * (p*p + qtq(1)) + qvec*qvec.t()*2 + Cq *2*p;
T2(1, 4) = x;
T2(2, 4) = y;
T2(3, 4) = z;
T2(4, 4) = 1;
/// the incremental transform calculated from the absolute poses of the two scans
Matrix T_inc = T1 * T2.i();
/// convert our 4x4 transform to column-wise opengl form
alignfx[0] = T_inc(1, 1);
alignfx[1] = T_inc(2, 1);
alignfx[2] = T_inc(3, 1);
alignfx[3] = 0.0;
alignfx[4] = T_inc(1, 2);
alignfx[5] = T_inc(2, 2);
alignfx[6] = T_inc(3, 2);
alignfx[7] = 0.0;
alignfx[8] = T_inc(1, 3);
alignfx[9] = T_inc(2, 3);
alignfx[10]= T_inc(3, 3);
alignfx[11]= 0.0;
alignfx[12]= T_inc(1, 4);
alignfx[13]= T_inc(2, 4);
alignfx[14]= T_inc(3, 4);
alignfx[15]= 1.0;
/////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////
return error;
}