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MLPnPsolver.cpp
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/**
* This file is part of ORB-SLAM3
*
* Copyright (C) 2017-2021 Carlos Campos, Richard Elvira, Juan J. Gómez Rodríguez, José M.M. Montiel and Juan D. Tardós, University of Zaragoza.
* Copyright (C) 2014-2016 Raúl Mur-Artal, José M.M. Montiel and Juan D. Tardós, University of Zaragoza.
*
* ORB-SLAM3 is free software: you can redistribute it and/or modify it under the terms of the GNU General Public
* License as published by the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* ORB-SLAM3 is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even
* the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along with ORB-SLAM3.
* If not, see <http://www.gnu.org/licenses/>.
*/
/******************************************************************************
* Author: Steffen Urban *
* Contact: [email protected] *
* License: Copyright (c) 2016 Steffen Urban, ANU. 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 ANU 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 ANU OR THE CONTRIBUTORS 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 "MLPnPsolver.h"
#include <Eigen/Sparse>
namespace ORB_SLAM3 {
MLPnPsolver::MLPnPsolver(const Frame &F, const vector<MapPoint *> &vpMapPointMatches):
mnInliersi(0), mnIterations(0), mnBestInliers(0), N(0), mpCamera(F.mpCamera){
mvpMapPointMatches = vpMapPointMatches;
mvBearingVecs.reserve(F.mvpMapPoints.size());
mvP2D.reserve(F.mvpMapPoints.size());
mvSigma2.reserve(F.mvpMapPoints.size());
mvP3Dw.reserve(F.mvpMapPoints.size());
mvKeyPointIndices.reserve(F.mvpMapPoints.size());
mvAllIndices.reserve(F.mvpMapPoints.size());
int idx = 0;
for(size_t i = 0, iend = mvpMapPointMatches.size(); i < iend; i++){
MapPoint* pMP = vpMapPointMatches[i];
if(pMP){
if(!pMP -> isBad()){
if(i >= F.mvKeysUn.size()) continue;
const cv::KeyPoint &kp = F.mvKeysUn[i];
mvP2D.push_back(kp.pt);
mvSigma2.push_back(F.mvLevelSigma2[kp.octave]);
//Bearing vector should be normalized
cv::Point3f cv_br = mpCamera->unproject(kp.pt);
cv_br /= cv_br.z;
bearingVector_t br(cv_br.x,cv_br.y,cv_br.z);
mvBearingVecs.push_back(br);
//3D coordinates
Eigen::Matrix<float,3,1> posEig = pMP -> GetWorldPos();
point_t pos(posEig(0),posEig(1),posEig(2));
mvP3Dw.push_back(pos);
mvKeyPointIndices.push_back(i);
mvAllIndices.push_back(idx);
idx++;
}
}
}
SetRansacParameters();
}
//RANSAC methods
bool MLPnPsolver::iterate(int nIterations, bool &bNoMore, vector<bool> &vbInliers, int &nInliers, Eigen::Matrix4f &Tout){
Tout.setIdentity();
bNoMore = false;
vbInliers.clear();
nInliers=0;
if(N<mRansacMinInliers)
{
bNoMore = true;
return false;
}
vector<size_t> vAvailableIndices;
int nCurrentIterations = 0;
while(mnIterations<mRansacMaxIts || nCurrentIterations<nIterations)
{
nCurrentIterations++;
mnIterations++;
vAvailableIndices = mvAllIndices;
//Bearing vectors and 3D points used for this ransac iteration
bearingVectors_t bearingVecs(mRansacMinSet);
points_t p3DS(mRansacMinSet);
vector<int> indexes(mRansacMinSet);
// Get min set of points
for(short i = 0; i < mRansacMinSet; ++i)
{
int randi = DUtils::Random::RandomInt(0, vAvailableIndices.size()-1);
int idx = vAvailableIndices[randi];
bearingVecs[i] = mvBearingVecs[idx];
