Merge pull request #3308 from edgarriba:master
This commit is contained in:
Vadim Pisarevsky
commit
8b7c0a7893
@ -588,6 +588,7 @@ Finds an object pose from 3D-2D point correspondences.
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* **SOLVEPNP_P3P** Method is based on the paper of X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang "Complete Solution Classification for the Perspective-Three-Point Problem". In this case the function requires exactly four object and image points.
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* **SOLVEPNP_P3P** Method is based on the paper of X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang "Complete Solution Classification for the Perspective-Three-Point Problem". In this case the function requires exactly four object and image points.
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* **SOLVEPNP_EPNP** Method has been introduced by F.Moreno-Noguer, V.Lepetit and P.Fua in the paper "EPnP: Efficient Perspective-n-Point Camera Pose Estimation".
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* **SOLVEPNP_EPNP** Method has been introduced by F.Moreno-Noguer, V.Lepetit and P.Fua in the paper "EPnP: Efficient Perspective-n-Point Camera Pose Estimation".
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* **SOLVEPNP_DLS** Method is based on the paper of Joel A. Hesch and Stergios I. Roumeliotis. "A Direct Least-Squares (DLS) Method for PnP".
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* **SOLVEPNP_DLS** Method is based on the paper of Joel A. Hesch and Stergios I. Roumeliotis. "A Direct Least-Squares (DLS) Method for PnP".
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* **SOLVEPNP_UPNP** Method is based on the paper of A.Penate-Sanchez, J.Andrade-Cetto, F.Moreno-Noguer. "Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation". In this case the function also estimates the parameters :math:`f_x` and :math:`f_y` assuming that both have the same value. Then the ``cameraMatrix`` is updated with the estimated focal length.
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The function estimates the object pose given a set of object points, their corresponding image projections, as well as the camera matrix and the distortion coefficients.
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The function estimates the object pose given a set of object points, their corresponding image projections, as well as the camera matrix and the distortion coefficients.
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@ -59,7 +59,9 @@ enum { LMEDS = 4, //!< least-median algorithm
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enum { SOLVEPNP_ITERATIVE = 0,
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enum { SOLVEPNP_ITERATIVE = 0,
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SOLVEPNP_EPNP = 1, // F.Moreno-Noguer, V.Lepetit and P.Fua "EPnP: Efficient Perspective-n-Point Camera Pose Estimation"
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SOLVEPNP_EPNP = 1, // F.Moreno-Noguer, V.Lepetit and P.Fua "EPnP: Efficient Perspective-n-Point Camera Pose Estimation"
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SOLVEPNP_P3P = 2, // X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang; "Complete Solution Classification for the Perspective-Three-Point Problem"
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SOLVEPNP_P3P = 2, // X.S. Gao, X.-R. Hou, J. Tang, H.-F. Chang; "Complete Solution Classification for the Perspective-Three-Point Problem"
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SOLVEPNP_DLS = 3 // Joel A. Hesch and Stergios I. Roumeliotis. "A Direct Least-Squares (DLS) Method for PnP"
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SOLVEPNP_DLS = 3, // Joel A. Hesch and Stergios I. Roumeliotis. "A Direct Least-Squares (DLS) Method for PnP"
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SOLVEPNP_UPNP = 4 // A.Penate-Sanchez, J.Andrade-Cetto, F.Moreno-Noguer. "Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation"
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};
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};
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enum { CALIB_CB_ADAPTIVE_THRESH = 1,
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enum { CALIB_CB_ADAPTIVE_THRESH = 1,
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@ -10,7 +10,7 @@ using namespace perf;
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using std::tr1::make_tuple;
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using std::tr1::make_tuple;
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using std::tr1::get;
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using std::tr1::get;
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CV_ENUM(pnpAlgo, SOLVEPNP_ITERATIVE, SOLVEPNP_EPNP, SOLVEPNP_P3P, SOLVEPNP_DLS)
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CV_ENUM(pnpAlgo, SOLVEPNP_ITERATIVE, SOLVEPNP_EPNP, SOLVEPNP_P3P, SOLVEPNP_DLS, SOLVEPNP_UPNP)
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typedef std::tr1::tuple<int, pnpAlgo> PointsNum_Algo_t;
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typedef std::tr1::tuple<int, pnpAlgo> PointsNum_Algo_t;
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typedef perf::TestBaseWithParam<PointsNum_Algo_t> PointsNum_Algo;
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typedef perf::TestBaseWithParam<PointsNum_Algo_t> PointsNum_Algo;
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@ -65,7 +65,7 @@ PERF_TEST_P(PointsNum_Algo, solvePnP,
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PERF_TEST_P(PointsNum_Algo, solvePnPSmallPoints,
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PERF_TEST_P(PointsNum_Algo, solvePnPSmallPoints,
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testing::Combine(
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testing::Combine(
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testing::Values(4), //TODO: find why results on 4 points are too unstable
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testing::Values(4), //TODO: find why results on 4 points are too unstable
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testing::Values((int)SOLVEPNP_P3P, (int)SOLVEPNP_DLS)
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testing::Values((int)SOLVEPNP_P3P, (int)SOLVEPNP_DLS, (int)SOLVEPNP_UPNP)
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)
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)
