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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 "gp4ps.h"
#include "PoseLib/misc/re3q3.h"
#include "PoseLib/misc/univariate.h"
namespace poselib {
// Solves for camera pose such that: p+lambda*x = R*X+t
// Note: This function assumes that the bearing vectors (x) are normalized!
int gp4ps(const std::vector<Eigen::Vector3d> &p, const std::vector<Eigen::Vector3d> &x,
const std::vector<Eigen::Vector3d> &X, std::vector<CameraPose> *output, std::vector<double> *output_scales,
bool filter_solutions) {
for (int i = 0; i < 4; ++i) {
for (int j = i + 1; j < 4; ++j) {
if ((X[i] - X[j]).squaredNorm() < 1e-10) {
// we have a duplicated 3d point
std::vector<Eigen::Vector3d> pp = p;
std::vector<Eigen::Vector3d> xp = x;
std::vector<Eigen::Vector3d> Xp = X;
std::swap(pp[0], pp[i]);
std::swap(xp[0], xp[i]);
std::swap(Xp[0], Xp[i]);
std::swap(pp[1], pp[j]);
std::swap(xp[1], xp[j]);
std::swap(Xp[1], Xp[j]);
return gp4ps_camposeco(pp, xp, Xp, output, output_scales);
}
}
}
return gp4ps_kukelova(p, x, X, output, output_scales, filter_solutions);
}
// Solves for camera pose such that: scale*p+lambda*x = R*X+t
int gp4ps_kukelova(const std::vector<Eigen::Vector3d> &p, const std::vector<Eigen::Vector3d> &x,
const std::vector<Eigen::Vector3d> &X, std::vector<CameraPose> *output,
std::vector<double> *output_scales, bool filter_solutions) {
Eigen::Matrix<double, 8, 13> A;
for (int i = 0; i < 4; ++i) {
// xx = [x3 0 -x1; 0 x3 -x2]
// eqs = [xx kron(X',xx), -xx*p] * [t; scale; vec(R)]
A.row(2 * i) << x[i](2), 0.0, -x[i](0), -p[i](0) * x[i](2) + p[i](2) * x[i](0), X[i](0) * x[i](2), 0.0,
-X[i](0) * x[i](0), X[i](1) * x[i](2), 0.0, -X[i](1) * x[i](0), X[i](2) * x[i](2), 0.0, -X[i](2) * x[i](0);
A.row(2 * i + 1) << 0.0, x[i](2), -x[i](1), -p[i](1) * x[i](2) + p[i](2) * x[i](1), 0.0, X[i](0) * x[i](2),
-X[i](0) * x[i](1), 0.0, X[i](1) * x[i](2), -X[i](1) * x[i](1), 0.0, X[i](2) * x[i](2), -X[i](2) * x[i](1);
}
Eigen::Matrix4d B = A.block<4, 4>(0, 0).inverse();
Eigen::Matrix<double, 3, 9> AR = A.block<3, 9>(4, 4) - A.block<3, 4>(4, 0) * B * A.block<4, 9>(0, 4);
Eigen::Matrix<double, 4, 8> solutions;
int n_sols = re3q3::re3q3_rotation(AR, &solutions);
Eigen::Vector4d ts;
output->clear();
output_scales->clear();
CameraPose best_pose;
double best_scale = 1.0;
double best_res = 0.0;
for (int i = 0; i < n_sols; ++i) {
CameraPose pose;
pose.q = solutions.col(i);
ts = -B * (A.block<4, 9>(0, 4) * quat_to_rotmatvec(pose.q));
pose.t = ts.block<3, 1>(0, 0);
double scale = ts(3);
if (filter_solutions) {
double res = std::abs(x[3].dot((pose.R() * X[3] + pose.t - scale * p[3]).normalized()));
if (res > best_res) {
best_pose = pose;
best_scale = scale;
best_res = res;
}
} else {
output->push_back(pose);
output_scales->push_back(scale);
}
}
if (filter_solutions && best_res > 0.0) {
output->push_back(best_pose);
output_scales->push_back(best_scale);
}
return output->size();
}
// Solves for camera pose such that: scale*p+lambda*x = R*X+t
// Assumes that X[0] == X[1] !
