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/****************************************************************************
History
$Log: point_matching.h,v $
****************************************************************************/
#ifndef _VCG_MATH_POINTMATCHING_H
#define _VCG_MATH_POINTMATCHING_H
#include <vcg/math/matrix33.h>
#include <vcg/math/quaternion.h>
#include <vcg/math/lin_algebra.h>
namespace vcg
{
template<class ScalarType>
class PointMatching
{
public:
typedef Point3<ScalarType> Point3x;
typedef Matrix33<ScalarType> Matrix33x;
typedef Matrix44<ScalarType> Matrix44x;
typedef Quaternion<ScalarType> Quaternionx;
/*
Compute a similarity matching (rigid + uniform scaling)
simply create a temporary point set with the correct scaling factor
*/
static bool ComputeSimilarityMatchMatrix( Matrix44x &res,
std::vector<Point3x> &Pfix, // vertici corrispondenti su fix (rossi)
std::vector<Point3x> &Pmov) // normali scelti su mov (verdi)
{
Quaternionx qtmp;
Point3x tr;
std::vector<Point3x> Pnew(Pmov.size());
ScalarType 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]);
#ifdef _DEBUG
printf("Scaling Factor is %f",scalingFactor/(i+1));
#endif
}
scalingFactor/=(Pmov.size()-1);
for(size_t i=0;i<Pmov.size();++i)
Pnew[i]=Pmov[i]/scalingFactor;
bool ret=ComputeRigidMatchMatrix(res,Pfix,Pnew,qtmp,tr);
if(!ret) return false;
Matrix44x scaleM; scaleM.SetDiagonal(1.0/scalingFactor);
res = res * scaleM;
return true;
}
static bool ComputeRigidMatchMatrix( Matrix44x &res,
std::vector<Point3x> &Pfix, // vertici corrispondenti su fix (rossi)
std::vector<Point3x> &Pmov) // normali scelti su mov (verdi)
{
Quaternionx qtmp;
Point3x tr;
return ComputeRigidMatchMatrix(res,Pfix,Pmov,qtmp,tr);
}
/*
Calcola la matrice di rototraslazione
che porta i punti Pmov su Pfix
Basata sul paper
Besl, McKay
A method for registration o f 3d Shapes
IEEE TPAMI Vol 14, No 2 1992
Esempio d'uso
const int np=1000;
std::vector<Point3x> pfix(np),pmov(np);
Matrix44x Rot,Trn,RotRes;
Rot.Rotate(30,Point3x(1,0,1));
Trn.Translate(0,0,100);
Rot=Trn*Rot;
for(int i=0;i<np;++i){
pfix[i]=Point3x(-150+rand()%1000,-150+rand()%1000,0);
pmov[i]=Rot.Apply(pfix[i]);
}
ComputeRigidMatchMatrix(RotRes,pfix,pmov);
RotRes.Invert();
assert( RotRes==Rot);
assert( RotRes.Apply(pmov[i]) == pfix[i] );
*/
static
bool ComputeWeightedRigidMatchMatrix(Matrix44x &res,
std::vector<Point3x> &Pfix,
std::vector<Point3x> &Pmov,
std::vector<ScalarType> weights,
Quaternionx &q,
Point3x &tr
)
{
Matrix33x ccm;
Point3x bfix,bmov; // baricenter of src e trg
ccm.WeightedCrossCovariance(weights,Pmov,Pfix,bmov,bfix);
Matrix33x cyc; // the cyclic components of the cross covariance matrix.
