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/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004 \/)\/ *
* 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 _AUTOALIGN_4PCS_H_
#define _AUTOALIGN_4PCS_H_
/**
implementation of the 4PCS method from the paper:
"4-Points Congruent Sets for Robust Pairwise Surface Registration"
D.Aiger, N.Mitra D.Cohen-Or, SIGGRAPH 2008
ps: the name of the variables are out of vcg standard but like the one
used in the paper pseudocode.
*/
#include <vcg/complex/complex.h>
#include <vcg/space/point_matching.h>
#include <vcg/complex/algorithms/closest.h>
#include <vcg/complex/algorithms/point_sampling.h>
#include <vcg/math/random_generator.h>
namespace vcg{
namespace tri{
template <class MeshType>
class FourPCS {
public:
/* mesh only for using spatial indexing functions (to remove) */
class PVertex; // dummy prototype never used
class PFace;
class PUsedTypes: public vcg::UsedTypes < vcg::Use<PVertex>::template AsVertexType,
vcg::Use<PFace >::template AsFaceType >{};
class PVertex : public vcg::Vertex< PUsedTypes,vcg::vertex::BitFlags,vcg::vertex::Coord3m ,vcg::vertex::Mark>{};
class PFace : public vcg::Face< PUsedTypes> {};
class PMesh : public vcg::tri::TriMesh< std::vector<PVertex>, std::vector<PFace> > {};
typedef typename MeshType::ScalarType ScalarType;
typedef typename MeshType::CoordType CoordType;
typedef typename vcg::Matrix44<ScalarType> Matrix44x;
typedef typename vcg::Box3<ScalarType> Box3x;
typedef typename MeshType::VertexIterator VertexIterator;
typedef typename MeshType::VertexPointer VertexPointer;
typedef typename MeshType::VertexType VertexType;
typedef vcg::Point4< vcg::Point3<ScalarType> > FourPoints;
typedef vcg::GridStaticPtr<typename PMesh::VertexType, ScalarType > GridType;
/* class for Parameters */
struct Param
{
ScalarType overlap; // overlap estimation as a percentage of overlapping points.
int sampleNumP; // number of samples on moving mesh P (it determines the sampling radius to be used to sample Q too)
float samplingRadius;
ScalarType deltaPerc; // Approximation Level (expressed as a percentage of the avg distance between samples)
ScalarType deltaAbs; // Approximation Level
int feetSize; // how many points in the neighborhood of each of the 4 points
int scoreFeet; // how many of the feetsize points must match (max feetsize*4) to try an early interrupt
ScalarType cosAngle; // max admittable angle that can be admitted between matching points in alignments (expressed as cos(ang) )
int seed; // random seed used. Need for repeatability.
void Default(){
overlap = 0.5;
sampleNumP=500;
samplingRadius=0;
deltaPerc = 0.5;
deltaAbs = 0;
feetSize = 25;
scoreFeet = 50;
seed =0;
cosAngle = 0; // normals must differ more than 90 degree to be considered bad.
}
};
struct Stat
{
Stat() : initTime(0),selectCoplanarBaseTime(0),findCongruentTime(0),testAlignmentTime(0)
{}
clock_t initTime;
clock_t selectCoplanarBaseTime;
clock_t findCongruentTime;
clock_t testAlignmentTime;
float init() {return 1000.0f*float(initTime)/float(CLOCKS_PER_SEC);}
float select() {return 1000.0f*float(selectCoplanarBaseTime)/float(CLOCKS_PER_SEC);}
float findCongruent() {return 1000.0f*float(findCongruentTime)/float(CLOCKS_PER_SEC);}
float testAlignment() {return 1000.0f*float(testAlignmentTime)/float(CLOCKS_PER_SEC);}
};
class Couple
{
public:
VertexPointer p0,p1;
Couple(VertexPointer i, VertexPointer j, float d) : p0(i),p1(j),dist(d){}