p3DS[i] = mvP3Dw[idx];
indexes[i] = i;
vAvailableIndices[randi] = vAvailableIndices.back();
vAvailableIndices.pop_back();
}
//By the moment, we are using MLPnP without covariance info
cov3_mats_t covs(1);
//Result
transformation_t result;
// Compute camera pose
computePose(bearingVecs,p3DS,covs,indexes,result);
//Save result
mRi[0][0] = result(0,0);
mRi[0][1] = result(0,1);
mRi[0][2] = result(0,2);
mRi[1][0] = result(1,0);
mRi[1][1] = result(1,1);
mRi[1][2] = result(1,2);
mRi[2][0] = result(2,0);
mRi[2][1] = result(2,1);
mRi[2][2] = result(2,2);
mti[0] = result(0,3);mti[1] = result(1,3);mti[2] = result(2,3);
// Check inliers
CheckInliers();
if(mnInliersi>=mRansacMinInliers)
{
// If it is the best solution so far, save it
if(mnInliersi>mnBestInliers)
{
mvbBestInliers = mvbInliersi;
mnBestInliers = mnInliersi;
cv::Mat Rcw(3,3,CV_64F,mRi);
cv::Mat tcw(3,1,CV_64F,mti);
Rcw.convertTo(Rcw,CV_32F);
tcw.convertTo(tcw,CV_32F);
mBestTcw.setIdentity();
mBestTcw.block<3,3>(0,0) = Converter::toMatrix3f(Rcw);
mBestTcw.block<3,1>(0,3) = Converter::toVector3f(tcw);
Eigen::Matrix<double, 3, 3, Eigen::RowMajor> eigRcw(mRi[0]);
Eigen::Vector3d eigtcw(mti);
}
if(Refine())
{
nInliers = mnRefinedInliers;
vbInliers = vector<bool>(mvpMapPointMatches.size(),false);
for(int i=0; i<N; i++)
{
if(mvbRefinedInliers[i])
vbInliers[mvKeyPointIndices[i]] = true;
}
Tout = mRefinedTcw;
return true;
}
}
}
if(mnIterations>=mRansacMaxIts)
{
bNoMore=true;
if(mnBestInliers>=mRansacMinInliers)
{
nInliers=mnBestInliers;
vbInliers = vector<bool>(mvpMapPointMatches.size(),false);
for(int i=0; i<N; i++)
{
if(mvbBestInliers[i])
vbInliers[mvKeyPointIndices[i]] = true;
}
Tout = mBestTcw;
return true;
}
}
return false;
}
void MLPnPsolver::SetRansacParameters(double probability, int minInliers, int maxIterations, int minSet, float epsilon, float th2){
mRansacProb = probability;
mRansacMinInliers = minInliers;
mRansacMaxIts = maxIterations;
mRansacEpsilon = epsilon;
mRansacMinSet = minSet;
N = mvP2D.size(); // number of correspondences
mvbInliersi.resize(N);
// Adjust Parameters according to number of correspondences
int nMinInliers = N*mRansacEpsilon;
if(nMinInliers<mRansacMinInliers)
nMinInliers=mRansacMinInliers;
if(nMinInliers<minSet)
nMinInliers=minSet;
mRansacMinInliers = nMinInliers;
if(mRansacEpsilon<(float)mRansacMinInliers/N)
mRansacEpsilon=(float)mRansacMinInliers/N;
// Set RANSAC iterations according to probability, epsilon, and max iterations
int nIterations;
if(mRansacMinInliers==N)
nIterations=1;
else
nIterations = ceil(log(1-mRansacProb)/log(1-pow(mRansacEpsilon,3)));
mRansacMaxIts = max(1,min(nIterations,mRansacMaxIts));
mvMaxError.resize(mvSigma2.size());
for(size_t i=0; i<mvSigma2.size(); i++)
mvMaxError[i] = mvSigma2[i]*th2;
}
void MLPnPsolver::CheckInliers(){
mnInliersi=0;
for(int i=0; i<N; i++)
{
point_t p = mvP3Dw[i];
cv::Point3f P3Dw(p(0),p(1),p(2));
cv::Point2f P2D = mvP2D[i];
float xc = mRi[0][0]*P3Dw.x+mRi[0][1]*P3Dw.y+mRi[0][2]*P3Dw.z+mti[0];
float yc = mRi[1][0]*P3Dw.x+mRi[1][1]*P3Dw.y+mRi[1][2]*P3Dw.z+mti[1];
float zc = mRi[2][0]*P3Dw.x+mRi[2][1]*P3Dw.y+mRi[2][2]*P3Dw.z+mti[2];
cv::Point3f P3Dc(xc,yc,zc);
cv::Point2f uv = mpCamera->project(P3Dc);
float distX = P2D.x-uv.x;
float distY = P2D.y-uv.y;
float error2 = distX*distX+distY*distY;
if(error2<mvMaxError[i])