int gp4ps_camposeco(const std::vector<Eigen::Vector3d> &p, const std::vector<Eigen::Vector3d> &x,
const std::vector<Eigen::Vector3d> &X, std::vector<CameraPose> *output,
std::vector<double> *output_scales) {
// Locally triangulate the 3D point
const double a = x[0].dot(x[1]);
const double b1 = x[0].dot(p[1] - p[0]);
const double b2 = x[1].dot(p[1] - p[0]);
const double lambda = (a * b2 - b1) / (a * a - 1);
const Eigen::Vector3d Xc = p[0] + lambda * x[0];
// Shift rig coordinate system by Xc
Eigen::Vector3d q0 = p[2] - Xc;
Eigen::Vector3d q1 = p[3] - Xc;
// Ensure q is orthogonal to x
q0 -= q0.dot(x[2]) * x[2];
q1 -= q1.dot(x[3]) * x[3];
const double D21 = (X[2] - X[0]).squaredNorm();
const double D31 = (X[3] - X[0]).squaredNorm();
const double D23 = (X[3] - X[2]).squaredNorm();
const double inv1 = 1.0 / D31;
const double k1 = -inv1 * D21;
const double k2 = inv1 * (D31 * (q0(0) * q0(0) + q0(1) * q0(1) + q0(2) * q0(2)) -
D21 * (q1(0) * q1(0) + q1(1) * q1(1) + q1(2) * q1(2)));
const double inv2 = 1.0 / (D21 * (x[2](0) * x[2](0) + x[2](1) * x[2](1) + x[2](2) * x[2](2)) -
D23 * (x[2](0) * x[2](0) + x[2](1) * x[2](1) + x[2](2) * x[2](2)));
const double k3 = inv2 * (-D21 * (2 * x[2](0) * x[3](0) + 2 * x[2](1) * x[3](1) + 2 * x[2](2) * x[3](2)));
const double k4 = inv2 * (D21 * (x[3](0) * x[3](0) + x[3](1) * x[3](1) + x[3](2) * x[3](2)));
const double k5 =
inv2 * (D21 * (2 * x[2](0) * (q0(0) - q1(0)) + 2 * x[2](1) * (q0(1) - q1(1)) + 2 * x[2](2) * (q0(2) - q1(2))) -
D23 * (2 * q0(0) * x[2](0) + 2 * q0(1) * x[2](1) + 2 * q0(2) * x[2](2)));
const double k6 =
inv2 * (-D21 * (2 * x[3](0) * (q0(0) - q1(0)) + 2 * x[3](1) * (q0(1) - q1(1)) + 2 * x[3](2) * (q0(2) - q1(2))));
const double k7 = inv2 * (D21 * ((q0(0) - q1(0)) * (q0(0) - q1(0)) + (q0(1) - q1(1)) * (q0(1) - q1(1)) +
(q0(2) - q1(2)) * (q0(2) - q1(2))) -
D23 * (q0(0) * q0(0) + q0(1) * q0(1) + q0(2) * q0(2)));
// Quartic in lambda3
const double inv_c4 = 1.0 / (k1 * k1 + k3 * k3 * k1 - 2 * k4 * k1 + k4 * k4);
const double c3 = inv_c4 * 2.0 * (k1 * k3 * k5 - k1 * k6 + k4 * k6);
const double c2 = inv_c4 * (k2 * k3 * k3 + k1 * k5 * k5 + k6 * k6 + 2.0 * k1 * k2 - 2.0 * k2 * k4 - 2.0 * k1 * k7 +
2.0 * k4 * k7);
const double c1 = inv_c4 * (2.0 * k2 * k3 * k5 - 2.0 * k2 * k6 + 2.0 * k6 * k7);
const double c0 = inv_c4 * (k2 * k2 + k2 * k5 * k5 + k7 * k7 - 2.0 * k2 * k7);
double roots[4];
const int n_sols = univariate::solve_quartic_real(c3, c2, c1, c0, roots);
Eigen::Matrix3d YY;
YY.col(0) = X[2] - X[0];
YY.col(1) = X[3] - X[0];
YY.col(2) = YY.col(0).cross(YY.col(1));
const double sY = YY.col(0).norm();
YY = YY.inverse().eval();
Eigen::Matrix3d XX;
output->clear();
output_scales->clear();
for (int i = 0; i < n_sols; ++i) {
const double lambda3 = roots[i];
const double lambda2 = (k2 - k7 + (k1 - k4) * lambda3 * lambda3 - k6 * lambda3) / (k3 * lambda3 + k5);
XX.col(0) = q0 + lambda2 * x[2];
XX.col(1) = q1 + lambda3 * x[3];
CameraPose pose;
double scale = sY / (XX.col(0)).norm();
XX.col(0) *= scale;
XX.col(1) *= scale;
XX.col(2) = XX.col(0).cross(XX.col(1));
pose.q = rotmat_to_quat(XX * YY);
pose.t = scale * Xc - pose.R() * X[0];
output->push_back(pose);
output_scales->push_back(scale);
}
return output->size();
}
} // namespace poselib
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