float dist;
bool operator < (const Couple & o) const {return dist < o.dist;}
VertexPointer operator[](const int &i) const {return (i==0)? this->p0 : this->p1;}
};
struct Candidate
{
Candidate():score(0){}
Candidate(FourPoints _p, vcg::Matrix44<ScalarType>_T):p(_p),T(_T){}
FourPoints p;
vcg::Matrix44<ScalarType> T;
int score;
inline bool operator <(const Candidate & o) const {return score > o.score;}
};
// class for the point 'ei'
struct EPoint{
EPoint(vcg::Point3<ScalarType> _p, int _i):pos(_p),pi(_i){}
vcg::Point3<ScalarType> pos;
int pi; //index to R[1|2]
void GetBBox(vcg::Box3<ScalarType> & b){b.Add(pos);}
};
Param par; /// parameters
Stat stat;
MeshType *P; // Moving Mesh (from which the coplanar base is selected)
MeshType *Q; // Fixed Mesh (mesh where to find the correspondences)
math::MarsenneTwisterRNG rnd;
std::vector<VertexPointer> subsetQ; // subset of the vertices in Q
std::vector<VertexPointer> subsetP; // random selection on P
ScalarType side; // side
PMesh Invr; // invariants
std::vector< Candidate > U; // the
int iwinner; // winner == U[iwinner]
std::vector<FourPoints> bases; // used bases
std::vector<VertexType*> ExtB[4]; // selection of vertices "close" to the four point
vcg::GridStaticPtr<typename MeshType::VertexType, ScalarType > ugridQ;
vcg::GridStaticPtr<typename MeshType::VertexType, ScalarType > ugridP;
/* returns the closest point between to segments x1-x2 and x3-x4. */
void IntersectionLineLine(const CoordType & x1,const CoordType & x2,const CoordType & x3,const CoordType & x4, CoordType&x)
{
CoordType a = x2-x1, b = x4-x3, c = x3-x1;
x = x1 + a * ((c^b).dot(a^b)) / (a^b).SquaredNorm();
}
void Init(MeshType &_movP,MeshType &_fixQ)
{
clock_t t0= clock();
P = &_movP;
Q = &_fixQ;
tri::UpdateBounding<MeshType>::Box(*P);
if(par.seed==0) rnd.initialize(time(0));
else rnd.initialize(par.seed);
ugridQ.Set(Q->vert.begin(),Q->vert.end());
ugridP.Set(P->vert.begin(),P->vert.end());
if(par.samplingRadius==0)
par.samplingRadius = tri::ComputePoissonDiskRadius(*P,par.sampleNumP);
tri::PoissonPruning(*P, subsetP, par.samplingRadius, par.seed);
tri::PoissonPruning(*Q, subsetQ, par.samplingRadius, par.seed);
par.deltaAbs = par.samplingRadius * par.deltaPerc;
side = P->bbox.Dim()[P->bbox.MaxDim()]*par.overlap; //rough implementation
stat.initTime+=clock()-t0;
}
// Try to select four coplanar points such that they are at least side distance and
//
bool SelectCoplanarBase(FourPoints &B, ScalarType &r1, ScalarType &r2)
{
clock_t t0= clock();
// choose the inter point distance
ScalarType dtol = side*0.1; //rough implementation
// **** first point: random
B[0] = P->vert[ rnd.generate(P->vert.size())].P();
// **** second point: a random point at distance side +-dtol
size_t i;
for(i = 0; i < P->vert.size(); ++i){
int id = rnd.generate(P->vert.size());
ScalarType dd = (P->vert[id].P() - B[0]).Norm();
if( ( dd < side + dtol) && (dd > side - dtol)){
B[1] = P->vert[id].P();
break;
}
}
if(i == P->vert.size()) return false;
// **** third point: at distance less than side*0.8 from middle way between B[0] and B[1]
const CoordType middle = (B[0]+B[1])/2.0;
for(i = 0; i < P->vert.size(); ++i){
int id = rnd.generate(P->vert.size());
if( Distance(P->vert[id].P(),middle) < side*0.8 ){
B[2] = P->vert[id].P();
break;
}
}
if(i == P->vert.size()) return false;
// **** fourth point:
ScalarType cpr = rnd.generate01();
CoordType crossP = B[0] *(1-cpr)+B[1]*cpr;
