mirror of
https://github.com/opencv/opencv.git
synced 2025-06-07 17:44:04 +08:00
Merge pull request #18371 from nathanrgodwin:sqpnp_dev
Added SQPnP algorithm to SolvePnP * Added sqpnp * Fixed test case * Added fix for duplicate point checking and inverse func reuse * Changes for 3x speedup Changed norm method (significant speed increase), changed nearest rotation computation to FOAM * Added symmetric 3x3 inverse and unrolled loops * Fixed error with SVD * Fixed error from with indices Indices were initialized negative. When nullspace is large, points coplanar, and rotation near 0, indices not changed.
This commit is contained in:
Nathan Godwin
GitHub
parent
ac24a72e66
commit
2255973b0f
@ -39,3 +39,11 @@
|
||||
year={2013},
|
||||
publisher={IEEE}
|
||||
}
|
||||
|
||||
@inproceedings{Terzakis20,
|
||||
author = {Terzakis, George and Lourakis, Manolis},
|
||||
year = {2020},
|
||||
month = {09},
|
||||
pages = {},
|
||||
title = {A Consistently Fast and Globally Optimal Solution to the Perspective-n-Point Problem}
|
||||
}
|
||||
|
||||
@ -464,6 +464,7 @@ enum SolvePnPMethod {
|
||||
//!< - point 1: [ squareLength / 2, squareLength / 2, 0]
|
||||
//!< - point 2: [ squareLength / 2, -squareLength / 2, 0]
|
||||
//!< - point 3: [-squareLength / 2, -squareLength / 2, 0]
|
||||
SOLVEPNP_SQPNP = 8, //!< SQPnP: A Consistently Fast and Globally OptimalSolution to the Perspective-n-Point Problem @cite Terzakis20
|
||||
#ifndef CV_DOXYGEN
|
||||
SOLVEPNP_MAX_COUNT //!< Used for count
|
||||
#endif
|
||||
@ -835,6 +836,9 @@ It requires 4 coplanar object points defined in the following order:
|
||||
- point 1: [ squareLength / 2, squareLength / 2, 0]
|
||||
- point 2: [ squareLength / 2, -squareLength / 2, 0]
|
||||
- point 3: [-squareLength / 2, -squareLength / 2, 0]
|
||||
- **SOLVEPNP_SQPNP** Method is based on the paper "A Consistently Fast and Globally Optimal Solution to the
|
||||
Perspective-n-Point Problem" by G. Terzakis and M.Lourakis (@cite Terzakis20). It requires 3 or more points.
|
||||
|
||||
|
||||
The function estimates the object pose given a set of object points, their corresponding image
|
||||
projections, as well as the camera intrinsic matrix and the distortion coefficients, see the figure below
|
||||
@ -958,6 +962,7 @@ a 3D point expressed in the world frame into the camera frame:
|
||||
- point 1: [ squareLength / 2, squareLength / 2, 0]
|
||||
- point 2: [ squareLength / 2, -squareLength / 2, 0]
|
||||
- point 3: [-squareLength / 2, -squareLength / 2, 0]
|
||||
- With **SOLVEPNP_SQPNP** input points must be >= 3
|
||||
*/
|
||||
CV_EXPORTS_W bool solvePnP( InputArray objectPoints, InputArray imagePoints,
|
||||
InputArray cameraMatrix, InputArray distCoeffs,
|
||||
|
||||
@ -47,6 +47,7 @@
|
||||
#include "p3p.h"
|
||||
#include "ap3p.h"
|
||||
#include "ippe.hpp"
|
||||
#include "sqpnp.hpp"
|
||||
#include "opencv2/calib3d/calib3d_c.h"
|
||||
#include <opencv2/core/utils/logger.hpp>
|
||||
|
||||
@ -751,7 +752,8 @@ int solvePnPGeneric( InputArray _opoints, InputArray _ipoints,
|
||||
|
||||
Mat opoints = _opoints.getMat(), ipoints = _ipoints.getMat();
|
||||
int npoints = std::max(opoints.checkVector(3, CV_32F), opoints.checkVector(3, CV_64F));
|
||||
CV_Assert( ( (npoints >= 4) || (npoints == 3 && flags == SOLVEPNP_ITERATIVE && useExtrinsicGuess) )
|
||||
CV_Assert( ( (npoints >= 4) || (npoints == 3 && flags == SOLVEPNP_ITERATIVE && useExtrinsicGuess)
|
||||
|| (npoints >= 3 && flags == SOLVEPNP_SQPNP) )
|
||||
&& npoints == std::max(ipoints.checkVector(2, CV_32F), ipoints.checkVector(2, CV_64F)) );
|
||||
|
||||
opoints = opoints.reshape(3, npoints);
|
||||
@ -936,6 +938,14 @@ int solvePnPGeneric( InputArray _opoints, InputArray _ipoints,
|
||||
}
|
||||
} catch (...) { }
|
||||
}
|
||||
else if (flags == SOLVEPNP_SQPNP)
|
||||
{
|
||||
Mat undistortedPoints;
|
||||
undistortPoints(ipoints, undistortedPoints, cameraMatrix, distCoeffs);
|
||||
|
||||
sqpnp::PoseSolver solver;
|
||||
solver.solve(opoints, undistortedPoints, vec_rvecs, vec_tvecs);
|
||||
}
|
||||
/*else if (flags == SOLVEPNP_DLS)
|
||||
{
|
||||
Mat undistortedPoints;
|
||||
@ -963,7 +973,8 @@ int solvePnPGeneric( InputArray _opoints, InputArray _ipoints,
|
||||
vec_tvecs.push_back(tvec);
|
||||
}*/
|
||||
else
|
||||
CV_Error(CV_StsBadArg, "The flags argument must be one of SOLVEPNP_ITERATIVE, SOLVEPNP_P3P, SOLVEPNP_EPNP or SOLVEPNP_DLS");
|
||||
CV_Error(CV_StsBadArg, "The flags argument must be one of SOLVEPNP_ITERATIVE, SOLVEPNP_P3P, "
|
||||
"SOLVEPNP_EPNP, SOLVEPNP_DLS, SOLVEPNP_UPNP, SOLVEPNP_AP3P, SOLVEPNP_IPPE, SOLVEPNP_IPPE_SQUARE or SOLVEPNP_SQPNP");
|
||||
|
||||
CV_Assert(vec_rvecs.size() == vec_tvecs.size());
|
||||
|
||||
|
||||
775
modules/calib3d/src/sqpnp.cpp
Normal file
775
modules/calib3d/src/sqpnp.cpp
Normal file
@ -0,0 +1,775 @@
|
||||
// This file is part of OpenCV project.
|
||||
// It is subject to the license terms in the LICENSE file found in the top-level directory
|
||||
// of this distribution and at http://opencv.org/license.html
|
||||
|
||||
// This file is based on file issued with the following license:
|
||||
|
||||
/*
|
||||
BSD 3-Clause License
|
||||
|
||||
Copyright (c) 2020, George Terzakis
|
||||
All rights reserved.
|
||||
|
||||
Redistribution and use in source and binary forms, with or without
|
||||
modification, are permitted provided that the following conditions are met:
|
||||
|
||||
1. Redistributions of source code must retain the above copyright notice, this
|
||||
list of conditions and the following disclaimer.
|
||||
|
||||
2. 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.