{
mvbInliersi[i]=true;
mnInliersi++;
}
else
{
mvbInliersi[i]=false;
}
}
}
bool MLPnPsolver::Refine(){
vector<int> vIndices;
vIndices.reserve(mvbBestInliers.size());
for(size_t i=0; i<mvbBestInliers.size(); i++)
{
if(mvbBestInliers[i])
{
vIndices.push_back(i);
}
}
//Bearing vectors and 3D points used for this ransac iteration
bearingVectors_t bearingVecs;
points_t p3DS;
vector<int> indexes;
for(size_t i=0; i<vIndices.size(); i++)
{
int idx = vIndices[i];
bearingVecs.push_back(mvBearingVecs[idx]);
p3DS.push_back(mvP3Dw[idx]);
indexes.push_back(i);
}
//By the moment, we are using MLPnP without covariance info
cov3_mats_t covs(1);
//Result
transformation_t result;
// Compute camera pose
computePose(bearingVecs,p3DS,covs,indexes,result);
// Check inliers
CheckInliers();
mnRefinedInliers =mnInliersi;
mvbRefinedInliers = mvbInliersi;
if(mnInliersi>mRansacMinInliers)
{
cv::Mat Rcw(3,3,CV_64F,mRi);
cv::Mat tcw(3,1,CV_64F,mti);
Rcw.convertTo(Rcw,CV_32F);
tcw.convertTo(tcw,CV_32F);
mRefinedTcw.setIdentity();
mRefinedTcw.block<3,3>(0,0) = Converter::toMatrix3f(Rcw);
mRefinedTcw.block<3,1>(0,3) = Converter::toVector3f(tcw);
Eigen::Matrix<double, 3, 3, Eigen::RowMajor> eigRcw(mRi[0]);
Eigen::Vector3d eigtcw(mti);
return true;
}
return false;
}
//MLPnP methods
void MLPnPsolver::computePose(const bearingVectors_t &f, const points_t &p, const cov3_mats_t &covMats,
const std::vector<int> &indices, transformation_t &result) {
size_t numberCorrespondences = indices.size();
assert(numberCorrespondences > 5);
bool planar = false;
// compute the nullspace of all vectors
std::vector<Eigen::MatrixXd> nullspaces(numberCorrespondences);
Eigen::MatrixXd points3(3, numberCorrespondences);
points_t points3v(numberCorrespondences);
points4_t points4v(numberCorrespondences);
for (size_t i = 0; i < numberCorrespondences; i++) {
bearingVector_t f_current = f[indices[i]];
points3.col(i) = p[indices[i]];
// nullspace of right vector
Eigen::JacobiSVD<Eigen::MatrixXd, Eigen::HouseholderQRPreconditioner>
svd_f(f_current.transpose(), Eigen::ComputeFullV);
nullspaces[i] = svd_f.matrixV().block(0, 1, 3, 2);
points3v[i] = p[indices[i]];
}
//////////////////////////////////////
// 1. test if we have a planar scene
//////////////////////////////////////
Eigen::Matrix3d planarTest = points3 * points3.transpose();
Eigen::FullPivHouseholderQR<Eigen::Matrix3d> rankTest(planarTest);
Eigen::Matrix3d eigenRot;
eigenRot.setIdentity();
// if yes -> transform points to new eigen frame
//if (minEigenVal < 1e-3 || minEigenVal == 0.0)
//rankTest.setThreshold(1e-10);
if (rankTest.rank() == 2) {
planar = true;
// self adjoint is faster and more accurate than general eigen solvers
// also has closed form solution for 3x3 self-adjoint matrices
// in addition this solver sorts the eigenvalues in increasing order
Eigen::SelfAdjointEigenSolver<Eigen::Matrix3d> eigen_solver(planarTest);
eigenRot = eigen_solver.eigenvectors().real();
eigenRot.transposeInPlace();
for (size_t i = 0; i < numberCorrespondences; i++)
points3.col(i) = eigenRot * points3.col(i);
}
//////////////////////////////////////
// 2. stochastic model
//////////////////////////////////////
Eigen::SparseMatrix<double> P(2 * numberCorrespondences,
2 * numberCorrespondences);
bool use_cov = false;
P.setIdentity(); // standard
