double
sampleEuclideanTransform(std::vector<Vector3d> const& left, std::vector<Vector3d> const& right,
int const minSample[3],
double inlierThresholdL, double inlierThresholdR,
Matrix3x3d& R, Vector3d& T, std::vector<int> &inliers)
{
inliers.clear();
int const N = left.size();
if (N < 3) throwV3DErrorHere("computeRobustEuclideanTransform(): at least 3 point correspondences required.");
vector<Vector3d> ptsLeftTrans(N), ptsRightTrans(N);
vector<Vector3d> left_pts(3), right_pts(3);
int const j0 = minSample[0];
int const j1 = minSample[1];
int const j2 = minSample[2];
left_pts[0] = left[j0]; left_pts[1] = left[j1]; left_pts[2] = left[j2];
right_pts[0] = right[j0]; right_pts[1] = right[j1]; right_pts[2] = right[j2];
Matrix3x3d R0, R0t;
Vector3d T0;
getEuclideanTransformation(left_pts, right_pts, R0, T0);
R0t = R0.transposed();
for (int i = 0; i < N; ++i) ptsLeftTrans[i] = (R0 * left[i] + T0);
for (int i = 0; i < N; ++i) ptsRightTrans[i] = R0t * (right[i] - T0);
double score = 0;
for (int i = 0; i < N; ++i)
{
double const distL = distance_L2(left[i], ptsRightTrans[i]);
double const distR = distance_L2(right[i], ptsLeftTrans[i]);
score += std::min(distL, inlierThresholdL);
score += std::min(distR, inlierThresholdR);
if (distL < inlierThresholdL && distR < inlierThresholdR) inliers.push_back(i);
} // end for (i)
R = R0;
T = T0;
return score;
} // end sampleEuclideanTransform()
void checkGLErrors(char const * location, ostream& os) {
GLuint errnum;
char const * errstr;
bool hasError = false;
while ((errnum = glGetError())) {
errstr = reinterpret_cast<const char *>(gluErrorString(errnum));
if (errstr)
os << errstr;
else
os << "Error " << errnum;
os << " at " << location << endl;
#ifdef WIN32
break;
#endif
}
if (hasError)
throwV3DErrorHere("");
}
void
computeConsistentRotations(int const nViews,
std::vector<Matrix3x3d> const& relativeRotations,
std::vector<std::pair<int, int> > const& viewPairs,
std::vector<Matrix3x3d>& rotations, int method)
{
#if !defined(V3DLIB_ENABLE_ARPACK)
if (method == V3D_CONSISTENT_ROTATION_METHOD_SPARSE_EIG)
method = V3D_CONSISTENT_ROTATION_METHOD_EIG_ATA;
#endif
int const nRelPoses = relativeRotations.size();
rotations.resize(nViews);
switch (method)
{
case V3D_CONSISTENT_ROTATION_METHOD_SVD:
{
Matrix<double> A(3*nRelPoses, 3*nViews, 0.0);
Matrix3x3d I;
makeIdentityMatrix(I);
scaleMatrixIP(-1.0, I);
for (int i = 0; i < nRelPoses; ++i)
{
int const view1 = viewPairs[i].first;
int const view2 = viewPairs[i].second;
Matrix3x3d const& Rrel = relativeRotations[i];
copyMatrixSlice(Rrel, 0, 0, 3, 3, A, 3*i, 3*view1);
copyMatrixSlice(I, 0, 0, 3, 3, A, 3*i, 3*view2);
} // end for (i)
SVD<double> svd(A);
int const startColumn = A.num_cols()-3; // last columns of right sing. vec for SVD
Matrix<double> const& V = svd.getV();
for (int i = 0; i < nViews; ++i)
{
copyMatrixSlice(V, 3*i, startColumn, 3, 3, rotations[i], 0, 0);
enforceRotationMatrix(rotations[i]);
}
break;
}
case V3D_CONSISTENT_ROTATION_METHOD_SVD_ATA:
case V3D_CONSISTENT_ROTATION_METHOD_EIG_ATA:
case V3D_CONSISTENT_ROTATION_METHOD_SPARSE_EIG:
{
vector<pair<int, int> > nzA;
vector<double> valsA;
nzA.reserve(12*nRelPoses);
valsA.reserve(12*nRelPoses);
for (int i = 0; i < nRelPoses; ++i)
{
int const view1 = viewPairs[i].first;
int const view2 = viewPairs[i].second;
Matrix3x3d const& Rrel = relativeRotations[i];
nzA.push_back(make_pair(3*i+0, 3*view1+0)); valsA.push_back(Rrel[0][0]);
nzA.push_back(make_pair(3*i+0, 3*view1+1)); valsA.push_back(Rrel[0][1]);
nzA.push_back(make_pair(3*i+0, 3*view1+2)); valsA.push_back(Rrel[0][2]);
nzA.push_back(make_pair(3*i+1, 3*view1+0)); valsA.push_back(Rrel[1][0]);
nzA.push_back(make_pair(3*i+1, 3*view1+1)); valsA.push_back(Rrel[1][1]);
nzA.push_back(make_pair(3*i+1, 3*view1+2)); valsA.push_back(Rrel[1][2]);
nzA.push_back(make_pair(3*i+2, 3*view1+0)); valsA.push_back(Rrel[2][0]);
nzA.push_back(make_pair(3*i+2, 3*view1+1)); valsA.push_back(Rrel[2][1]);
nzA.push_back(make_pair(3*i+2, 3*view1+2)); valsA.push_back(Rrel[2][2]);
nzA.push_back(make_pair(3*i+0, 3*view2+0)); valsA.push_back(-1.0);
nzA.push_back(make_pair(3*i+1, 3*view2+1)); valsA.push_back(-1.0);
nzA.push_back(make_pair(3*i+2, 3*view2+2)); valsA.push_back(-1.0);
} // end for (i)
CCS_Matrix<double> A(3*nRelPoses, 3*nViews, nzA, valsA);
if (method == V3D_CONSISTENT_ROTATION_METHOD_SPARSE_EIG)
{
#if defined(V3DLIB_ENABLE_ARPACK)
Vector<double> sigma;
Matrix<double> V;
SparseSymmetricEigConfig cfg;
cfg.maxArnoldiIterations = 100000;
computeSparseSVD(A, V3D_ARPACK_SMALLEST_MAGNITUDE_EIGENVALUES, 3, sigma, V, cfg);
//computeSparseSVD(A, V3D_ARPACK_SMALLEST_EIGENVALUES, 3, sigma, V, cfg);
for (int i = 0; i < nViews; ++i)
{
copyMatrixSlice(V, 3*i, 0, 3, 1, rotations[i], 0, 2);
copyMatrixSlice(V, 3*i, 1, 3, 1, rotations[i], 0, 1);
copyMatrixSlice(V, 3*i, 2, 3, 1, rotations[i], 0, 0);
}
#endif
}
else
{
Matrix<double> AtA(3*nViews, 3*nViews);
multiply_At_A_SparseDense(A, AtA);
if (method == V3D_CONSISTENT_ROTATION_METHOD_SVD_ATA)
{
SVD<double> svd(AtA);
int const startColumn = A.num_cols()-3; // last columns of right sing. vec for SVD
Matrix<double> const& V = svd.getV();
for (int i = 0; i < nViews; ++i)
copyMatrixSlice(V, 3*i, startColumn, 3, 3, rotations[i], 0, 0);
}
else
{
Eigenvalue<double> svd(AtA);
int const startColumn = 0; // first columns of eigenvector matrix
Matrix<double> const& V = svd.getV();
for (int i = 0; i < nViews; ++i)
copyMatrixSlice(V, 3*i, startColumn, 3, 3, rotations[i], 0, 0);
} // end if
} // end if
break;
}
default:
throwV3DErrorHere("Unknown method argument for computeConsistentRotations().");
} // end switch
for (int i = 0; i < nViews; ++i)
enforceRotationMatrix(rotations[i]);
// Remove gauge freedom by setting R[0] = I.
Matrix3x3d const R0t = rotations[0].transposed();
for (int i = 0; i < nViews; ++i)
rotations[i] = rotations[i] * R0t;
// Note: it seems, that either all Rs have det(R)=1 or all have det(R)=-1.
// Since we remove the gauge freedem by multiplying all rotations with R_0^t,
// we always end up with det(R)=1 and any code to enforce a positive determinant
// is not necessary.
} // end computeConsistentRotations()
