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// Copyright (c) 2020, Viktor Larsson
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * Neither the name of the copyright holder nor the
// names of its contributors may be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT HOLDER> BE LIABLE FOR ANY
// DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
// (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
// LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
// ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#include "p5lp_radial.h"
#include "PoseLib/misc/univariate.h"
namespace poselib {
int p5lp_radial(const std::vector<Eigen::Vector3d> &l, const std::vector<Eigen::Vector3d> &X,
std::vector<CameraPose> *output) {
std::vector<Eigen::Vector2d> x(5, Eigen::Vector2d::Zero());
for (size_t i = 0; i < 5; ++i) {
x[i] << l[i](1), -l[i](0);
}
// Note: Assumes that l[i](2) = 0 !
return p5lp_radial(x, X, output);
}
int p5lp_radial(const std::vector<Eigen::Vector2d> &x, const std::vector<Eigen::Vector3d> &X,
std::vector<CameraPose> *output) {
// Setup nullspace
Eigen::Matrix<double, 8, 5> cc;
for (int i = 0; i < 5; i++) {
cc(0, i) = -x[i](1) * X[i](0);
cc(1, i) = -x[i](1) * X[i](1);
cc(2, i) = -x[i](1) * X[i](2);
cc(3, i) = -x[i](1);
cc(4, i) = x[i](0) * X[i](0);
cc(5, i) = x[i](0) * X[i](1);
cc(6, i) = x[i](0) * X[i](2);
cc(7, i) = x[i](0);
}
Eigen::Matrix<double, 8, 8> Q = cc.householderQr().householderQ();
Eigen::Matrix<double, 8, 3> N = Q.rightCols(3);
// Compute coefficients for sylvester resultant
double c11_1 = N(0, 1) * N(4, 1) + N(1, 1) * N(5, 1) + N(2, 1) * N(6, 1);
double c12_1 = N(0, 1) * N(4, 2) + N(0, 2) * N(4, 1) + N(1, 1) * N(5, 2) + N(1, 2) * N(5, 1) + N(2, 1) * N(6, 2) +
N(2, 2) * N(6, 1);
double c12_2 = N(0, 0) * N(4, 1) + N(0, 1) * N(4, 0) + N(1, 0) * N(5, 1) + N(1, 1) * N(5, 0) + N(2, 0) * N(6, 1) +
N(2, 1) * N(6, 0);
double c13_1 = N(0, 2) * N(4, 2) + N(1, 2) * N(5, 2) + N(2, 2) * N(6, 2);
double c13_2 = N(0, 0) * N(4, 2) + N(0, 2) * N(4, 0) + N(1, 0) * N(5, 2) + N(1, 2) * N(5, 0) + N(2, 0) * N(6, 2) +
N(2, 2) * N(6, 0);
double c13_3 = N(0, 0) * N(4, 0) + N(1, 0) * N(5, 0) + N(2, 0) * N(6, 0);
double c21_1 = N(0, 1) * N(0, 1) + N(1, 1) * N(1, 1) + N(2, 1) * N(2, 1) - N(4, 1) * N(4, 1) - N(5, 1) * N(5, 1) -
N(6, 1) * N(6, 1);
double c22_1 = 2 * N(0, 1) * N(0, 2) + 2 * N(1, 1) * N(1, 2) + 2 * N(2, 1) * N(2, 2) - 2 * N(4, 1) * N(4, 2) -
2 * N(5, 1) * N(5, 2) - 2 * N(6, 1) * N(6, 2);
double c22_2 = 2 * N(0, 0) * N(0, 1) + 2 * N(1, 0) * N(1, 1) + 2 * N(2, 0) * N(2, 1) - 2 * N(4, 0) * N(4, 1) -
2 * N(5, 0) * N(5, 1) - 2 * N(6, 0) * N(6, 1);
double c23_1 = N(0, 2) * N(0, 2) + N(1, 2) * N(1, 2) + N(2, 2) * N(2, 2) - N(4, 2) * N(4, 2) - N(5, 2) * N(5, 2) -
N(6, 2) * N(6, 2);
double c23_2 = 2 * N(0, 0) * N(0, 2) + 2 * N(1, 0) * N(1, 2) + 2 * N(2, 0) * N(2, 2) - 2 * N(4, 0) * N(4, 2) -
2 * N(5, 0) * N(5, 2) - 2 * N(6, 0) * N(6, 2);
double c23_3 = N(0, 0) * N(0, 0) + N(1, 0) * N(1, 0) + N(2, 0) * N(2, 0) - N(4, 0) * N(4, 0) - N(5, 0) * N(5, 0) -
N(6, 0) * N(6, 0);
double a4 = c11_1 * c11_1 * c23_3 * c23_3 - c11_1 * c12_2 * c22_2 * c23_3 - 2 * c11_1 * c13_3 * c21_1 * c23_3 +
c11_1 * c13_3 * c22_2 * c22_2 + c12_2 * c12_2 * c21_1 * c23_3 - c12_2 * c13_3 * c21_1 * c22_2 +
c13_3 * c13_3 * c21_1 * c21_1;
double a3 = c11_1 * c13_2 * c22_2 * c22_2 + 2 * c13_2 * c13_3 * c21_1 * c21_1 + c12_2 * c12_2 * c21_1 * c23_2 +