// if we do have covariance information
// -> fill covariance matrix
if (covMats.size() == numberCorrespondences) {
use_cov = true;
int l = 0;
for (size_t i = 0; i < numberCorrespondences; ++i) {
// invert matrix
cov2_mat_t temp = nullspaces[i].transpose() * covMats[i] * nullspaces[i];
temp = temp.inverse().eval();
P.coeffRef(l, l) = temp(0, 0);
P.coeffRef(l, l + 1) = temp(0, 1);
P.coeffRef(l + 1, l) = temp(1, 0);
P.coeffRef(l + 1, l + 1) = temp(1, 1);
l += 2;
}
}
//////////////////////////////////////
// 3. fill the design matrix A
//////////////////////////////////////
const int rowsA = 2 * numberCorrespondences;
int colsA = 12;
Eigen::MatrixXd A;
if (planar) {
colsA = 9;
A = Eigen::MatrixXd(rowsA, 9);
} else
A = Eigen::MatrixXd(rowsA, 12);
A.setZero();
// fill design matrix
if (planar) {
for (size_t i = 0; i < numberCorrespondences; ++i) {
point_t pt3_current = points3.col(i);
// r12
A(2 * i, 0) = nullspaces[i](0, 0) * pt3_current[1];
A(2 * i + 1, 0) = nullspaces[i](0, 1) * pt3_current[1];
// r13
A(2 * i, 1) = nullspaces[i](0, 0) * pt3_current[2];
A(2 * i + 1, 1) = nullspaces[i](0, 1) * pt3_current[2];
// r22
A(2 * i, 2) = nullspaces[i](1, 0) * pt3_current[1];
A(2 * i + 1, 2) = nullspaces[i](1, 1) * pt3_current[1];
// r23
A(2 * i, 3) = nullspaces[i](1, 0) * pt3_current[2];
A(2 * i + 1, 3) = nullspaces[i](1, 1) * pt3_current[2];
// r32
A(2 * i, 4) = nullspaces[i](2, 0) * pt3_current[1];
A(2 * i + 1, 4) = nullspaces[i](2, 1) * pt3_current[1];
// r33
A(2 * i, 5) = nullspaces[i](2, 0) * pt3_current[2];
A(2 * i + 1, 5) = nullspaces[i](2, 1) * pt3_current[2];
// t1
A(2 * i, 6) = nullspaces[i](0, 0);
A(2 * i + 1, 6) = nullspaces[i](0, 1);
// t2
A(2 * i, 7) = nullspaces[i](1, 0);
A(2 * i + 1, 7) = nullspaces[i](1, 1);
// t3
A(2 * i, 8) = nullspaces[i](2, 0);
A(2 * i + 1, 8) = nullspaces[i](2, 1);
}
} else {
for (size_t i = 0; i < numberCorrespondences; ++i) {
point_t pt3_current = points3.col(i);
// r11
A(2 * i, 0) = nullspaces[i](0, 0) * pt3_current[0];
A(2 * i + 1, 0) = nullspaces[i](0, 1) * pt3_current[0];
// r12
A(2 * i, 1) = nullspaces[i](0, 0) * pt3_current[1];
A(2 * i + 1, 1) = nullspaces[i](0, 1) * pt3_current[1];
// r13
A(2 * i, 2) = nullspaces[i](0, 0) * pt3_current[2];
A(2 * i + 1, 2) = nullspaces[i](0, 1) * pt3_current[2];
// r21
A(2 * i, 3) = nullspaces[i](1, 0) * pt3_current[0];
A(2 * i + 1, 3) = nullspaces[i](1, 1) * pt3_current[0];
// r22
A(2 * i, 4) = nullspaces[i](1, 0) * pt3_current[1];
A(2 * i + 1, 4) = nullspaces[i](1, 1) * pt3_current[1];
// r23
A(2 * i, 5) = nullspaces[i](1, 0) * pt3_current[2];
A(2 * i + 1, 5) = nullspaces[i](1, 1) * pt3_current[2];
// r31
A(2 * i, 6) = nullspaces[i](2, 0) * pt3_current[0];
A(2 * i + 1, 6) = nullspaces[i](2, 1) * pt3_current[0];
// r32
A(2 * i, 7) = nullspaces[i](2, 0) * pt3_current[1];
A(2 * i + 1, 7) = nullspaces[i](2, 1) * pt3_current[1];
// r33
A(2 * i, 8) = nullspaces[i](2, 0) * pt3_current[2];
A(2 * i + 1, 8) = nullspaces[i](2, 1) * pt3_current[2];
// t1
A(2 * i, 9) = nullspaces[i](0, 0);
A(2 * i + 1, 9) = nullspaces[i](0, 1);
// t2
A(2 * i, 10) = nullspaces[i](1, 0);
A(2 * i + 1, 10) = nullspaces[i](1, 1);
// t3
A(2 * i, 11) = nullspaces[i](2, 0);
A(2 * i + 1, 11) = nullspaces[i](2, 1);
}
}
//////////////////////////////////////
// 4. solve least squares