cyc=ccm - ccm.transpose();
Matrix44x QQ;
QQ.SetZero();
Point3x D(cyc[1][2],cyc[2][0],cyc[0][1]);
Matrix33x 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[0][1] = D[0]; QQ[0][2] = D[1]; QQ[0][3] = D[2];
QQ[1][0] = D[0]; QQ[2][0] = D[1]; QQ[3][0] = D[2];
int i,j;
for(i=0;i<3;i++)
for(j=0;j<3;j++)
QQ[i+1][j+1]=RM[i][j];
// printf(" Quaternion Matrix\n");
// print(QQ);
Point4d d;
Matrix44x v;
int nrot;
Jacobi(QQ,d,v,nrot);
// printf("Done %i iterations\n %f %f %f %f\n",nrot,d[0],d[1],d[2],d[3]);
// print(v);
// Now search the maximum eigenvalue
double maxv=0;
int maxind=-1;
for(i=0;i<4;i++)
if(maxv<fabs(d[i])) {
q=Quaternionx(v[0][i],v[1][i],v[2][i],v[3][i]);
maxind=i;
maxv=d[i];
}
// The corresponding eigenvector define the searched rotation,
Matrix44x Rot;
q.ToMatrix(Rot);
// the translation (last row) is simply the difference between the transformed src barycenter and the trg baricenter
tr= (bfix - Rot *bmov);
//res[3][0]=tr[0];res[3][1]=tr[1];res[3][2]=tr[2];
Matrix44x Trn;
Trn.SetTranslate(tr);
res=Trn*Rot;
return true;
}
static
bool ComputeRigidMatchMatrix(Matrix44x &res,
std::vector<Point3x> &Pfix,
std::vector<Point3x> &Pmov,
Quaternionx &q,
Point3x &tr)
{
Matrix33x ccm;
Point3x bfix,bmov; // baricenter of src e trg
ccm.CrossCovariance(Pmov,Pfix,bmov,bfix);
Matrix33x cyc; // the cyclic components of the cross covariance matrix.
cyc=ccm-ccm.transpose();
Matrix44x QQ;
QQ.SetZero();
Point3x D(cyc[1][2],cyc[2][0],cyc[0][1]);
Matrix33x 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[0][1] = D[0]; QQ[0][2] = D[1]; QQ[0][3] = D[2];
QQ[1][0] = D[0]; QQ[2][0] = D[1]; QQ[3][0] = D[2];
int i,j;
for(i=0;i<3;i++)
for(j=0;j<3;j++)
QQ[i+1][j+1]=RM[i][j];
// printf(" Quaternion Matrix\n");
// print(QQ);
Point4d d;
Matrix44x v;
int nrot;
//QQ.Jacobi(d,v,nrot);
Jacobi(QQ,d,v,nrot);
// printf("Done %i iterations\n %f %f %f %f\n",nrot,d[0],d[1],d[2],d[3]);
// print(v);
// Now search the maximum eigenvalue
double maxv=0;
int maxind=-1;
for(i=0;i<4;i++)
if(maxv<fabs(d[i])) {
q=Quaternionx(v[0][i],v[1][i],v[2][i],v[3][i]);
maxind=i;
maxv=d[i];
}
// The corresponding eigenvector define the searched rotation,
Matrix44x Rot;
q.ToMatrix(Rot);
// the translation (last row) is simply the difference between the transformed src barycenter and the trg baricenter
tr= (bfix - Rot*bmov);
//res[3][0]=tr[0];res[3][1]=tr[1];res[3][2]=tr[2];
Matrix44x Trn;
Trn.SetTranslate(tr);
res=Trn*Rot;
return true;
}
// Dati due insiemi di punti e normali corrispondenti calcola la migliore trasformazione
// che li fa corrispondere
static bool ComputeMatchMatrix( Matrix44x &res,
std::vector<Point3x> &Ps, // vertici corrispondenti su src (rossi)
std::vector<Point3x> &Ns, // normali corrispondenti su src (rossi)
std::vector<Point3x> &Pt) // vertici scelti su trg (verdi)
// vector<Point3x> &Nt) // normali scelti su trg (verdi)
{
assert(0);
// Da qui in poi non compila che ha bisogno dei minimiquadrati
#if 0
int sz=Ps.size();
Matrix<double> A(sz,12);
Vector<double> b(sz);
Vector<double> x(12);
//inizializzo il vettore per minimi quadrati