|
||||
|
||||
3. 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 THE COPYRIGHT HOLDER OR 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 "precomp.hpp"
|
||||
#include "sqpnp.hpp"
|
||||
|
||||
#include <opencv2/calib3d.hpp>
|
||||
|
||||
namespace cv {
|
||||
namespace sqpnp {
|
||||
|
||||
const double PoseSolver::RANK_TOLERANCE = 1e-7;
|
||||
const double PoseSolver::SQP_SQUARED_TOLERANCE = 1e-10;
|
||||
const double PoseSolver::SQP_DET_THRESHOLD = 1.001;
|
||||
const double PoseSolver::ORTHOGONALITY_SQUARED_ERROR_THRESHOLD = 1e-8;
|
||||
const double PoseSolver::EQUAL_VECTORS_SQUARED_DIFF = 1e-10;
|
||||
const double PoseSolver::EQUAL_SQUARED_ERRORS_DIFF = 1e-6;
|
||||
const double PoseSolver::POINT_VARIANCE_THRESHOLD = 1e-5;
|
||||
const double PoseSolver::SQRT3 = std::sqrt(3);
|
||||
const int PoseSolver::SQP_MAX_ITERATION = 15;
|
||||
|
||||
//No checking done here for overflow, since this is not public all call instances
|
||||
//are assumed to be valid
|
||||
template <typename tp, int snrows, int sncols,
|
||||
int dnrows, int dncols>
|
||||
void set(int row, int col, cv::Matx<tp, dnrows, dncols>& dest,
|
||||
const cv::Matx<tp, snrows, sncols>& source)
|
||||
{
|
||||
for (int y = 0; y < snrows; y++)
|
||||
{
|
||||
for (int x = 0; x < sncols; x++)
|
||||
{
|
||||
dest(row + y, col + x) = source(y, x);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
PoseSolver::PoseSolver()
|
||||
: num_null_vectors_(-1),
|
||||
num_solutions_(0)
|
||||
{
|
||||
}
|
||||
|
||||
|
||||
void PoseSolver::solve(InputArray objectPoints, InputArray imagePoints, OutputArrayOfArrays rvecs,
|
||||
OutputArrayOfArrays tvecs)
|
||||
{
|
||||
//Input checking
|
||||
int objType = objectPoints.getMat().type();
|
||||
CV_CheckType(objType, objType == CV_32FC3 || objType == CV_64FC3,
|
||||
"Type of objectPoints must be CV_32FC3 or CV_64FC3");
|
||||
|
||||
int imgType = imagePoints.getMat().type();
|
||||
CV_CheckType(imgType, imgType == CV_32FC2 || imgType == CV_64FC2,
|
||||
"Type of imagePoints must be CV_32FC2 or CV_64FC2");
|
||||
|
||||
CV_Assert(objectPoints.rows() == 1 || objectPoints.cols() == 1);
|
||||
CV_Assert(objectPoints.rows() >= 3 || objectPoints.cols() >= 3);
|
||||
CV_Assert(imagePoints.rows() == 1 || imagePoints.cols() == 1);
|
||||
CV_Assert(imagePoints.rows() * imagePoints.cols() == objectPoints.rows() * objectPoints.cols());
|
||||
|
||||
Mat _imagePoints;
|
||||
if (imgType == CV_32FC2)
|
||||
{
|
||||
imagePoints.getMat().convertTo(_imagePoints, CV_64F);
|
||||
}
|
||||
else
|
||||
{
|
||||
_imagePoints = imagePoints.getMat();
|
||||
}
|
||||
|
||||
Mat _objectPoints;
|
||||
if (objType == CV_32FC3)
|
||||
{
|
||||
objectPoints.getMat().convertTo(_objectPoints, CV_64F);
|
||||
}
|
||||
else
|
||||
{
|
||||
_objectPoints = objectPoints.getMat();
|
||||
}
|
||||
|
||||
num_null_vectors_ = -1;
|
||||
num_solutions_ = 0;
|
||||
|
||||
computeOmega(_objectPoints, _imagePoints);
|
||||
solveInternal();
|
||||
|
||||
int depthRot = rvecs.fixedType() ? rvecs.depth() : CV_64F;
|
||||
int depthTrans = tvecs.fixedType() ? tvecs.depth() : CV_64F;
|
||||
|
||||
rvecs.create(num_solutions_, 1, CV_MAKETYPE(depthRot, rvecs.fixedType() && rvecs.kind() == _InputArray::STD_VECTOR ? 3 : 1));
|
||||
tvecs.create(num_solutions_, 1, CV_MAKETYPE(depthTrans, tvecs.fixedType() && tvecs.kind() == _InputArray::STD_VECTOR ? 3 : 1));
|
||||
|
||||
for (int i = 0; i < num_solutions_; i++)
|
||||
{
|
||||
|
||||
Mat rvec;
|
||||
Mat rotation = Mat(solutions_[i].r_hat).reshape(1, 3);
|
||||
Rodrigues(rotation, rvec);
|
||||
|
||||
rvecs.getMatRef(i) = rvec;
|
||||
tvecs.getMatRef(i) = Mat(solutions_[i].t);
|
||||
}
|
||||
}
|
||||
|
||||
void PoseSolver::computeOmega(InputArray objectPoints, InputArray imagePoints)
|
||||
{
|
||||
omega_ = cv::Matx<double, 9, 9>::zeros();
|
||||
cv::Matx<double, 3, 9> qa_sum = cv::Matx<double, 3, 9>::zeros();
|
||||
|
||||
cv::Point2d sum_img(0, 0);
|
||||
cv::Point3d sum_obj(0, 0, 0);
|
||||
double sq_norm_sum = 0;
|
||||
|
||||
Mat _imagePoints = imagePoints.getMat();
|
||||
Mat _objectPoints = objectPoints.getMat();
|
||||
|
||||
int n = _objectPoints.cols * _objectPoints.rows;
|
||||
|
||||
for (int i = 0; i < n; i++)
|
||||
{
|
||||
const cv::Point2d& img_pt = _imagePoints.at<cv::Point2d>(i);
|
||||
const cv::Point3d& obj_pt = _objectPoints.at<cv::Point3d>(i);
|
||||
|
||||
sum_img += img_pt;
|
||||
sum_obj += obj_pt;
|
||||
|
||||
const double& x = img_pt.x, & y = img_pt.y;
|
||||
const double& X = obj_pt.x, & Y = obj_pt.y, & Z = obj_pt.z;
|
||||
double sq_norm = x * x + y * y;
|
||||
sq_norm_sum += sq_norm;
|
||||
|
||||
double X2 = X * X,
|
||||