//////////////////////////////////////
Eigen::MatrixXd AtPA;
if (use_cov)
AtPA = A.transpose() * P * A; // setting up the full normal equations seems to be unstable
else
AtPA = A.transpose() * A;
Eigen::JacobiSVD<Eigen::MatrixXd> svd_A(AtPA, Eigen::ComputeFullV);
Eigen::MatrixXd result1 = svd_A.matrixV().col(colsA - 1);
////////////////////////////////
// now we treat the results differently,
// depending on the scene (planar or not)
////////////////////////////////
rotation_t Rout;
translation_t tout;
if (planar) // planar case
{
rotation_t tmp;
// until now, we only estimated
// row one and two of the transposed rotation matrix
tmp << 0.0, result1(0, 0), result1(1, 0),
0.0, result1(2, 0), result1(3, 0),
0.0, result1(4, 0), result1(5, 0);
// row 3
tmp.col(0) = tmp.col(1).cross(tmp.col(2));
tmp.transposeInPlace();
double scale = 1.0 / std::sqrt(std::abs(tmp.col(1).norm() * tmp.col(2).norm()));
// find best rotation matrix in frobenius sense
Eigen::JacobiSVD<Eigen::MatrixXd> svd_R_frob(tmp, Eigen::ComputeFullU | Eigen::ComputeFullV);
rotation_t Rout1 = svd_R_frob.matrixU() * svd_R_frob.matrixV().transpose();
// test if we found a good rotation matrix
if (Rout1.determinant() < 0)
Rout1 *= -1.0;
// rotate this matrix back using the eigen frame
Rout1 = eigenRot.transpose() * Rout1;
translation_t t = scale * translation_t(result1(6, 0), result1(7, 0), result1(8, 0));
Rout1.transposeInPlace();
Rout1 *= -1;
if (Rout1.determinant() < 0.0)
Rout1.col(2) *= -1;
// now we have to find the best out of 4 combinations
rotation_t R1, R2;
R1.col(0) = Rout1.col(0);
R1.col(1) = Rout1.col(1);
R1.col(2) = Rout1.col(2);
R2.col(0) = -Rout1.col(0);
R2.col(1) = -Rout1.col(1);
R2.col(2) = Rout1.col(2);
vector<transformation_t, Eigen::aligned_allocator<transformation_t>> Ts(4);
Ts[0].block<3, 3>(0, 0) = R1;
Ts[0].block<3, 1>(0, 3) = t;
Ts[1].block<3, 3>(0, 0) = R1;
Ts[1].block<3, 1>(0, 3) = -t;
Ts[2].block<3, 3>(0, 0) = R2;
Ts[2].block<3, 1>(0, 3) = t;
Ts[3].block<3, 3>(0, 0) = R2;
Ts[3].block<3, 1>(0, 3) = -t;
vector<double> normVal(4);
for (int i = 0; i < 4; ++i) {
point_t reproPt;
double norms = 0.0;
for (int p = 0; p < 6; ++p) {
reproPt = Ts[i].block<3, 3>(0, 0) * points3v[p] + Ts[i].block<3, 1>(0, 3);
reproPt = reproPt / reproPt.norm();
norms += (1.0 - reproPt.transpose() * f[indices[p]]);
}
normVal[i] = norms;
}
std::vector<double>::iterator
findMinRepro = std::min_element(std::begin(normVal), std::end(normVal));
int idx = std::distance(std::begin(normVal), findMinRepro);
Rout = Ts[idx].block<3, 3>(0, 0);
tout = Ts[idx].block<3, 1>(0, 3);
} else // non-planar
{
rotation_t tmp;
tmp << result1(0, 0), result1(3, 0), result1(6, 0),
result1(1, 0), result1(4, 0), result1(7, 0),
result1(2, 0), result1(5, 0), result1(8, 0);
// get the scale
double scale = 1.0 /
std::pow(std::abs(tmp.col(0).norm() * tmp.col(1).norm() * tmp.col(2).norm()), 1.0 / 3.0);
//double scale = 1.0 / std::sqrt(std::abs(tmp.col(0).norm() * tmp.col(1).norm()));
// find best rotation matrix in frobenius sense
Eigen::JacobiSVD<Eigen::MatrixXd> svd_R_frob(tmp, Eigen::ComputeFullU | Eigen::ComputeFullV);
Rout = svd_R_frob.matrixU() * svd_R_frob.matrixV().transpose();
// test if we found a good rotation matrix
if (Rout.determinant() < 0)
Rout *= -1.0;
// scale translation