CoordType B4 = B[2]+(crossP-B[2]).Normalize()*side;
CoordType n = ((B[0]-B[1]).normalized() ^ (B[2]-B[1]).normalized()).normalized();
ScalarType radius = dtol;
std::vector<typename MeshType::VertexType*> closests;
std::vector<ScalarType> distances;
std::vector<CoordType> points;
vcg::tri::GetInSphereVertex<
MeshType,
vcg::GridStaticPtr<typename MeshType::VertexType, ScalarType >,
std::vector<typename MeshType::VertexType*>,
std::vector<ScalarType>,
std::vector<CoordType>
>(*P,ugridP,B4,radius,closests,distances,points);
if(closests.empty())
return false;
int bestInd = -1; ScalarType bestv=std::numeric_limits<float>::max();
for(i = 0; i <closests.size(); ++i){
ScalarType dist_from_plane = fabs((closests[i]->P() - B[1]).normalized().dot(n));
if( dist_from_plane < bestv){
bestv = dist_from_plane;
bestInd = i;
}
}
if(bestv >dtol)
return false;
B[3] = closests[bestInd]->P();
//printf("B[3] %d\n", (typename MeshType::VertexType*)closests[best] - &(*P->vert.begin()));
// compute r1 and r2
CoordType x;
// std::swap(B[1],B[2]);
IntersectionLineLine(B[0],B[1],B[2],B[3],x);
r1 = (x - B[0]).dot(B[1]-B[0]) / (B[1]-B[0]).SquaredNorm();
r2 = (x - B[2]).dot(B[3]-B[2]) / (B[3]-B[2]).SquaredNorm();
if( ((B[0]+(B[1]-B[0])*r1)-(B[2]+(B[3]-B[2])*r2)).Norm() > par.deltaAbs )
return false;
radius = side*0.5;
std::vector< CoordType > samples;
std::vector<ScalarType > dists;
for(int i = 0 ; i< 4; ++i){
vcg::tri::GetKClosestVertex<
MeshType,
vcg::GridStaticPtr<typename MeshType::VertexType, ScalarType >,
std::vector<VertexType*>,
std::vector<ScalarType>,
std::vector< CoordType > >(*P,ugridP, par.feetSize ,B[i],radius, ExtB[i], dists, samples);
}
qDebug("ExtB %i",ExtB[0].size()+ExtB[1].size()+ExtB[2].size()+ExtB[3].size());
stat.selectCoplanarBaseTime+=clock()-t0;
return true;
}
bool IsTransfCongruent(const FourPoints &B, const FourPoints &fp, vcg::Matrix44<ScalarType> & mat)
{
std::vector<vcg::Point3<ScalarType> > fix(4);
std::vector<vcg::Point3<ScalarType> > mov(4);
for(int i = 0 ; i < 4; ++i) {
mov[i]=B[i];
fix[i]=fp[i];
}
if(fabs( Distance(fix[0],fix[1]) - Distance(mov[0],mov[1]) ) > par.deltaAbs) return false;
if(fabs( Distance(fix[0],fix[2]) - Distance(mov[0],mov[2]) ) > par.deltaAbs) return false;
if(fabs( Distance(fix[0],fix[3]) - Distance(mov[0],mov[3]) ) > par.deltaAbs) return false;
if(fabs( Distance(fix[1],fix[2]) - Distance(mov[1],mov[2]) ) > par.deltaAbs) return false;
if(fabs( Distance(fix[1],fix[3]) - Distance(mov[1],mov[3]) ) > par.deltaAbs) return false;
if(fabs( Distance(fix[2],fix[3]) - Distance(mov[2],mov[3]) ) > par.deltaAbs) return false;
vcg::ComputeRigidMatchMatrix(fix,mov,mat);
ScalarType maxSquaredDistance = 0.0;
for(int i = 0; i < 4; ++i)
maxSquaredDistance =std::max(maxSquaredDistance, SquaredDistance(mat * mov[i] ,fix[i]));
return sqrt(maxSquaredDistance) < par.deltaAbs;
}
/// Compute the vector R1 of couple of points on FixQ at a given distance.
/// Used by FindCongruent
void ComputeR1(std::vector<Couple > &R1)
{
R1.clear();
for(size_t vi = 0; vi < subsetQ.size(); ++vi)
for(size_t vj = vi; vj < subsetQ.size(); ++vj){
ScalarType d = Distance(subsetQ[vi]->P(),subsetQ[vj]->P());
if( (d < side+par.deltaAbs))
{
R1.push_back(Couple(subsetQ[vi],subsetQ[vj], d));
R1.push_back(Couple(subsetQ[vj],subsetQ[vi], d));
}
}
std::sort(R1.begin(),R1.end());
}
// Find congruent elements of a base B, on Q, with approximation delta
// and put them in the U vector.