XY = X * Y,
|
||||
XZ = X * Z,
|
||||
Y2 = Y * Y,
|
||||
YZ = Y * Z,
|
||||
Z2 = Z * Z;
|
||||
|
||||
omega_(0, 0) += X2;
|
||||
omega_(0, 1) += XY;
|
||||
omega_(0, 2) += XZ;
|
||||
omega_(1, 1) += Y2;
|
||||
omega_(1, 2) += YZ;
|
||||
omega_(2, 2) += Z2;
|
||||
|
||||
|
||||
//Populating this manually saves operations by only calculating upper triangle
|
||||
omega_(0, 6) += -x * X2; omega_(0, 7) += -x * XY; omega_(0, 8) += -x * XZ;
|
||||
omega_(1, 7) += -x * Y2; omega_(1, 8) += -x * YZ;
|
||||
omega_(2, 8) += -x * Z2;
|
||||
|
||||
omega_(3, 6) += -y * X2; omega_(3, 7) += -y * XY; omega_(3, 8) += -y * XZ;
|
||||
omega_(4, 7) += -y * Y2; omega_(4, 8) += -y * YZ;
|
||||
omega_(5, 8) += -y * Z2;
|
||||
|
||||
|
||||
omega_(6, 6) += sq_norm * X2; omega_(6, 7) += sq_norm * XY; omega_(6, 8) += sq_norm * XZ;
|
||||
omega_(7, 7) += sq_norm * Y2; omega_(7, 8) += sq_norm * YZ;
|
||||
omega_(8, 8) += sq_norm * Z2;
|
||||
|
||||
//Compute qa_sum
|
||||
qa_sum(0, 0) += X; qa_sum(0, 1) += Y; qa_sum(0, 2) += Z;
|
||||
qa_sum(1, 3) += X; qa_sum(1, 4) += Y; qa_sum(1, 5) += Z;
|
||||
|
||||
qa_sum(0, 6) += -x * X; qa_sum(0, 7) += -x * Y; qa_sum(0, 8) += -x * Z;
|
||||
qa_sum(1, 6) += -y * X; qa_sum(1, 7) += -y * Y; qa_sum(1, 8) += -y * Z;
|
||||
|
||||
qa_sum(2, 0) += -x * X; qa_sum(2, 1) += -x * Y; qa_sum(2, 2) += -x * Z;
|
||||
qa_sum(2, 3) += -y * X; qa_sum(2, 4) += -y * Y; qa_sum(2, 5) += -y * Z;
|
||||
|
||||
qa_sum(2, 6) += sq_norm * X; qa_sum(2, 7) += sq_norm * Y; qa_sum(2, 8) += sq_norm * Z;
|
||||
}
|
||||
|
||||
|
||||
omega_(1, 6) = omega_(0, 7); omega_(2, 6) = omega_(0, 8); omega_(2, 7) = omega_(1, 8);
|
||||
omega_(4, 6) = omega_(3, 7); omega_(5, 6) = omega_(3, 8); omega_(5, 7) = omega_(4, 8);
|
||||
omega_(7, 6) = omega_(6, 7); omega_(8, 6) = omega_(6, 8); omega_(8, 7) = omega_(7, 8);
|
||||
|
||||
|
||||
omega_(3, 3) = omega_(0, 0); omega_(3, 4) = omega_(0, 1); omega_(3, 5) = omega_(0, 2);
|
||||
omega_(4, 4) = omega_(1, 1); omega_(4, 5) = omega_(1, 2);
|
||||
omega_(5, 5) = omega_(2, 2);
|
||||
|
||||
//Mirror upper triangle to lower triangle
|
||||
for (int r = 0; r < 9; r++)
|
||||
{
|
||||
for (int c = 0; c < r; c++)
|
||||
{
|
||||
omega_(r, c) = omega_(c, r);
|
||||
}
|
||||
}
|
||||
|
||||
cv::Matx<double, 3, 3> q;
|
||||
q(0, 0) = n; q(0, 1) = 0; q(0, 2) = -sum_img.x;
|
||||
q(1, 0) = 0; q(1, 1) = n; q(1, 2) = -sum_img.y;
|
||||
q(2, 0) = -sum_img.x; q(2, 1) = -sum_img.y; q(2, 2) = sq_norm_sum;
|
||||
|
||||
double inv_n = 1.0 / n;
|
||||
double detQ = n * (n * sq_norm_sum - sum_img.y * sum_img.y - sum_img.x * sum_img.x);
|
||||
double point_coordinate_variance = detQ * inv_n * inv_n * inv_n;
|
||||
|
||||
CV_Assert(point_coordinate_variance >= POINT_VARIANCE_THRESHOLD);
|
||||
|
||||
Matx<double, 3, 3> q_inv;
|
||||
analyticalInverse3x3Symm(q, q_inv);
|
||||
|
||||
p_ = -q_inv * qa_sum;
|
||||
|
||||
omega_ += qa_sum.t() * p_;
|
||||
|
||||
cv::SVD omega_svd(omega_, cv::SVD::FULL_UV);
|
||||
s_ = omega_svd.w;
|
||||
u_ = cv::Mat(omega_svd.vt.t());
|
||||
|
||||
CV_Assert(s_(0) >= 1e-7);
|
||||
|
||||
while (s_(7 - num_null_vectors_) < RANK_TOLERANCE) num_null_vectors_++;
|
||||
|
||||
CV_Assert(++num_null_vectors_ <= 6);
|
||||
|
||||
point_mean_ = cv::Vec3d(sum_obj.x / n, sum_obj.y / n, sum_obj.z / n);
|
||||
}
|
||||
|
||||
void PoseSolver::solveInternal()
|
||||
{
|
||||
double min_sq_err = std::numeric_limits<double>::max();
|
||||
int num_eigen_points = num_null_vectors_ > 0 ? num_null_vectors_ : 1;
|
||||
|
||||
for (int i = 9 - num_eigen_points; i < 9; i++)
|
||||
{
|
||||
const cv::Matx<double, 9, 1> e = SQRT3 * u_.col(i);
|
||||
double orthogonality_sq_err = orthogonalityError(e);
|
||||
|
||||
SQPSolution solutions[2];
|
||||
|
||||
//If e is orthogonal, we can skip SQP
|
||||
if (orthogonality_sq_err < ORTHOGONALITY_SQUARED_ERROR_THRESHOLD)
|
||||
{
|
||||
solutions[0].r_hat = det3x3(e) * e;
|
||||
solutions[0].t = p_ * solutions[0].r_hat;
|
||||
checkSolution(solutions[0], min_sq_err);
|
||||
}
|
||||
else
|
||||
{
|
||||
Matx<double, 9, 1> r;
|
||||
nearestRotationMatrix(e, r);
|
||||
solutions[0] = runSQP(r);
|
||||
solutions[0].t = p_ * solutions[0].r_hat;
|
||||
checkSolution(solutions[0], min_sq_err);
|
||||
|
||||
nearestRotationMatrix(-e, r);
|
||||
solutions[1] = runSQP(r);
|
||||
solutions[1].t = p_ * solutions[1].r_hat;
|
||||
checkSolution(solutions[1], min_sq_err);
|
||||
}
|
||||
}
|
||||
|
||||
int c = 1;
|
||||
|
||||
while (min_sq_err > 3 * s_[9 - num_eigen_points - c] && 9 - num_eigen_points - c > 0)
|
||||
{
|
||||
int index = 9 - num_eigen_points - c;
|
||||
|
||||
const cv::Matx<double, 9, 1> e = u_.col(index);
|
||||
SQPSolution solutions[2];