tout = Rout * (scale * translation_t(result1(9, 0), result1(10, 0), result1(11, 0)));
// find correct direction in terms of reprojection error, just take the first 6 correspondences
vector<double> error(2);
vector<Eigen::Matrix4d, Eigen::aligned_allocator<Eigen::Matrix4d>> Ts(2);
for (int s = 0; s < 2; ++s) {
error[s] = 0.0;
Ts[s] = Eigen::Matrix4d::Identity();
Ts[s].block<3, 3>(0, 0) = Rout;
if (s == 0)
Ts[s].block<3, 1>(0, 3) = tout;
else
Ts[s].block<3, 1>(0, 3) = -tout;
Ts[s] = Ts[s].inverse().eval();
for (int p = 0; p < 6; ++p) {
bearingVector_t v = Ts[s].block<3, 3>(0, 0) * points3v[p] + Ts[s].block<3, 1>(0, 3);
v = v / v.norm();
error[s] += (1.0 - v.transpose() * f[indices[p]]);
}
}
if (error[0] < error[1])
tout = Ts[0].block<3, 1>(0, 3);
else
tout = Ts[1].block<3, 1>(0, 3);
Rout = Ts[0].block<3, 3>(0, 0);
}
//////////////////////////////////////
// 5. gauss newton
//////////////////////////////////////
rodrigues_t omega = rot2rodrigues(Rout);
Eigen::VectorXd minx(6);
minx[0] = omega[0];
minx[1] = omega[1];
minx[2] = omega[2];
minx[3] = tout[0];
minx[4] = tout[1];
minx[5] = tout[2];
mlpnp_gn(minx, points3v, nullspaces, P, use_cov);
Rout = rodrigues2rot(rodrigues_t(minx[0], minx[1], minx[2]));
tout = translation_t(minx[3], minx[4], minx[5]);
// result inverse as opengv uses this convention
result.block<3, 3>(0, 0) = Rout;
result.block<3, 1>(0, 3) = tout;
}
Eigen::Matrix3d MLPnPsolver::rodrigues2rot(const Eigen::Vector3d &omega) {
rotation_t R = Eigen::Matrix3d::Identity();
Eigen::Matrix3d skewW;
skewW << 0.0, -omega(2), omega(1),
omega(2), 0.0, -omega(0),
-omega(1), omega(0), 0.0;
double omega_norm = omega.norm();
if (omega_norm > std::numeric_limits<double>::epsilon())
R = R + sin(omega_norm) / omega_norm * skewW
+ (1 - cos(omega_norm)) / (omega_norm * omega_norm) * (skewW * skewW);
return R;
}
Eigen::Vector3d MLPnPsolver::rot2rodrigues(const Eigen::Matrix3d &R) {
rodrigues_t omega;
omega << 0.0, 0.0, 0.0;
double trace = R.trace() - 1.0;
double wnorm = acos(trace / 2.0);
if (wnorm > std::numeric_limits<double>::epsilon())
{
omega[0] = (R(2, 1) - R(1, 2));
omega[1] = (R(0, 2) - R(2, 0));
omega[2] = (R(1, 0) - R(0, 1));
double sc = wnorm / (2.0*sin(wnorm));
omega *= sc;
}
return omega;
}
void MLPnPsolver::mlpnp_gn(Eigen::VectorXd &x, const points_t &pts, const std::vector<Eigen::MatrixXd> &nullspaces,
const Eigen::SparseMatrix<double> Kll, bool use_cov) {
const int numObservations = pts.size();
const int numUnknowns = 6;
// check redundancy
assert((2 * numObservations - numUnknowns) > 0);
// =============
// set all matrices up
// =============
Eigen::VectorXd r(2 * numObservations);
Eigen::VectorXd rd(2 * numObservations);
Eigen::MatrixXd Jac(2 * numObservations, numUnknowns);
Eigen::VectorXd g(numUnknowns, 1);
Eigen::VectorXd dx(numUnknowns, 1); // result vector
Jac.setZero();
r.setZero();
dx.setZero();
g.setZero();
int it_cnt = 0;
bool stop = false;
const int maxIt = 5;
double epsP = 1e-5;
Eigen::MatrixXd JacTSKll;
Eigen::MatrixXd A;
// solve simple gradient descent
while (it_cnt < maxIt && !stop) {
mlpnp_residuals_and_jacs(x, pts,
nullspaces,
r, Jac, true);
if (use_cov)
JacTSKll = Jac.transpose() * Kll;
else
JacTSKll = Jac.transpose();
A = JacTSKll * Jac;
// get system matrix
g = JacTSKll * r;
// solve
Eigen::LDLT<Eigen::MatrixXd> chol(A);