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)
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)
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{
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{
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@ -103,7 +103,7 @@ PERF_TEST_P(PointsNum_Algo, solvePnPSmallPoints,
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solvePnP(points3d, points2d, intrinsics, distortion, rvec, tvec, false, algo);
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solvePnP(points3d, points2d, intrinsics, distortion, rvec, tvec, false, algo);
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}
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}
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SANITY_CHECK(rvec, 1e-4);
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SANITY_CHECK(rvec, 1e-1);
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SANITY_CHECK(tvec, 1e-2);
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SANITY_CHECK(tvec, 1e-2);
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}
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}
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@ -41,6 +41,7 @@
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//M*/
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//M*/
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#include "precomp.hpp"
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#include "precomp.hpp"
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#include "upnp.h"
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#include "dls.h"
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#include "dls.h"
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#include "epnp.h"
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#include "epnp.h"
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#include "p3p.h"
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#include "p3p.h"
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@ -107,6 +108,16 @@ bool cv::solvePnP( InputArray _opoints, InputArray _ipoints,
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cv::Rodrigues(R, rvec);
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cv::Rodrigues(R, rvec);
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return result;
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return result;
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}
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}
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else if (flags == SOLVEPNP_UPNP)
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{
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upnp PnP(cameraMatrix, opoints, ipoints);
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cv::Mat R, rvec = _rvec.getMat(), tvec = _tvec.getMat();
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double f = PnP.compute_pose(R, tvec);
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cv::Rodrigues(R, rvec);
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cameraMatrix.at<double>(0,0) = cameraMatrix.at<double>(1,1) = f;
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return true;
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}
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else
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else
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CV_Error(CV_StsBadArg, "The flags argument must be one of SOLVEPNP_ITERATIVE, SOLVEPNP_P3P, SOLVEPNP_EPNP or SOLVEPNP_DLS");
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CV_Error(CV_StsBadArg, "The flags argument must be one of SOLVEPNP_ITERATIVE, SOLVEPNP_P3P, SOLVEPNP_EPNP or SOLVEPNP_DLS");
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return false;
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return false;
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@ -205,6 +216,7 @@ bool cv::solvePnPRansac(InputArray _opoints, InputArray _ipoints,
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int model_points = 4; // minimum of number of model points
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int model_points = 4; // minimum of number of model points
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if( flags == cv::SOLVEPNP_ITERATIVE ) model_points = 6;
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if( flags == cv::SOLVEPNP_ITERATIVE ) model_points = 6;
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else if( flags == cv::SOLVEPNP_UPNP ) model_points = 6;
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else if( flags == cv::SOLVEPNP_EPNP ) model_points = 5;
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else if( flags == cv::SOLVEPNP_EPNP ) model_points = 5;
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double param1 = reprojectionError; // reprojection error
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double param1 = reprojectionError; // reprojection error
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811
modules/calib3d/src/upnp.cpp
Normal file
811
modules/calib3d/src/upnp.cpp
Normal file
@ -0,0 +1,811 @@
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//M*//////////////////////////////////////////////////////////////////////////////////////
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//
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// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
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//
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// By downloading, copying, installing or using the software you agree to this license.
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// If you do not agree to this license, do not download, install,
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// copy or use the software.
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//
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//
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// License Agreement
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// For Open Source Computer Vision Library
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//
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// Copyright (C) 2000, Intel Corporation, all rights reserved.
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// Copyright (C) 2013, OpenCV Foundation, all rights reserved.
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// Third party copyrights are property of their respective owners.