|
||||
|
||||
Matx<double, 9, 1> r;
|
||||
nearestRotationMatrix(e, r);
|
||||
solutions[0] = runSQP(r);
|
||||
solutions[0].t = p_ * solutions[0].r_hat;
|
||||
checkSolution(solutions[0], min_sq_err);
|
||||
|
||||
nearestRotationMatrix(-e, r);
|
||||
solutions[1] = runSQP(r);
|
||||
solutions[1].t = p_ * solutions[1].r_hat;
|
||||
checkSolution(solutions[1], min_sq_err);
|
||||
|
||||
c++;
|
||||
}
|
||||
}
|
||||
|
||||
PoseSolver::SQPSolution PoseSolver::runSQP(const cv::Matx<double, 9, 1>& r0)
|
||||
{
|
||||
cv::Matx<double, 9, 1> r = r0;
|
||||
|
||||
double delta_squared_norm = std::numeric_limits<double>::max();
|
||||
cv::Matx<double, 9, 1> delta;
|
||||
|
||||
int step = 0;
|
||||
while (delta_squared_norm > SQP_SQUARED_TOLERANCE && step++ < SQP_MAX_ITERATION)
|
||||
{
|
||||
solveSQPSystem(r, delta);
|
||||
r += delta;
|
||||
delta_squared_norm = cv::norm(delta, cv::NORM_L2SQR);
|
||||
}
|
||||
|
||||
SQPSolution solution;
|
||||
|
||||
double det_r = det3x3(r);
|
||||
if (det_r < 0)
|
||||
{
|
||||
r = -r;
|
||||
det_r = -det_r;
|
||||
}
|
||||
|
||||
if (det_r > SQP_DET_THRESHOLD)
|
||||
{
|
||||
nearestRotationMatrix(r, solution.r_hat);
|
||||
}
|
||||
else
|
||||
{
|
||||
solution.r_hat = r;
|
||||
}
|
||||
|
||||
return solution;
|
||||
}
|
||||
|
||||
void PoseSolver::solveSQPSystem(const cv::Matx<double, 9, 1>& r, cv::Matx<double, 9, 1>& delta)
|
||||
{
|
||||
double sqnorm_r1 = r(0) * r(0) + r(1) * r(1) + r(2) * r(2),
|
||||
sqnorm_r2 = r(3) * r(3) + r(4) * r(4) + r(5) * r(5),
|
||||
sqnorm_r3 = r(6) * r(6) + r(7) * r(7) + r(8) * r(8);
|
||||
double dot_r1r2 = r(0) * r(3) + r(1) * r(4) + r(2) * r(5),
|
||||
dot_r1r3 = r(0) * r(6) + r(1) * r(7) + r(2) * r(8),
|
||||
dot_r2r3 = r(3) * r(6) + r(4) * r(7) + r(5) * r(8);
|
||||
|
||||
cv::Matx<double, 9, 3> N;
|
||||
cv::Matx<double, 9, 6> H;
|
||||
cv::Matx<double, 6, 6> JH;
|
||||
|
||||
computeRowAndNullspace(r, H, N, JH);
|
||||
|
||||
cv::Matx<double, 6, 1> g;
|
||||
g(0) = 1 - sqnorm_r1; g(1) = 1 - sqnorm_r2; g(2) = 1 - sqnorm_r3; g(3) = -dot_r1r2; g(4) = -dot_r2r3; g(5) = -dot_r1r3;
|
||||
|
||||
cv::Matx<double, 6, 1> x;
|
||||
x(0) = g(0) / JH(0, 0);
|
||||
x(1) = g(1) / JH(1, 1);
|
||||
x(2) = g(2) / JH(2, 2);
|
||||
x(3) = (g(3) - JH(3, 0) * x(0) - JH(3, 1) * x(1)) / JH(3, 3);
|
||||
x(4) = (g(4) - JH(4, 1) * x(1) - JH(4, 2) * x(2) - JH(4, 3) * x(3)) / JH(4, 4);
|
||||
x(5) = (g(5) - JH(5, 0) * x(0) - JH(5, 2) * x(2) - JH(5, 3) * x(3) - JH(5, 4) * x(4)) / JH(5, 5);
|
||||
|
||||
delta = H * x;
|
||||
|
||||
|
||||
cv::Matx<double, 3, 9> nt_omega = N.t() * omega_;
|
||||
cv::Matx<double, 3, 3> W = nt_omega * N, W_inv;
|
||||
|
||||
analyticalInverse3x3Symm(W, W_inv);
|
||||
|
||||
cv::Matx<double, 3, 1> y = -W_inv * nt_omega * (delta + r);
|
||||
delta += N * y;
|
||||
}
|
||||
|
||||
bool PoseSolver::analyticalInverse3x3Symm(const cv::Matx<double, 3, 3>& Q,
|
||||
cv::Matx<double, 3, 3>& Qinv,
|
||||
const double& threshold)
|
||||
{
|
||||
// 1. Get the elements of the matrix
|
||||
double a = Q(0, 0),
|
||||
b = Q(1, 0), d = Q(1, 1),
|
||||
c = Q(2, 0), e = Q(2, 1), f = Q(2, 2);
|
||||
|
||||
// 2. Determinant
|
||||
double t2, t4, t7, t9, t12;
|
||||
t2 = e * e;
|
||||
t4 = a * d;
|
||||
t7 = b * b;
|
||||
t9 = b * c;
|
||||
t12 = c * c;
|
||||
double det = -t4 * f + a * t2 + t7 * f - 2.0 * t9 * e + t12 * d;
|
||||
|
||||
if (fabs(det) < threshold) return false;
|
||||
|
||||
// 3. Inverse
|
||||
double t15, t20, t24, t30;
|
||||
t15 = 1.0 / det;
|
||||
t20 = (-b * f + c * e) * t15;
|
||||
t24 = (b * e - c * d) * t15;
|
||||
t30 = (a * e - t9) * t15;
|
||||
Qinv(0, 0) = (-d * f + t2) * t15;
|
||||
Qinv(0, 1) = Qinv(1, 0) = -t20;
|
||||
Qinv(0, 2) = Qinv(2, 0) = -t24;
|
||||
Qinv(1, 1) = -(a * f - t12) * t15;
|
||||
Qinv(1, 2) = Qinv(2, 1) = t30;
|
||||
Qinv(2, 2) = -(t4 - t7) * t15;
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
void PoseSolver::computeRowAndNullspace(const cv::Matx<double, 9, 1>& r,
|
||||
cv::Matx<double, 9, 6>& H,
|
||||
cv::Matx<double, 9, 3>& N,
|
||||
cv::Matx<double, 6, 6>& K,
|
||||
const double& norm_threshold)
|
||||
{
|
||||
H = cv::Matx<double, 9, 6>::zeros();
|
||||
|
||||
// 1. q1
|
||||
double norm_r1 = sqrt(r(0) * r(0) + r(1) * r(1) + r(2) * r(2));
|
||||
double inv_norm_r1 = norm_r1 > 1e-5 ? 1.0 / norm_r1 : 0.0;
|
||||
H(0, 0) = r(0) * inv_norm_r1;
|
||||
H(1, 0) = r(1) * inv_norm_r1;
|
||||
H(2, 0) = r(2) * inv_norm_r1;
|
||||
K(0, 0) = 2 * norm_r1;
|
||||
|
||||
// 2. q2
|
||||
double norm_r2 = sqrt(r(3) * r(3) + r(4) * r(4) + r(5) * r(5));
|
||||
double inv_norm_r2 = 1.0 / norm_r2;
|
||||
H(3, 1) = r(3) * inv_norm_r2;
|
||||
H(4, 1) = r(4) * inv_norm_r2;
