The camera model (three-dimensional reconstruction task ------- 3 [2] - Code)

This section task is to achieve the direct linear transformation singular value bound.

FundamentalMatrix fundamental_8_point (math::Matrix<double, 3, 8> const& points1
                         , math::Matrix<double, 3, 8> const& points2
                        ){
    /* direct linear transform */
    math::Matrix<double, 8, 9> A;
    for(int i=0; i<8; i++)
    {
        math::Vec3d p1  = points1.col(i);
        math::Vec3d p2 = points2.col(i);

        A(i, 0) = p1[0]*p2[0];
        A(i, 1) = p1[1]*p2[0];
        A(i, 2) = p2[0];
        A(i, 3) = p1[0]*p2[1];
        A(i, 4) = p1[1]*p2[1];
        A(i, 5) = p2[1];
        A(i, 6) = p1[0];
        A(i, 7) = p1[1];
        A(i, 8) = 1.0;
    }

    math::Matrix<double, 9, 9> vv;
    math::matrix_svd<double, 8, 9>(A, nullptr, nullptr, &vv);
    math::Vector<double, 9> f = vv.col(8);

    FundamentalMatrix F;
    F(0,0) = f[0]; F(0,1) = f[1]; F(0,2) = f[2];
    F(1,0) = f[3]; F(1,1) = f[4]; F(1,2) = f[5];
    F(2,0) = f[6]; F(2,1) = f[7]; F(2,2) = f[8];

    /* singularity constraint */
    math::Matrix<double, 3, 3> U, S, V;
    math::matrix_svd(F, &U, &S, &V);
    S(2,2)=0;
    F = U*S*V.transpose();

    return F;
}