void DecomposeEssentialUsingHorn90(double _E[9], double _R1[9], double _R2[9], double _t1[3], double _t2[3]) {
//from : http://people.csail.mit.edu/bkph/articles/Essential.pdf
#ifdef USE_EIGEN
using namespace Eigen;
Matrix3d E = Map<Matrix<double,3,3,RowMajor> >(_E);
Matrix3d EEt = E * E.transpose();
Vector3d e0e1 = E.col(0).cross(E.col(1)),e1e2 = E.col(1).cross(E.col(2)),e2e0 = E.col(2).cross(E.col(0));
Vector3d b1,b2;
#if 1
//Method 1
Matrix3d bbt = 0.5 * EEt.trace() * Matrix3d::Identity() - EEt; //Horn90 (12)
Vector3d bbt_diag = bbt.diagonal();
if (bbt_diag(0) > bbt_diag(1) && bbt_diag(0) > bbt_diag(2)) {
b1 = bbt.row(0) / sqrt(bbt_diag(0));
b2 = -b1;
} else if (bbt_diag(1) > bbt_diag(0) && bbt_diag(1) > bbt_diag(2)) {
b1 = bbt.row(1) / sqrt(bbt_diag(1));
b2 = -b1;
} else {
b1 = bbt.row(2) / sqrt(bbt_diag(2));
b2 = -b1;
}
#else
//Method 2
if (e0e1.norm() > e1e2.norm() && e0e1.norm() > e2e0.norm()) {
b1 = e0e1.normalized() * sqrt(0.5 * EEt.trace()); //Horn90 (18)
b2 = -b1;
} else if (e1e2.norm() > e0e1.norm() && e1e2.norm() > e2e0.norm()) {
b1 = e1e2.normalized() * sqrt(0.5 * EEt.trace()); //Horn90 (18)
b2 = -b1;
} else {
b1 = e2e0.normalized() * sqrt(0.5 * EEt.trace()); //Horn90 (18)
b2 = -b1;
}
#endif
//Horn90 (19)
Matrix3d cofactors; cofactors.col(0) = e1e2; cofactors.col(1) = e2e0; cofactors.col(2) = e0e1;
cofactors.transposeInPlace();
//B = [b]_x , see Horn90 (6) and http://en.wikipedia.org/wiki/Cross_product#Conversion_to_matrix_multiplication
Matrix3d B1; B1 << 0,-b1(2),b1(1),
b1(2),0,-b1(0),
-b1(1),b1(0),0;
Matrix3d B2; B2 << 0,-b2(2),b2(1),
b2(2),0,-b2(0),
-b2(1),b2(0),0;
Map<Matrix<double,3,3,RowMajor> > R1(_R1),R2(_R2);
//Horn90 (24)
R1 = (cofactors.transpose() - B1*E) / b1.dot(b1);
R2 = (cofactors.transpose() - B2*E) / b2.dot(b2);
Map<Vector3d> t1(_t1),t2(_t2);
t1 = b1; t2 = b2;
cout << "Horn90 provided " << endl << R1 << endl << "and" << endl << R2 << endl;
#endif
}