|
||||
H(5, 1) = r(5) * inv_norm_r2;
|
||||
K(1, 0) = 0;
|
||||
K(1, 1) = 2 * norm_r2;
|
||||
|
||||
// 3. q3 = (r3'*q2)*q2 - (r3'*q1)*q1 ; q3 = q3/norm(q3)
|
||||
double norm_r3 = sqrt(r(6) * r(6) + r(7) * r(7) + r(8) * r(8));
|
||||
double inv_norm_r3 = 1.0 / norm_r3;
|
||||
H(6, 2) = r(6) * inv_norm_r3;
|
||||
H(7, 2) = r(7) * inv_norm_r3;
|
||||
H(8, 2) = r(8) * inv_norm_r3;
|
||||
K(2, 0) = K(2, 1) = 0;
|
||||
K(2, 2) = 2 * norm_r3;
|
||||
|
||||
// 4. q4
|
||||
double dot_j4q1 = r(3) * H(0, 0) + r(4) * H(1, 0) + r(5) * H(2, 0),
|
||||
dot_j4q2 = r(0) * H(3, 1) + r(1) * H(4, 1) + r(2) * H(5, 1);
|
||||
|
||||
H(0, 3) = r(3) - dot_j4q1 * H(0, 0);
|
||||
H(1, 3) = r(4) - dot_j4q1 * H(1, 0);
|
||||
H(2, 3) = r(5) - dot_j4q1 * H(2, 0);
|
||||
H(3, 3) = r(0) - dot_j4q2 * H(3, 1);
|
||||
H(4, 3) = r(1) - dot_j4q2 * H(4, 1);
|
||||
H(5, 3) = r(2) - dot_j4q2 * H(5, 1);
|
||||
double inv_norm_j4 = 1.0 / sqrt(H(0, 3) * H(0, 3) + H(1, 3) * H(1, 3) + H(2, 3) * H(2, 3) +
|
||||
H(3, 3) * H(3, 3) + H(4, 3) * H(4, 3) + H(5, 3) * H(5, 3));
|
||||
|
||||
H(0, 3) *= inv_norm_j4;
|
||||
H(1, 3) *= inv_norm_j4;
|
||||
H(2, 3) *= inv_norm_j4;
|
||||
H(3, 3) *= inv_norm_j4;
|
||||
H(4, 3) *= inv_norm_j4;
|
||||
H(5, 3) *= inv_norm_j4;
|
||||
|
||||
K(3, 0) = r(3) * H(0, 0) + r(4) * H(1, 0) + r(5) * H(2, 0);
|
||||
K(3, 1) = r(0) * H(3, 1) + r(1) * H(4, 1) + r(2) * H(5, 1);
|
||||
K(3, 2) = 0;
|
||||
K(3, 3) = r(3) * H(0, 3) + r(4) * H(1, 3) + r(5) * H(2, 3) + r(0) * H(3, 3) + r(1) * H(4, 3) + r(2) * H(5, 3);
|
||||
|
||||
// 5. q5
|
||||
double dot_j5q2 = r(6) * H(3, 1) + r(7) * H(4, 1) + r(8) * H(5, 1);
|
||||
double dot_j5q3 = r(3) * H(6, 2) + r(4) * H(7, 2) + r(5) * H(8, 2);
|
||||
double dot_j5q4 = r(6) * H(3, 3) + r(7) * H(4, 3) + r(8) * H(5, 3);
|
||||
|
||||
H(0, 4) = -dot_j5q4 * H(0, 3);
|
||||
H(1, 4) = -dot_j5q4 * H(1, 3);
|
||||
H(2, 4) = -dot_j5q4 * H(2, 3);
|
||||
H(3, 4) = r(6) - dot_j5q2 * H(3, 1) - dot_j5q4 * H(3, 3);
|
||||
H(4, 4) = r(7) - dot_j5q2 * H(4, 1) - dot_j5q4 * H(4, 3);
|
||||
H(5, 4) = r(8) - dot_j5q2 * H(5, 1) - dot_j5q4 * H(5, 3);
|
||||
H(6, 4) = r(3) - dot_j5q3 * H(6, 2); H(7, 4) = r(4) - dot_j5q3 * H(7, 2); H(8, 4) = r(5) - dot_j5q3 * H(8, 2);
|
||||
|
||||
Matx<double, 9, 1> q4 = H.col(4);
|
||||
q4 /= cv::norm(q4);
|
||||
set<double, 9, 1, 9, 6>(0, 4, H, q4);
|
||||
|
||||
K(4, 0) = 0;
|
||||
K(4, 1) = r(6) * H(3, 1) + r(7) * H(4, 1) + r(8) * H(5, 1);
|
||||
K(4, 2) = r(3) * H(6, 2) + r(4) * H(7, 2) + r(5) * H(8, 2);
|
||||
K(4, 3) = r(6) * H(3, 3) + r(7) * H(4, 3) + r(8) * H(5, 3);
|
||||
K(4, 4) = r(6) * H(3, 4) + r(7) * H(4, 4) + r(8) * H(5, 4) + r(3) * H(6, 4) + r(4) * H(7, 4) + r(5) * H(8, 4);
|
||||
|
||||
|
||||
// 4. q6
|
||||
double dot_j6q1 = r(6) * H(0, 0) + r(7) * H(1, 0) + r(8) * H(2, 0);
|
||||
double dot_j6q3 = r(0) * H(6, 2) + r(1) * H(7, 2) + r(2) * H(8, 2);
|
||||
double dot_j6q4 = r(6) * H(0, 3) + r(7) * H(1, 3) + r(8) * H(2, 3);
|
||||
double dot_j6q5 = r(0) * H(6, 4) + r(1) * H(7, 4) + r(2) * H(8, 4) + r(6) * H(0, 4) + r(7) * H(1, 4) + r(8) * H(2, 4);
|
||||
|
||||
H(0, 5) = r(6) - dot_j6q1 * H(0, 0) - dot_j6q4 * H(0, 3) - dot_j6q5 * H(0, 4);
|
||||
H(1, 5) = r(7) - dot_j6q1 * H(1, 0) - dot_j6q4 * H(1, 3) - dot_j6q5 * H(1, 4);
|
||||
H(2, 5) = r(8) - dot_j6q1 * H(2, 0) - dot_j6q4 * H(2, 3) - dot_j6q5 * H(2, 4);
|
||||
|
||||
H(3, 5) = -dot_j6q5 * H(3, 4) - dot_j6q4 * H(3, 3);
|
||||
H(4, 5) = -dot_j6q5 * H(4, 4) - dot_j6q4 * H(4, 3);
|
||||
H(5, 5) = -dot_j6q5 * H(5, 4) - dot_j6q4 * H(5, 3);
|
||||
|
||||
H(6, 5) = r(0) - dot_j6q3 * H(6, 2) - dot_j6q5 * H(6, 4);
|
||||
H(7, 5) = r(1) - dot_j6q3 * H(7, 2) - dot_j6q5 * H(7, 4);
|
||||
H(8, 5) = r(2) - dot_j6q3 * H(8, 2) - dot_j6q5 * H(8, 4);
|
||||
|
||||
Matx<double, 9, 1> q5 = H.col(5);
|
||||
q5 /= cv::norm(q5);
|
||||
set<double, 9, 1, 9, 6>(0, 5, H, q5);
|
||||
|
||||
K(5, 0) = r(6) * H(0, 0) + r(7) * H(1, 0) + r(8) * H(2, 0);
|
||||
K(5, 1) = 0; K(5, 2) = r(0) * H(6, 2) + r(1) * H(7, 2) + r(2) * H(8, 2);
|
||||
K(5, 3) = r(6) * H(0, 3) + r(7) * H(1, 3) + r(8) * H(2, 3);
|
||||
K(5, 4) = r(6) * H(0, 4) + r(7) * H(1, 4) + r(8) * H(2, 4) + r(0) * H(6, 4) + r(1) * H(7, 4) + r(2) * H(8, 4);
|
||||
K(5, 5) = r(6) * H(0, 5) + r(7) * H(1, 5) + r(8) * H(2, 5) + r(0) * H(6, 5) + r(1) * H(7, 5) + r(2) * H(8, 5);
|
||||
|
||||
// Great! Now H is an orthogonalized, sparse basis of the Jacobian row space and K is filled.
|
||||
//
|
||||
// Now get a projector onto the null space H:
|
||||
const cv::Matx<double, 9, 9> Pn = cv::Matx<double, 9, 9>::eye() - (H * H.t());
|
||||
|
||||
// Now we need to pick 3 columns of P with non-zero norm (> 0.3) and some angle between them (> 0.3).