2 * c11_1 * c11_1 * c23_2 * c23_3 - c11_1 * c12_1 * c22_2 * c23_3 - c11_1 * c12_2 * c22_1 * c23_3 -
c11_1 * c12_2 * c22_2 * c23_2 - 2 * c11_1 * c13_2 * c21_1 * c23_3 - 2 * c11_1 * c13_3 * c21_1 * c23_2 +
2 * c11_1 * c13_3 * c22_1 * c22_2 + 2 * c12_1 * c12_2 * c21_1 * c23_3 - c12_1 * c13_3 * c21_1 * c22_2 -
c12_2 * c13_2 * c21_1 * c22_2 - c12_2 * c13_3 * c21_1 * c22_1;
double a2 = c11_1 * c11_1 * c23_2 * c23_2 + c13_2 * c13_2 * c21_1 * c21_1 + c11_1 * c13_1 * c22_2 * c22_2 +
c11_1 * c13_3 * c22_1 * c22_1 + 2 * c13_1 * c13_3 * c21_1 * c21_1 + c12_2 * c12_2 * c21_1 * c23_1 +
c12_1 * c12_1 * c21_1 * c23_3 + 2 * c11_1 * c11_1 * c23_1 * c23_3 - c11_1 * c12_1 * c22_1 * c23_3 -
c11_1 * c12_1 * c22_2 * c23_2 - c11_1 * c12_2 * c22_1 * c23_2 - c11_1 * c12_2 * c22_2 * c23_1 -
2 * c11_1 * c13_1 * c21_1 * c23_3 - 2 * c11_1 * c13_2 * c21_1 * c23_2 +
2 * c11_1 * c13_2 * c22_1 * c22_2 - 2 * c11_1 * c13_3 * c21_1 * c23_1 +
2 * c12_1 * c12_2 * c21_1 * c23_2 - c12_1 * c13_2 * c21_1 * c22_2 - c12_1 * c13_3 * c21_1 * c22_1 -
c12_2 * c13_1 * c21_1 * c22_2 - c12_2 * c13_2 * c21_1 * c22_1;
double a1 = c11_1 * c13_2 * c22_1 * c22_1 + 2 * c13_1 * c13_2 * c21_1 * c21_1 + c12_1 * c12_1 * c21_1 * c23_2 +
2 * c11_1 * c11_1 * c23_1 * c23_2 - c11_1 * c12_1 * c22_1 * c23_2 - c11_1 * c12_1 * c22_2 * c23_1 -
c11_1 * c12_2 * c22_1 * c23_1 - 2 * c11_1 * c13_1 * c21_1 * c23_2 + 2 * c11_1 * c13_1 * c22_1 * c22_2 -
2 * c11_1 * c13_2 * c21_1 * c23_1 + 2 * c12_1 * c12_2 * c21_1 * c23_1 - c12_1 * c13_1 * c21_1 * c22_2 -
c12_1 * c13_2 * c21_1 * c22_1 - c12_2 * c13_1 * c21_1 * c22_1;
double a0 = c11_1 * c11_1 * c23_1 * c23_1 - c11_1 * c12_1 * c22_1 * c23_1 - 2 * c11_1 * c13_1 * c21_1 * c23_1 +
c11_1 * c13_1 * c22_1 * c22_1 + c12_1 * c12_1 * c21_1 * c23_1 - c12_1 * c13_1 * c21_1 * c22_1 +
c13_1 * c13_1 * c21_1 * c21_1;
a4 = 1.0 / a4;
a3 *= a4;
a2 *= a4;
a1 *= a4;
a0 *= a4;
double roots[4];
int n_roots = univariate::solve_quartic_real(a3, a2, a1, a0, roots);
CameraPose pose;
output->clear();
for (int i = 0; i < n_roots; i++) {
// We have two quadratic polynomials in y after substituting x
double a = roots[i];
double c1a = c11_1;
double c1b = c12_1 + c12_2 * a;
double c1c = c13_1 + c13_2 * a + c13_3 * a * a;
double c2a = c21_1;
double c2b = c22_1 + c22_2 * a;
double c2c = c23_1 + c23_2 * a + c23_3 * a * a;
// we solve the first one
double bb[2];
if (!univariate::solve_quadratic_real(c1a, c1b, c1c, bb))
continue;
// and check the residuals of the other
double res1 = c2a * bb[0] * bb[0] + c2b * bb[0] + c2c;
double res2;
// For data where X(3,:) = 0 there is only a single solution
// In this case the second solution will be NaN
if (std::isnan(bb[1]))
res2 = std::numeric_limits<double>::max();
else
res2 = c2a * bb[1] * bb[1] + c2b * bb[1] + c2c;
double b = (std::abs(res1) > std::abs(res2)) ? bb[1] : bb[0];
Eigen::Matrix<double, 8, 1> p = N.col(0) * a + N.col(1) * b + N.col(2);
Eigen::Matrix3d R;
R.row(0) << p(0), p(1), p(2);
R.row(1) << p(4), p(5), p(6);
Eigen::Vector3d t(p(3), p(7), 0.0);
double scale = R.row(0).norm();
R.row(0) /= scale;
R.row(1) /= scale;
t /= scale;
R.row(2) = R.row(0).cross(R.row(1));
// Select sign using first point
if ((R * X[0] + t).topRows<2>().dot(x[0]) < 0) {
R.block<2, 3>(0, 0) = -R.block<2, 3>(0, 0);
t = -t;
}
output->emplace_back(R, t);
}
return n_roots;
}
} // namespace poselib
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