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//
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// Redistribution and use in source and binary forms, with or without modification,
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// are permitted provided that the following conditions are met:
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//
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// * Redistribution's of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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//
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// * Redistribution's in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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//
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// * The name of the copyright holders may not be used to endorse or promote products
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// derived from this software without specific prior written permission.
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//
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// This software is provided by the copyright holders and contributors "as is" and
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// any express or implied warranties, including, but not limited to, the implied
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// warranties of merchantability and fitness for a particular purpose are disclaimed.
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// In no event shall the Intel Corporation or contributors be liable for any direct,
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// indirect, incidental, special, exemplary, or consequential damages
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// (including, but not limited to, procurement of substitute goods or services;
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// loss of use, data, or profits; or business interruption) however caused
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// and on any theory of liability, whether in contract, strict liability,
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// or tort (including negligence or otherwise) arising in any way out of
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// the use of this software, even if advised of the possibility of such damage.
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//
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//M*/
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/****************************************************************************************\
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* Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation.
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* Contributed by Edgar Riba
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\****************************************************************************************/
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#include "precomp.hpp"
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#include "upnp.h"
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#include <limits>
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using namespace std;
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using namespace cv;
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upnp::upnp(const Mat& cameraMatrix, const Mat& opoints, const Mat& ipoints)
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{
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if (cameraMatrix.depth() == CV_32F)
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init_camera_parameters<float>(cameraMatrix);
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else
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init_camera_parameters<double>(cameraMatrix);
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number_of_correspondences = std::max(opoints.checkVector(3, CV_32F), opoints.checkVector(3, CV_64F));
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pws.resize(3 * number_of_correspondences);
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us.resize(2 * number_of_correspondences);
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if (opoints.depth() == ipoints.depth())
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{
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if (opoints.depth() == CV_32F)
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init_points<Point3f,Point2f>(opoints, ipoints);
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else
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init_points<Point3d,Point2d>(opoints, ipoints);
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}
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else if (opoints.depth() == CV_32F)
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init_points<Point3f,Point2d>(opoints, ipoints);
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else
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init_points<Point3d,Point2f>(opoints, ipoints);
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alphas.resize(4 * number_of_correspondences);
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pcs.resize(3 * number_of_correspondences);
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max_nr = 0;
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A1 = NULL;
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A2 = NULL;
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}
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upnp::~upnp()
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{
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if (A1)
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delete[] A1;
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if (A2)
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delete[] A2;
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}
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double upnp::compute_pose(Mat& R, Mat& t)
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{
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choose_control_points();
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compute_alphas();
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Mat * M = new Mat(2 * number_of_correspondences, 12, CV_64F);
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for(int i = 0; i < number_of_correspondences; i++)
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{
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fill_M(M, 2 * i, &alphas[0] + 4 * i, us[2 * i], us[2 * i + 1]);
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}
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double mtm[12 * 12], d[12], ut[12 * 12], vt[12 * 12];
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Mat MtM = Mat(12, 12, CV_64F, mtm);
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Mat D = Mat(12, 1, CV_64F, d);
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Mat Ut = Mat(12, 12, CV_64F, ut);
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Mat Vt = Mat(12, 12, CV_64F, vt);
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MtM = M->t() * (*M);