|
||||
//
|
||||
// Find the 3 columns of Pn with largest norms
|
||||
int index1 = 0,
|
||||
index2 = 0,
|
||||
index3 = 0;
|
||||
double max_norm1 = std::numeric_limits<double>::min();
|
||||
double min_dot12 = std::numeric_limits<double>::max();
|
||||
double min_dot1323 = std::numeric_limits<double>::max();
|
||||
|
||||
|
||||
double col_norms[9];
|
||||
for (int i = 0; i < 9; i++)
|
||||
{
|
||||
col_norms[i] = cv::norm(Pn.col(i));
|
||||
if (col_norms[i] >= norm_threshold)
|
||||
{
|
||||
if (max_norm1 < col_norms[i])
|
||||
{
|
||||
max_norm1 = col_norms[i];
|
||||
index1 = i;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
Matx<double, 9, 1> v1 = Pn.col(index1);
|
||||
v1 /= max_norm1;
|
||||
set<double, 9, 1, 9, 3>(0, 0, N, v1);
|
||||
|
||||
for (int i = 0; i < 9; i++)
|
||||
{
|
||||
if (i == index1) continue;
|
||||
if (col_norms[i] >= norm_threshold)
|
||||
{
|
||||
double cos_v1_x_col = fabs(Pn.col(i).dot(v1) / col_norms[i]);
|
||||
|
||||
if (cos_v1_x_col <= min_dot12)
|
||||
{
|
||||
index2 = i;
|
||||
min_dot12 = cos_v1_x_col;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
Matx<double, 9, 1> v2 = Pn.col(index2);
|
||||
Matx<double, 9, 1> n0 = N.col(0);
|
||||
v2 -= v2.dot(n0) * n0;
|
||||
v2 /= cv::norm(v2);
|
||||
set<double, 9, 1, 9, 3>(0, 1, N, v2);
|
||||
|
||||
for (int i = 0; i < 9; i++)
|
||||
{
|
||||
if (i == index2 || i == index1) continue;
|
||||
if (col_norms[i] >= norm_threshold)
|
||||
{
|
||||
double cos_v1_x_col = fabs(Pn.col(i).dot(v1) / col_norms[i]);
|
||||
double cos_v2_x_col = fabs(Pn.col(i).dot(v2) / col_norms[i]);
|
||||
|
||||
if (cos_v1_x_col + cos_v2_x_col <= min_dot1323)
|
||||
{
|
||||
index3 = i;
|
||||
min_dot1323 = cos_v2_x_col + cos_v2_x_col;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
Matx<double, 9, 1> v3 = Pn.col(index3);
|
||||
Matx<double, 9, 1> n1 = N.col(1);
|
||||
v3 -= (v3.dot(n1)) * n1 - (v3.dot(n0)) * n0;
|
||||
v3 /= cv::norm(v3);
|
||||
set<double, 9, 1, 9, 3>(0, 2, N, v3);
|
||||
|
||||
}
|
||||
|
||||
// faster nearest rotation computation based on FOAM (see: http://users.ics.forth.gr/~lourakis/publ/2018_iros.pdf )
|
||||
/* Solve the nearest orthogonal approximation problem
|
||||
* i.e., given e, find R minimizing ||R-e||_F
|
||||
*
|
||||
* The computation borrows from Markley's FOAM algorithm
|
||||
* "Attitude Determination Using Vector Observations: A Fast Optimal Matrix Algorithm", J. Astronaut. Sci.
|
||||
*
|
||||
* See also M. Lourakis: "An Efficient Solution to Absolute Orientation", ICPR 2016
|
||||
*
|
||||
* Copyright (C) 2019 Manolis Lourakis (lourakis **at** ics forth gr)
|
||||
* Institute of Computer Science, Foundation for Research & Technology - Hellas
|
||||
* Heraklion, Crete, Greece.
|
||||
*/
|
||||
void PoseSolver::nearestRotationMatrix(const cv::Matx<double, 9, 1>& e,
|
||||
cv::Matx<double, 9, 1>& r)
|
||||
{
|
||||
register int i;
|
||||
double l, lprev, det_e, e_sq, adj_e_sq, adj_e[9];
|
||||
|
||||
// e's adjoint
|
||||
adj_e[0] = e(4) * e(8) - e(5) * e(7); adj_e[1] = e(2) * e(7) - e(1) * e(8); adj_e[2] = e(1) * e(5) - e(2) * e(4);
|
||||
adj_e[3] = e(5) * e(6) - e(3) * e(8); adj_e[4] = e(0) * e(8) - e(2) * e(6); adj_e[5] = e(2) * e(3) - e(0) * e(5);
|
||||
adj_e[6] = e(3) * e(7) - e(4) * e(6); adj_e[7] = e(1) * e(6) - e(0) * e(7); adj_e[8] = e(0) * e(4) - e(1) * e(3);
|
||||
|
||||
// det(e), ||e||^2, ||adj(e)||^2
|
||||
det_e = e(0) * e(4) * e(8) - e(0) * e(5) * e(7) - e(1) * e(3) * e(8) + e(2) * e(3) * e(7) + e(1) * e(6) * e(5) - e(2) * e(6) * e(4);
|
||||
e_sq = e(0) * e(0) + e(1) * e(1) + e(2) * e(2) + e(3) * e(3) + e(4) * e(4) + e(5) * e(5) + e(6) * e(6) + e(7) * e(7) + e(8) * e(8);
|
||||
adj_e_sq = adj_e[0] * adj_e[0] + adj_e[1] * adj_e[1] + adj_e[2] * adj_e[2] + adj_e[3] * adj_e[3] + adj_e[4] * adj_e[4] + adj_e[5] * adj_e[5] + adj_e[6] * adj_e[6] + adj_e[7] * adj_e[7] + adj_e[8] * adj_e[8];
|
||||
|
||||
// compute l_max with Newton-Raphson from FOAM's characteristic polynomial, i.e. eq.(23) - (26)
|
||||
for (i = 200, l = 2.0, lprev = 0.0; fabs(l - lprev) > 1E-12 * fabs(lprev) && i > 0; --i) {
|
||||
double tmp, p, pp;
|
||||
|
||||
tmp = (l * l - e_sq);
|
||||
p = (tmp * tmp - 8.0 * l * det_e - 4.0 * adj_e_sq);
|
||||
pp = 8.0 * (0.5 * tmp * l - det_e);
|
||||
|
||||
lprev = l;
|
||||
l -= p / pp;
|
||||
}
|
||||
|
||||
// the rotation matrix equals ((l^2 + e_sq)*e + 2*l*adj(e') - 2*e*e'*e) / (l*(l*l-e_sq) - 2*det(e)), i.e. eq.(14) using (18), (19)
|
||||
{
|
||||
// compute (l^2 + e_sq)*e
|
||||
double tmp[9], e_et[9], denom;
|
||||
const double a = l * l + e_sq;
|
||||
|
||||
// e_et=e*e'
|
||||
e_et[0] = e(0) * e(0) + e(1) * e(1) + e(2) * e(2);
|
||||
e_et[1] = e(0) * e(3) + e(1) * e(4) + e(2) * e(5);
|
||||
e_et[2] = e(0) * e(6) + e(1) * e(7) + e(2) * e(8);
|
||||
|
||||
e_et[3] = e_et[1];
|
||||
e_et[4] = e(3) * e(3) + e(4) * e(4) + e(5) * e(5);
|
||||
e_et[5] = e(3) * e(6) + e(4) * e(7) + e(5) * e(8);
|
||||
|
||||
e_et[6] = e_et[2];
|
||||
e_et[7] = e_et[5];
|
||||
e_et[8] = e(6) * e(6) + e(7) * e(7) + e(8) * e(8);
|
||||
|
||||
// tmp=e_et*e
|
||||
tmp[0] = e_et[0] * e(0) + e_et[1] * e(3) + e_et[2] * e(6);
|
||||
tmp[1] = e_et[0] * e(1) + e_et[1] * e(4) + e_et[2] * e(7);
|
||||
tmp[2] = e_et[0] * e(2) + e_et[1] * e(5) + e_et[2] * e(8);
|
||||
|
||||
tmp[3] = e_et[3] * e(0) + e_et[4] * e(3) + e_et[5] * e(6);
|
||||
tmp[4] = e_et[3] * e(1) + e_et[4] * e(4) + e_et[5] * e(7);