bool FindCongruent(const std::vector<Couple > &R1, const FourPoints &B, const ScalarType r1, const ScalarType r2)
{
clock_t t0=clock();
int n_base=0;
bool done = false;
int n_closests = 0, n_congr = 0;
int ac =0 ,acf = 0,tr = 0,trf =0;
ScalarType d1,d2;
d1 = (B[1]-B[0]).Norm();
d2 = (B[3]-B[2]).Norm();
typename std::vector<Couple>::const_iterator bR1,eR1,bR2,eR2,ite;
bR1 = std::lower_bound(R1.begin(),R1.end(),Couple(0,0,d1-par.deltaAbs));
eR1 = std::lower_bound(R1.begin(),R1.end(),Couple(0,0,d1+par.deltaAbs));
bR2 = std::lower_bound(R1.begin(),R1.end(),Couple(0,0,d2-par.deltaAbs));
eR2 = std::lower_bound(R1.begin(),R1.end(),Couple(0,0,d2+par.deltaAbs));
// in [bR1,eR1) there are all the pairs at a distance d1 +- par.delta
// in [bR1,eR1) there are all the pairs at a distance d2 +- par.delta
if(bR1 == R1.end()) return false;// if there are no such pairs return
if(bR2 == R1.end()) return false; // if there are no such pairs return
// put [bR1,eR1) in a mesh to have the search operator for free (lazy me)
Invr.Clear();
typename PMesh::VertexIterator vii;
int i = &(*bR1)-&(*R1.begin());
for(ite = bR1; ite != eR1;++ite){
vii = vcg::tri::Allocator<PMesh>::AddVertices(Invr,1);
// (*vii).P() = Q->vert[R1[i][0]].P() + (Q->vert[R1[i][1]].P()-Q->vert[R1[i][0]].P()) * r1;
(*vii).P() .Import( ite->p0->P() + ( ite->p1->P() - ite->p0->P()) * r1);
++i;
}
if(Invr.vert.empty() ) return false;
// per vertex attribute 'index' remaps a vertex of Invr to its corresponding point in R1
typename PMesh::template PerVertexAttributeHandle<int> id = vcg::tri::Allocator<PMesh>::template AddPerVertexAttribute<int>(Invr,std::string("index"));
i = &(*bR1)-&(*R1.begin());
for(vii = Invr.vert.begin(); vii != Invr.vert.end();++vii,++i) id[vii] = i;
vcg::tri::UpdateBounding<PMesh>::Box(Invr);
std::vector<EPoint> R2inv;
i = &(*bR2)-&(*R1.begin());
// R2inv contains all the points generated by the couples in R2 (with the reference to remap into R2)
for(ite = bR2; ite != eR2;++ite){
// R2inv.push_back( EPoint( Q->vert[R1[i][0]].P() + (Q->vert[R1[i][1]].P()-Q->vert[R1[i][0]].P()) * r2,i));
R2inv.push_back( EPoint( R1[i].p0->P() + (R1[i].p1->P() - R1[i].p0->P()) * r2,i));
++i;
}
GridType ugrid; // griglia
ugrid.Set(Invr.vert.begin(),Invr.vert.end());
n_closests = 0; n_congr = 0; ac =0 ; acf = 0; tr = 0; trf = 0;
printf("R2Inv.size = %d \n",R2inv.size());
for(uint i = 0 ; i < R2inv.size() ; ++i)
{
std::vector<typename PMesh::VertexType*> closests;
// for each point in R2inv get all the points in R1 closer than par.delta
vcg::Matrix44<ScalarType> mat;
Box3x bb;
bb.Add(R2inv[i].pos+CoordType(par.deltaAbs,par.deltaAbs, par.deltaAbs));
bb.Add(R2inv[i].pos-CoordType(par.deltaAbs,par.deltaAbs, par.deltaAbs));
vcg::tri::GetInBoxVertex<PMesh,GridType,std::vector<typename PMesh::VertexType*> >
(Invr,ugrid,bb,closests);
if(closests.size() > 5)
closests.resize(5);
n_closests+=closests.size();
for(uint ip = 0; ip < closests.size(); ++ip)
{
FourPoints p;
p[0] = R1[id[closests[ip]]][0]->cP();
p[1] = R1[id[closests[ip]]][1]->cP();
p[2] = R1[ R2inv[i].pi][0]->cP();
p[3] = R1[ R2inv[i].pi][1]->cP();
n_base++;
if(!IsTransfCongruent(B,p,mat)) {
trf++;
}
else{
tr++;