dx = chol.solve(g);
// this is to prevent the solution from falling into a wrong minimum
// if the linear estimate is spurious
if (dx.array().abs().maxCoeff() > 5.0 || dx.array().abs().minCoeff() > 1.0)
break;
// observation update
Eigen::MatrixXd dl = Jac * dx;
if (dl.array().abs().maxCoeff() < epsP) {
stop = true;
x = x - dx;
break;
} else
x = x - dx;
++it_cnt;
}//while
// result
}
void MLPnPsolver::mlpnp_residuals_and_jacs(const Eigen::VectorXd &x, const points_t &pts,
const std::vector<Eigen::MatrixXd> &nullspaces, Eigen::VectorXd &r,
Eigen::MatrixXd &fjac, bool getJacs) {
rodrigues_t w(x[0], x[1], x[2]);
translation_t T(x[3], x[4], x[5]);
rotation_t R = rodrigues2rot(w);
int ii = 0;
Eigen::MatrixXd jacs(2, 6);
for (int i = 0; i < pts.size(); ++i)
{
Eigen::Vector3d ptCam = R*pts[i] + T;
ptCam /= ptCam.norm();
r[ii] = nullspaces[i].col(0).transpose()*ptCam;
r[ii + 1] = nullspaces[i].col(1).transpose()*ptCam;
if (getJacs)
{
// jacs
mlpnpJacs(pts[i],
nullspaces[i].col(0), nullspaces[i].col(1),
w, T,
jacs);
// r
fjac(ii, 0) = jacs(0, 0);
fjac(ii, 1) = jacs(0, 1);
fjac(ii, 2) = jacs(0, 2);
fjac(ii, 3) = jacs(0, 3);
fjac(ii, 4) = jacs(0, 4);
fjac(ii, 5) = jacs(0, 5);
// s
fjac(ii + 1, 0) = jacs(1, 0);
fjac(ii + 1, 1) = jacs(1, 1);
fjac(ii + 1, 2) = jacs(1, 2);
fjac(ii + 1, 3) = jacs(1, 3);
fjac(ii + 1, 4) = jacs(1, 4);
fjac(ii + 1, 5) = jacs(1, 5);
}
ii += 2;
}
}
void MLPnPsolver::mlpnpJacs(const point_t& pt, const Eigen::Vector3d& nullspace_r,
const Eigen::Vector3d& nullspace_s, const rodrigues_t& w,
const translation_t& t, Eigen::MatrixXd& jacs){
double r1 = nullspace_r[0];
double r2 = nullspace_r[1];
double r3 = nullspace_r[2];
double s1 = nullspace_s[0];
double s2 = nullspace_s[1];
double s3 = nullspace_s[2];
double X1 = pt[0];
double Y1 = pt[1];
double Z1 = pt[2];
double w1 = w[0];
double w2 = w[1];
double w3 = w[2];
double t1 = t[0];
double t2 = t[1];
double t3 = t[2];
double t5 = w1*w1;
double t6 = w2*w2;
double t7 = w3*w3;
double t8 = t5+t6+t7;
double t9 = sqrt(t8);
double t10 = sin(t9);
double t11 = 1.0/sqrt(t8);
double t12 = cos(t9);
double t13 = t12-1.0;
double t14 = 1.0/t8;
double t16 = t10*t11*w3;
double t17 = t13*t14*w1*w2;
double t19 = t10*t11*w2;
double t20 = t13*t14*w1*w3;
double t24 = t6+t7;
double t27 = t16+t17;
double t28 = Y1*t27;
double t29 = t19-t20;
double t30 = Z1*t29;
double t31 = t13*t14*t24;
double t32 = t31+1.0;
double t33 = X1*t32;
double t15 = t1-t28+t30+t33;
double t21 = t10*t11*w1;
double t22 = t13*t14*w2*w3;
double t45 = t5+t7;
double t53 = t16-t17;
double t54 = X1*t53;
double t55 = t21+t22;
double t56 = Z1*t55;
double t57 = t13*t14*t45;
double t58 = t57+1.0;
double t59 = Y1*t58;
double t18 = t2+t54-t56+t59;
double t34 = t5+t6;
double t38 = t19+t20;
double t39 = X1*t38;
double t40 = t21-t22;
double t41 = Y1*t40;
double t42 = t13*t14*t34;
double t43 = t42+1.0;
double t44 = Z1*t43;
double t23 = t3-t39+t41+t44;
double t25 = 1.0/pow(t8,3.0/2.0);
double t26 = 1.0/(t8*t8);
double t35 = t12*t14*w1*w2;
double t36 = t5*t10*t25*w3;
double t37 = t5*t13*t26*w3*2.0;
double t46 = t10*t25*w1*w3;
double t47 = t5*t10*t25*w2;
double t48 = t5*t13*t26*w2*2.0;
double t49 = t10*t11;
double t50 = t5*t12*t14;
double t51 = t13*t26*w1*w2*w3*2.0;
double t52 = t10*t25*w1*w2*w3;
double t60 = t15*t15;
double t61 = t18*t18;