|
||||
tmp[5] = e_et[3] * e(2) + e_et[4] * e(5) + e_et[5] * e(8);
|
||||
|
||||
tmp[6] = e_et[6] * e(0) + e_et[7] * e(3) + e_et[8] * e(6);
|
||||
tmp[7] = e_et[6] * e(1) + e_et[7] * e(4) + e_et[8] * e(7);
|
||||
tmp[8] = e_et[6] * e(2) + e_et[7] * e(5) + e_et[8] * e(8);
|
||||
|
||||
// compute R as (a*e + 2*(l*adj(e)' - tmp))*denom; note that adj(e')=adj(e)'
|
||||
denom = l * (l * l - e_sq) - 2.0 * det_e;
|
||||
denom = 1.0 / denom;
|
||||
r(0) = (a * e(0) + 2.0 * (l * adj_e[0] - tmp[0])) * denom;
|
||||
r(1) = (a * e(1) + 2.0 * (l * adj_e[3] - tmp[1])) * denom;
|
||||
r(2) = (a * e(2) + 2.0 * (l * adj_e[6] - tmp[2])) * denom;
|
||||
|
||||
r(3) = (a * e(3) + 2.0 * (l * adj_e[1] - tmp[3])) * denom;
|
||||
r(4) = (a * e(4) + 2.0 * (l * adj_e[4] - tmp[4])) * denom;
|
||||
r(5) = (a * e(5) + 2.0 * (l * adj_e[7] - tmp[5])) * denom;
|
||||
|
||||
r(6) = (a * e(6) + 2.0 * (l * adj_e[2] - tmp[6])) * denom;
|
||||
r(7) = (a * e(7) + 2.0 * (l * adj_e[5] - tmp[7])) * denom;
|
||||
r(8) = (a * e(8) + 2.0 * (l * adj_e[8] - tmp[8])) * denom;
|
||||
}
|
||||
}
|
||||
|
||||
double PoseSolver::det3x3(const cv::Matx<double, 9, 1>& e)
|
||||
{
|
||||
return e(0) * e(4) * e(8) + e(1) * e(5) * e(6) + e(2) * e(3) * e(7)
|
||||
- e(6) * e(4) * e(2) - e(7) * e(5) * e(0) - e(8) * e(3) * e(1);
|
||||
}
|
||||
|
||||
inline bool PoseSolver::positiveDepth(const SQPSolution& solution) const
|
||||
{
|
||||
const cv::Matx<double, 9, 1>& r = solution.r_hat;
|
||||
const cv::Matx<double, 3, 1>& t = solution.t;
|
||||
const cv::Vec3d& mean = point_mean_;
|
||||
return (r(6) * mean(0) + r(7) * mean(1) + r(8) * mean(2) + t(2) > 0);
|
||||
}
|
||||
|
||||
void PoseSolver::checkSolution(SQPSolution& solution, double& min_error)
|
||||
{
|
||||
if (positiveDepth(solution))
|
||||
{
|
||||
solution.sq_error = (omega_ * solution.r_hat).ddot(solution.r_hat);
|
||||
if (fabs(min_error - solution.sq_error) > EQUAL_SQUARED_ERRORS_DIFF)
|
||||
{
|
||||
if (min_error > solution.sq_error)
|
||||
{
|
||||
min_error = solution.sq_error;
|
||||
solutions_[0] = solution;
|
||||
num_solutions_ = 1;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
bool found = false;
|
||||
for (int i = 0; i < num_solutions_; i++)
|
||||
{
|
||||
if (cv::norm(solutions_[i].r_hat - solution.r_hat, cv::NORM_L2SQR) < EQUAL_VECTORS_SQUARED_DIFF)
|
||||
{
|
||||
if (solutions_[i].sq_error > solution.sq_error)
|
||||
{
|
||||
solutions_[i] = solution;
|
||||
}
|
||||
found = true;
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
if (!found)
|
||||
{
|
||||
solutions_[num_solutions_++] = solution;
|
||||
}
|
||||
if (min_error > solution.sq_error) min_error = solution.sq_error;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
double PoseSolver::orthogonalityError(const cv::Matx<double, 9, 1>& e)
|
||||
{
|
||||
double sq_norm_e1 = e(0) * e(0) + e(1) * e(1) + e(2) * e(2);
|
||||
double sq_norm_e2 = e(3) * e(3) + e(4) * e(4) + e(5) * e(5);
|
||||
double sq_norm_e3 = e(6) * e(6) + e(7) * e(7) + e(8) * e(8);
|
||||
double dot_e1e2 = e(0) * e(3) + e(1) * e(4) + e(2) * e(5);
|
||||
double dot_e1e3 = e(0) * e(6) + e(1) * e(7) + e(2) * e(8);
|
||||
double dot_e2e3 = e(3) * e(6) + e(4) * e(7) + e(5) * e(8);
|
||||
|
||||
return (sq_norm_e1 - 1) * (sq_norm_e1 - 1) + (sq_norm_e2 - 1) * (sq_norm_e2 - 1) + (sq_norm_e3 - 1) * (sq_norm_e3 - 1) +
|
||||
2 * (dot_e1e2 * dot_e1e2 + dot_e1e3 * dot_e1e3 + dot_e2e3 * dot_e2e3);
|
||||
}
|
||||
|
||||
}
|
||||
}
|
||||
194
modules/calib3d/src/sqpnp.hpp
Normal file
194
modules/calib3d/src/sqpnp.hpp
Normal file
@ -0,0 +1,194 @@
|
||||
// This file is part of OpenCV project.
|
||||
// It is subject to the license terms in the LICENSE file found in the top-level directory
|
||||
// of this distribution and at http://opencv.org/license.html
|
||||
|
||||
// This file is based on file issued with the following license:
|
||||
|
||||
/*
|
||||
BSD 3-Clause License
|
||||
|
||||
Copyright (c) 2020, George Terzakis
|
||||
All rights reserved.
|
||||
|
||||
Redistribution and use in source and binary forms, with or without
|
||||
modification, are permitted provided that the following conditions are met:
|
||||
|
||||
1. Redistributions of source code must retain the above copyright notice, this
|
||||
list of conditions and the following disclaimer.
|
||||
|
||||
2. 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.
|
||||
|
||||
3. 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 THE COPYRIGHT HOLDER OR 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.
|
||||
*/
|
||||
|
||||
#ifndef OPENCV_CALIB3D_SQPNP_HPP
|
||||
#define OPENCV_CALIB3D_SQPNP_HPP
|
||||
|
||||
#include <opencv2/core.hpp>
|
||||
|
||||
namespace cv {
|
||||
namespace sqpnp {
|
||||
|
||||
|
||||
class PoseSolver {
|
||||
public:
|
||||
/**
|
||||
* @brief PoseSolver constructor
|
||||
*/
|
||||
PoseSolver();
|
||||
|
||||
/**
|
||||
* @brief Finds the possible poses of a camera given a set of 3D points
|
||||
* and their corresponding 2D image projections. The poses are
|
||||
* sorted by lowest squared error (which corresponds to lowest
|
||||
* reprojection error).
|
||||
* @param objectPoints Array or vector of 3 or more 3D points defined in object coordinates.
|
||||
* 1xN/Nx1 3-channel (float or double) where N is the number of points.
|
||||
* @param imagePoints Array or vector of corresponding 2D points, 1xN/Nx1 2-channel.