// la matrice di trasf che calcolo con LeastSquares cerca avvicinare il piu'
// possibile le coppie di punti che trovo ho scelto
// Le coppie di punti sono gia' trasformate secondo la matrice <In> quindi come scelta iniziale
// per il metodo minimiquadrati scelgo l'identica (e.g. se ho allineato a mano perfettamente e
// le due mesh sono perfettamente uguali DEVE restituire l'identica)
res.SetIdentity();
int i,j,k;
for(i=0; i<=2; ++i)
for(j=0; j<=3; ++j)
x[i*4+j] = res[i][j];
//costruzione della matrice
for(i=0;i<sz;++i)
{
for(j=0;j<3;++j)
for(k=0;k<4;++k)
if(k<3)
{
A[i][k+j*4] = Ns[i][j]*Pt[i][k];
}
else
{
A[i][k+j*4] = Ns[i][j];
}
b[i] = Ps[i]*Ns[i];
}
const int maxiter = 4096;
int iter;
LSquareGC(x,A,b,1e-16,maxiter,iter);
TRACE("LSQ Solution");
for(int ind=0; ind<12; ++ind) {
if((ind%4)==0) TRACE("\n");
TRACE("%8.5lf ", x[ind]);
} TRACE("\n");
if(iter==maxiter)
{
TRACE("I minimi quadrati non convergono!!\n");
return false;
}
else { TRACE("Convergenza in %d passi\n",iter); }
//Devo riapplicare la matrice di trasformazione globale a
//trg inserendo il risultato nel vettore trgvert contenente
//copia dei suoi vertici
Matrix44x tmp;
for(i=0; i<=2; ++i)
for(j=0; j<=3; ++j)
res[j][i] = x[i*4+j];
res[0][3] = 0.0;
res[1][3] = 0.0;
res[2][3] = 0.0;
res[3][3] = 1.0;
/*
res.Transpose();
Point3x scv,shv,rtv,trv;
res.Decompose(scv,shv,rtv,trv);
vcg::print(res);
printf("Scale %f %f %f\n",scv[0],scv[1],scv[2]);
printf("Shear %f %f %f\n",shv[0],shv[1],shv[2]);
printf("Rotat %f %f %f\n",rtv[0],rtv[1],rtv[2]);
printf("Trans %f %f %f\n",trv[0],trv[1],trv[2]);
printf("----\n"); res.Decompose(scv,shv,rtv,trv);
vcg::print(res);
printf("Scale %f %f %f\n",scv[0],scv[1],scv[2]);
printf("Shear %f %f %f\n",shv[0],shv[1],shv[2]);
printf("Rotat %f %f %f\n",rtv[0],rtv[1],rtv[2]);
printf("Trans %f %f %f\n",trv[0],trv[1],trv[2]);
res.Transpose();
*/
#endif
return true;
}
/*
****** Questa parte per compilare ha bisogno di leastsquares e matrici generiche
****** Da controllare meglio
static void CreatePairMatrix( Matrix<double> & A2, const Point3x & p, const Point3x & n, double d )
{
double t1 = p[0]*p[0];
double t2 = n[0]*n[0];
double t4 = t1*n[0];
double t5 = t4*n[1];
double t6 = t4*n[2];
double t7 = p[0]*t2;
double t8 = t7*p[1];
double t9 = p[0]*n[0];
double t10 = p[1]*n[1];
double t11 = t9*t10;
double t12 = p[1]*n[2];
double t13 = t9*t12;
double t14 = t7*p[2];
double t15 = p[2]*n[1];
double t16 = t9*t15;
double t17 = p[2]*n[2];
double t18 = t9*t17;
double t19 = t9*n[1];
double t20 = t9*n[2];
double t21 = t9*d;
double t22 = n[1]*n[1];
double t25 = t1*n[1]*n[2];
double t26 = p[0]*t22;
double t27 = t26*p[1];
double t28 = p[0]*n[1];
double t29 = t28*t12;
double t30 = t26*p[2];
double t31 = t28*t17;
double t32 = t28*n[2];
double t33 = t28*d;
double t34 = n[2]*n[2];
double t36 = p[0]*t34;
double t41 = p[1]*p[1]; double t43 = t41*n[0];
double t46 = p[1]*t2; double t48 = p[1]*n[0];
double t49 = t48*t15; double t50 = t48*t17;
double t51 = t48*n[1]; double t52 = t48*n[2];
double t57 = p[1]*t22; double t59 = t10*t17;