double t62 = t23*t23;
double t63 = t60+t61+t62;
double t64 = t5*t10*t25;
double t65 = 1.0/sqrt(t63);
double t66 = Y1*r2*t6;
double t67 = Z1*r3*t7;
double t68 = r1*t1*t5;
double t69 = r1*t1*t6;
double t70 = r1*t1*t7;
double t71 = r2*t2*t5;
double t72 = r2*t2*t6;
double t73 = r2*t2*t7;
double t74 = r3*t3*t5;
double t75 = r3*t3*t6;
double t76 = r3*t3*t7;
double t77 = X1*r1*t5;
double t78 = X1*r2*w1*w2;
double t79 = X1*r3*w1*w3;
double t80 = Y1*r1*w1*w2;
double t81 = Y1*r3*w2*w3;
double t82 = Z1*r1*w1*w3;
double t83 = Z1*r2*w2*w3;
double t84 = X1*r1*t6*t12;
double t85 = X1*r1*t7*t12;
double t86 = Y1*r2*t5*t12;
double t87 = Y1*r2*t7*t12;
double t88 = Z1*r3*t5*t12;
double t89 = Z1*r3*t6*t12;
double t90 = X1*r2*t9*t10*w3;
double t91 = Y1*r3*t9*t10*w1;
double t92 = Z1*r1*t9*t10*w2;
double t102 = X1*r3*t9*t10*w2;
double t103 = Y1*r1*t9*t10*w3;
double t104 = Z1*r2*t9*t10*w1;
double t105 = X1*r2*t12*w1*w2;
double t106 = X1*r3*t12*w1*w3;
double t107 = Y1*r1*t12*w1*w2;
double t108 = Y1*r3*t12*w2*w3;
double t109 = Z1*r1*t12*w1*w3;
double t110 = Z1*r2*t12*w2*w3;
double t93 = t66+t67+t68+t69+t70+t71+t72+t73+t74+t75+t76+t77+t78+t79+t80+t81+t82+t83+t84+t85+t86+t87+t88+t89+t90+t91+t92-t102-t103-t104-t105-t106-t107-t108-t109-t110;
double t94 = t10*t25*w1*w2;
double t95 = t6*t10*t25*w3;
double t96 = t6*t13*t26*w3*2.0;
double t97 = t12*t14*w2*w3;
double t98 = t6*t10*t25*w1;
double t99 = t6*t13*t26*w1*2.0;
double t100 = t6*t10*t25;
double t101 = 1.0/pow(t63,3.0/2.0);
double t111 = t6*t12*t14;
double t112 = t10*t25*w2*w3;
double t113 = t12*t14*w1*w3;
double t114 = t7*t10*t25*w2;
double t115 = t7*t13*t26*w2*2.0;
double t116 = t7*t10*t25*w1;
double t117 = t7*t13*t26*w1*2.0;
double t118 = t7*t12*t14;
double t119 = t13*t24*t26*w1*2.0;
double t120 = t10*t24*t25*w1;
double t121 = t119+t120;
double t122 = t13*t26*t34*w1*2.0;
double t123 = t10*t25*t34*w1;
double t131 = t13*t14*w1*2.0;
double t124 = t122+t123-t131;
double t139 = t13*t14*w3;
double t125 = -t35+t36+t37+t94-t139;
double t126 = X1*t125;
double t127 = t49+t50+t51+t52-t64;
double t128 = Y1*t127;
double t129 = t126+t128-Z1*t124;
double t130 = t23*t129*2.0;
double t132 = t13*t26*t45*w1*2.0;
double t133 = t10*t25*t45*w1;
double t138 = t13*t14*w2;
double t134 = -t46+t47+t48+t113-t138;
double t135 = X1*t134;
double t136 = -t49-t50+t51+t52+t64;
double t137 = Z1*t136;
double t140 = X1*s1*t5;
double t141 = Y1*s2*t6;
double t142 = Z1*s3*t7;
double t143 = s1*t1*t5;
double t144 = s1*t1*t6;
double t145 = s1*t1*t7;
double t146 = s2*t2*t5;
double t147 = s2*t2*t6;
double t148 = s2*t2*t7;
double t149 = s3*t3*t5;
double t150 = s3*t3*t6;
double t151 = s3*t3*t7;
double t152 = X1*s2*w1*w2;
double t153 = X1*s3*w1*w3;
double t154 = Y1*s1*w1*w2;
double t155 = Y1*s3*w2*w3;
double t156 = Z1*s1*w1*w3;
double t157 = Z1*s2*w2*w3;
double t158 = X1*s1*t6*t12;
double t159 = X1*s1*t7*t12;
double t160 = Y1*s2*t5*t12;
double t161 = Y1*s2*t7*t12;
double t162 = Z1*s3*t5*t12;
double t163 = Z1*s3*t6*t12;
double t164 = X1*s2*t9*t10*w3;
double t165 = Y1*s3*t9*t10*w1;
double t166 = Z1*s1*t9*t10*w2;
double t183 = X1*s3*t9*t10*w2;
double t184 = Y1*s1*t9*t10*w3;
double t185 = Z1*s2*t9*t10*w1;
double t186 = X1*s2*t12*w1*w2;
double t187 = X1*s3*t12*w1*w3;
double t188 = Y1*s1*t12*w1*w2;
double t189 = Y1*s3*t12*w2*w3;
double t190 = Z1*s1*t12*w1*w3;