|
||||
* @param rvec The output rotation solutions (up to 18 3x1 rotation vectors)
|
||||
* @param tvec The output translation solutions (up to 18 3x1 vectors)
|
||||
*/
|
||||
void solve(InputArray objectPoints, InputArray imagePoints, OutputArrayOfArrays rvec,
|
||||
OutputArrayOfArrays tvec);
|
||||
|
||||
private:
|
||||
struct SQPSolution
|
||||
{
|
||||
cv::Matx<double, 9, 1> r_hat;
|
||||
cv::Matx<double, 3, 1> t;
|
||||
double sq_error;
|
||||
};
|
||||
|
||||
/*
|
||||
* @brief Computes the 9x9 PSD Omega matrix and supporting matrices.
|
||||
* @param objectPoints Array or vector of 3 or more 3D points defined in object coordinates.
|
||||
* 1xN/Nx1 3-channel (float or double) where N is the number of points.
|
||||
* @param imagePoints Array or vector of corresponding 2D points, 1xN/Nx1 2-channel.
|
||||
*/
|
||||
void computeOmega(InputArray objectPoints, InputArray imagePoints);
|
||||
|
||||
/*
|
||||
* @brief Computes the 9x9 PSD Omega matrix and supporting matrices.
|
||||
*/
|
||||
void solveInternal();
|
||||
|
||||
/*
|
||||
* @brief Produces the distance from being orthogonal for a given 3x3 matrix
|
||||
* in row-major form.
|
||||
* @param e The vector to test representing a 3x3 matrix in row major form.
|
||||
* @return The distance the matrix is from being orthogonal.
|
||||
*/
|
||||
static double orthogonalityError(const cv::Matx<double, 9, 1>& e);
|
||||
|
||||
/*
|
||||
* @brief Processes a solution and sorts it by error.
|
||||
* @param solution The solution to evaluate.
|
||||
* @param min_error The current minimum error.
|
||||
*/
|
||||
void checkSolution(SQPSolution& solution, double& min_error);
|
||||
|
||||
/*
|
||||
* @brief Computes the determinant of a matrix stored in row-major format.
|
||||
* @param e Vector representing a 3x3 matrix stored in row-major format.
|
||||
* @return The determinant of the matrix.
|
||||
*/
|
||||
static double det3x3(const cv::Matx<double, 9, 1>& e);
|
||||
|
||||
/*
|
||||
* @brief Tests the cheirality for a given solution.
|
||||
* @param solution The solution to evaluate.
|
||||
*/
|
||||
inline bool positiveDepth(const SQPSolution& solution) const;
|
||||
|
||||
/*
|
||||
* @brief Determines the nearest rotation matrix to a given rotaiton matrix.
|
||||
* Input and output are 9x1 vector representing a vector stored in row-major
|
||||
* form.
|
||||
* @param e The input 3x3 matrix stored in a vector in row-major form.
|
||||
* @param r The nearest rotation matrix to the input e (again in row-major form).
|
||||
*/
|
||||
static void nearestRotationMatrix(const cv::Matx<double, 9, 1>& e,
|
||||
cv::Matx<double, 9, 1>& r);
|
||||
|
||||
/*
|
||||
* @brief Runs the sequential quadratic programming on orthogonal matrices.
|
||||
* @param r0 The start point of the solver.
|
||||
*/
|
||||
SQPSolution runSQP(const cv::Matx<double, 9, 1>& r0);
|
||||
|
||||
/*
|
||||
* @brief Steps down the gradient for the given matrix r to solve the SQP system.
|
||||
* @param r The current matrix step.
|
||||
* @param delta The next step down the gradient.
|
||||
*/
|
||||
void solveSQPSystem(const cv::Matx<double, 9, 1>& r, cv::Matx<double, 9, 1>& delta);
|
||||
|
||||
/*
|
||||
* @brief Analytically computes the inverse of a symmetric 3x3 matrix using the
|
||||
* lower triangle.
|
||||
* @param Q The matrix to invert.
|
||||
* @param Qinv The inverse of Q.
|
||||
* @param threshold The threshold to determine if Q is singular and non-invertible.
|
||||
*/
|
||||
bool analyticalInverse3x3Symm(const cv::Matx<double, 3, 3>& Q,
|
||||
cv::Matx<double, 3, 3>& Qinv,
|
||||
const double& threshold = 1e-8);
|
||||
|
||||
/*
|
||||
* @brief Computes the 3D null space and 6D normal space of the constraint Jacobian
|
||||
* at a 9D vector r (representing a rank-3 matrix). Note that K is lower
|
||||
* triangular so upper triangle is undefined.
|
||||
* @param r 9D vector representing a rank-3 matrix.
|
||||
* @param H 6D row space of the constraint Jacobian at r.
|
||||
* @param N 3D null space of the constraint Jacobian at r.
|
||||
* @param K The constraint Jacobian at r.
|
||||
* @param norm_threshold Threshold for column vector norm of Pn (the projection onto the null space
|
||||
* of the constraint Jacobian).
|
||||
*/
|
||||
void computeRowAndNullspace(const cv::Matx<double, 9, 1>& r,
|
||||
cv::Matx<double, 9, 6>& H,
|
||||
cv::Matx<double, 9, 3>& N,
|
||||
cv::Matx<double, 6, 6>& K,
|
||||
const double& norm_threshold = 0.1);
|
||||
|
||||
static const double RANK_TOLERANCE;
|
||||
static const double SQP_SQUARED_TOLERANCE;
|
||||
static const double SQP_DET_THRESHOLD;
|
||||
static const double ORTHOGONALITY_SQUARED_ERROR_THRESHOLD;
|
||||
static const double EQUAL_VECTORS_SQUARED_DIFF;
|
||||
static const double EQUAL_SQUARED_ERRORS_DIFF;
|
||||
static const double POINT_VARIANCE_THRESHOLD;
|
||||
static const int SQP_MAX_ITERATION;
|
||||
static const double SQRT3;
|
||||
|
||||
cv::Matx<double, 9, 9> omega_;
|
||||
cv::Vec<double, 9> s_;
|
||||
cv::Matx<double, 9, 9> u_;
|
||||
cv::Matx<double, 3, 9> p_;
|
||||
cv::Vec3d point_mean_;
|
||||
int num_null_vectors_;
|
||||
|
||||
SQPSolution solutions_[18];
|
||||
int num_solutions_;
|
||||
|
||||
};
|
||||
|
||||
}
|
||||
}
|
||||
|
||||
#endif
|
||||
@ -190,6 +190,8 @@ static std::string printMethod(int method)
|
||||
return "SOLVEPNP_IPPE";
|
||||
case 7:
|
||||
return "SOLVEPNP_IPPE_SQUARE";
|
||||
case 8:
|
||||
return "SOLVEPNP_SQPNP";
|
||||
default:
|
||||
return "Unknown value";
|
||||
}
|
||||
@ -206,6 +208,7 @@ public:
|
||||
eps[SOLVEPNP_AP3P] = 1.0e-2;
|
||||
eps[SOLVEPNP_DLS] = 1.0e-2;
|
||||
eps[SOLVEPNP_UPNP] = 1.0e-2;
|
||||
eps[SOLVEPNP_SQPNP] = 1.0e-2;
|
||||
totalTestsCount = 10;
|
||||
pointsCount = 500;
|
||||
}
|
||||
@ -436,6 +439,7 @@ public:
|
||||
eps[SOLVEPNP_UPNP] = 1.0e-6; //UPnP is remapped to EPnP, so we use the same threshold
|
||||
eps[SOLVEPNP_IPPE] = 1.0e-6;
|
||||
eps[SOLVEPNP_IPPE_SQUARE] = 1.0e-6;
|
||||
eps[SOLVEPNP_SQPNP] = 1.0e-6;
|
||||
|
||||
totalTestsCount = 1000;
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user