n_congr++;
Candidate c(p,mat);
EvaluateAlignment(c);
if( c.score > par.scoreFeet)
U.push_back(c);
}
}
}
vcg::tri::Allocator<PMesh>::DeletePerVertexAttribute(Invr,id);
printf("n_closests %5d = (An %5d ) + ( Tr %5d ) + (OK) %5d\n",n_closests,acf,trf,n_congr);
stat.findCongruentTime += clock()-t0;
return done;
}
int EvaluateSample(Candidate & fp, const CoordType & tp, const CoordType & np)
{
CoordType ttp = fp.T * tp;
vcg::Point4<ScalarType> np4 = fp.T * vcg::Point4<ScalarType>(np[0],np[1],np[2],0.0);
CoordType tnp(np4[0],np4[1],np4[2]);
ScalarType dist ;
VertexType* v = vcg::tri::GetClosestVertex(*Q, ugridQ, ttp, par.deltaAbs*2.0, dist );
if(v!=0)
{
if( v->N().dot(tnp) > par.cosAngle ) return 1;
else return -1;
}
else return 0;
}
// Check a candidate against the small subset of points ExtB
void EvaluateAlignment(Candidate & fp){
int n_delta_close = 0;
for(int i = 0 ; i< 4; ++i) {
for(uint j = 0; j < ExtB[i].size();++j){
n_delta_close+=EvaluateSample(fp, ExtB[i][j]->P(), ExtB[i][j]->cN());
}
}
fp.score = n_delta_close;
}
void TestAlignment(Candidate & fp)
{
clock_t t0 = clock();
int n_delta_close = 0;
for(uint j = 0; j < subsetP.size();++j){
CoordType np = subsetP[j]->N();
CoordType tp = subsetP[j]->P();
n_delta_close+=EvaluateSample(fp,tp,np);
}
fp.score = n_delta_close;
stat.testAlignmentTime += clock()-t0;
}
bool Align(Matrix44x & result, vcg::CallBackPos * cb )
{
int maxAttempt =100;
int scoreThr = par.sampleNumP*0.8;
Candidate bestC;
std::vector<Couple > R1;
ComputeR1(R1);
for(int i = 0; i < maxAttempt && bestC.score<scoreThr ; ++i )
{
FourPoints B;
ScalarType r1,r2;
if(SelectCoplanarBase(B,r1,r2))
{
U.clear();
FindCongruent(R1,B,r1,r2);
qDebug("Attempt %i found %i candidate best score %i",i,U.size(),bestC.score);
for(size_t i = 0 ; i < U.size() ;++i)
{
TestAlignment(U[i]);
if(U[i].score > bestC.score)
bestC = U[i];
}
}
}
result = bestC.T;
return bestC.score >0;
}
bool Align(int L, Matrix44x & result, vcg::CallBackPos * cb )
{
int bestv = 0;
bool found;
int n_tries = 0;
U.clear();
if(L==0)
{
// overlap is expressed as the probability that a point in P(mov) can be found in Q (fix)
L = (log(1.0-0.9) / log(1.0-pow((float)par.overlap,3.f)))+1;
printf("using %d bases\n",L);
}
std::vector<Couple > R1;
ComputeR1(R1);
for(int t = 0; t < L; ++t )
{
FourPoints B;
ScalarType r1,r2;
do
{
n_tries = 0;
do
{
n_tries++;
found = SelectCoplanarBase(B,r1,r2);
}
while(!found && (n_tries < 50));
if(!found) {
par.overlap*=0.9;
side = P->bbox.Dim()[P->bbox.MaxDim()]*par.overlap; //rough implementation
ComputeR1(R1);
}
} while (!found && (par.overlap >0.1));
if(par.overlap < 0.1) {
printf("FAILED");
return false;
}
bases.push_back(B);
if(cb) cb(t*100/L,"Trying bases");
if(FindCongruent(R1,B,r1,r2))
break;
}
if(U.empty()) return false;
// std::sort(U.begin(),U.end());
if(cb) cb(90,"TestAlignment");
bestv = -std::numeric_limits<float>::max();
iwinner = 0;
for(int i = 0 ; i < U.size() ;++i)
{
TestAlignment(U[i]);
if(U[i].score > bestv){
bestv = U[i].score;
iwinner = i;
}
}
result = U[iwinner].T;
Invr.Clear();
return true;
}
}; // end class
} // namespace tri
} // namespace vcg
#endif
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