double t60 = t10*n[2]; double t63 = p[1]*t34;
double t66 = p[2]*p[2]; double t68 = t66*n[0];
double t72 = p[2]*n[0]; double t73 = t72*n[1];
double t74 = t72*n[2]; double t80 = t15*n[2];
A2[0][0] = t1*t2; A2[0][1] = t5; A2[0][2] = t6;
A2[0][3] = t8; A2[0][4] = t11; A2[0][5] = t13;
A2[0][6] = t14; A2[0][7] = t16; A2[0][8] = t18;
A2[0][9] = t7; A2[0][10] = t19; A2[0][11] = t20;
A2[0][12] = -t21;
A2[1][1] = t1*t22; A2[1][2] = t25; A2[1][3] = t11;
A2[1][4] = t27; A2[1][5] = t29; A2[1][6] = t16;
A2[1][7] = t30; A2[1][8] = t31; A2[1][9] = t19;
A2[1][10] = t26; A2[1][11] = t32; A2[1][12] = -t33;
A2[2][2] = t1*t34; A2[2][3] = t13; A2[2][4] = t29;
A2[2][5] = t36*p[1]; A2[2][6] = t18; A2[2][7] = t31;
A2[2][8] = t36*p[2]; A2[2][9] = t20; A2[2][10] = t32;
A2[2][11] = t36; A2[2][12] = -p[0]*n[2]*d;
A2[3][3] = t41*t2; A2[3][4] = t43*n[1]; A2[3][5] = t43*n[2];
A2[3][6] = t46*p[2]; A2[3][7] = t49; A2[3][8] = t50;
A2[3][9] = t46; A2[3][10] = t51; A2[3][11] = t52;
A2[3][12] = -t48*d;
A2[4][4] = t41*t22; A2[4][5] = t41*n[1]*n[2]; A2[4][6] = t49;
A2[4][7] = t57*p[2]; A2[4][8] = t59; A2[4][9] = t51;
A2[4][10] = t57; A2[4][11] = t60; A2[4][12] = -t10*d;
A2[5][5] = t41*t34; A2[5][6] = t50; A2[5][7] = t59;
A2[5][8] = t63*p[2]; A2[5][9] = t52; A2[5][10] = t60;
A2[5][11] = t63; A2[5][12] = -t12*d;
A2[6][6] = t66*t2; A2[6][7] = t68*n[1]; A2[6][8] = t68*n[2];
A2[6][9] = p[2]*t2; A2[6][10] = t73; A2[6][11] = t74;
A2[6][12] = -t72*d;
A2[7][7] = t66*t22; A2[7][8] = t66*n[1]*n[2]; A2[7][9] = t73;
A2[7][10] = p[2]*t22; A2[7][11] = t80; A2[7][12] = -t15*d;
A2[8][8] = t66*t34; A2[8][9] = t74; A2[8][10] = t80;
A2[8][11] = p[2]*t34; A2[8][12] = -t17*d;
A2[9][9] = t2; A2[9][10] = n[0]*n[1];
A2[9][11] = n[0]*n[2]; A2[9][12] = -n[0]*d;
A2[10][10] = t22; A2[10][11] = n[1]*n[2]; A2[10][12] = -n[1]*d;
A2[11][11] = t34; A2[11][12] = -n[2]*d;
A2[12][12] = d*d;
}
// Dati due insiemi di punti e normali corrispondenti calcola la migliore trasformazione
// che li fa corrispondere
static bool ComputeMatchMatrix2( Matrix44x &res,
std::vector<Point3x> &Ps, // vertici corrispondenti su src (rossi)
std::vector<Point3x> &Ns, // normali corrispondenti su src (rossi)
std::vector<Point3x> &Pt) // vertici scelti su trg (verdi)
//vector<Point3x> &Nt) // normali scelti su trg (verdi)
{
const int N = 13;
int i,j,k;
Matrixd AT(N,N);
Matrixd TT(N,N);
// Azzeramento matrice totale (solo tri-superiore)
for(i=0;i<N;++i)
for(j=i;j<N;++j)
AT[i][j] = 0;
// Calcolo matrici locali e somma
for(k=0;k<Ps.size();++k)
{
CreatePairMatrix(TT,Pt[k],Ns[k],Ps[k]*Ns[k]);
for(i=0;i<N;++i)
for(j=i;j<N;++j)
AT[i][j] += TT[i][j];
}
for(i=0;i<N;++i)
for(j=0;j<i;++j)
AT[i][j] = AT[j][i];
std::vector<double> q;
double error;
affine_ls2(AT,q,error);
//printf("error: %g \n",error);
res[0][0] = q[0];
res[0][1] = q[1];
res[0][2] = q[2];
res[0][3] = 0;
res[1][0] = q[3];
res[1][1] = q[4];
res[1][2] = q[5];
res[1][3] = 0;
res[2][0] = q[6];
res[2][1] = q[7];
res[2][2] = q[8];
res[2][3] = 0;
res[3][0] = q[9];
res[3][1] = q[10];
res[3][2] = q[11];
res[3][3] = q[12];
return true;
}
*/
};
} // end namespace
#endif