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SVD::compute(MtM, D, Ut, Vt, SVD::MODIFY_A | SVD::FULL_UV);
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Mat(Ut.t()).copyTo(Ut);
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M->release();
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double l_6x12[6 * 12], rho[6];
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Mat L_6x12 = Mat(6, 12, CV_64F, l_6x12);
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Mat Rho = Mat(6, 1, CV_64F, rho);
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compute_L_6x12(ut, l_6x12);
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compute_rho(rho);
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double Betas[3][4], Efs[3][1], rep_errors[3];
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double Rs[3][3][3], ts[3][3];
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find_betas_and_focal_approx_1(&Ut, &Rho, Betas[1], Efs[1]);
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gauss_newton(&L_6x12, &Rho, Betas[1], Efs[1]);
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rep_errors[1] = compute_R_and_t(ut, Betas[1], Rs[1], ts[1]);
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find_betas_and_focal_approx_2(&Ut, &Rho, Betas[2], Efs[2]);
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gauss_newton(&L_6x12, &Rho, Betas[2], Efs[2]);
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rep_errors[2] = compute_R_and_t(ut, Betas[2], Rs[2], ts[2]);
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int N = 1;
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if (rep_errors[2] < rep_errors[1]) N = 2;
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Mat(3, 1, CV_64F, ts[N]).copyTo(t);
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Mat(3, 3, CV_64F, Rs[N]).copyTo(R);
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fu = fv = Efs[N][0];
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return fu;
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}
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void upnp::copy_R_and_t(const double R_src[3][3], const double t_src[3],
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double R_dst[3][3], double t_dst[3])
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{
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for(int i = 0; i < 3; i++) {
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for(int j = 0; j < 3; j++)
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R_dst[i][j] = R_src[i][j];
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t_dst[i] = t_src[i];
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}
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}
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void upnp::estimate_R_and_t(double R[3][3], double t[3])
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{
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double pc0[3], pw0[3];
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pc0[0] = pc0[1] = pc0[2] = 0.0;
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pw0[0] = pw0[1] = pw0[2] = 0.0;
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for(int i = 0; i < number_of_correspondences; i++) {
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const double * pc = &pcs[3 * i];
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const double * pw = &pws[3 * i];
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for(int j = 0; j < 3; j++) {
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pc0[j] += pc[j];
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pw0[j] += pw[j];
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}
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}
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for(int j = 0; j < 3; j++) {
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pc0[j] /= number_of_correspondences;
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pw0[j] /= number_of_correspondences;
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}
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double abt[3 * 3], abt_d[3], abt_u[3 * 3], abt_v[3 * 3];
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Mat ABt = Mat(3, 3, CV_64F, abt);
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Mat ABt_D = Mat(3, 1, CV_64F, abt_d);
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Mat ABt_U = Mat(3, 3, CV_64F, abt_u);
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Mat ABt_V = Mat(3, 3, CV_64F, abt_v);
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ABt.setTo(0.0);
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for(int i = 0; i < number_of_correspondences; i++) {
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double * pc = &pcs[3 * i];
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double * pw = &pws[3 * i];
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for(int j = 0; j < 3; j++) {
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abt[3 * j ] += (pc[j] - pc0[j]) * (pw[0] - pw0[0]);
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abt[3 * j + 1] += (pc[j] - pc0[j]) * (pw[1] - pw0[1]);
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abt[3 * j + 2] += (pc[j] - pc0[j]) * (pw[2] - pw0[2]);
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}
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}
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SVD::compute(ABt, ABt_D, ABt_U, ABt_V, SVD::MODIFY_A);
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Mat(ABt_V.t()).copyTo(ABt_V);
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for(int i = 0; i < 3; i++)
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for(int j = 0; j < 3; j++)
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R[i][j] = dot(abt_u + 3 * i, abt_v + 3 * j);
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const double det =
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R[0][0] * R[1][1] * R[2][2] + R[0][1] * R[1][2] * R[2][0] + R[0][2] * R[1][0] * R[2][1] -
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R[0][2] * R[1][1] * R[2][0] - R[0][1] * R[1][0] * R[2][2] - R[0][0] * R[1][2] * R[2][1];
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if (det < 0) {
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||||||
|
R[2][0] = -R[2][0];
|
||||||
|
R[2][1] = -R[2][1];
|
||||||
|
R[2][2] = -R[2][2];
|
||||||
|
}
|
||||||
|
|
||||||
|
t[0] = pc0[0] - dot(R[0], pw0);
|
||||||
|
t[1] = pc0[1] - dot(R[1], pw0);
|
||||||
|
t[2] = pc0[2] - dot(R[2], pw0);
|
||||||
|
}
|
||||||
|
|
||||||
|
void upnp::solve_for_sign(void)
|
||||||
|
{
|
||||||
|
if (pcs[2] < 0.0) {
|
||||||
|
for(int i = 0; i < 4; i++)
|
||||||
|
for(int j = 0; j < 3; j++)
|
||||||
|
ccs[i][j] = -ccs[i][j];
|
||||||
|
|
||||||
|
for(int i = 0; i < number_of_correspondences; i++) {
|
||||||
|
pcs[3 * i ] = -pcs[3 * i];
|
||||||
|
pcs[3 * i + 1] = -pcs[3 * i + 1];
|
||||||
|
pcs[3 * i + 2] = -pcs[3 * i + 2];
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
double upnp::compute_R_and_t(const double * ut, const double * betas,
|
||||||
|
double R[3][3], double t[3])
|
||||||
|
{
|
||||||
|
compute_ccs(betas, ut);
|
||||||
|
compute_pcs();
|
||||||
|
|
||||||
|
solve_for_sign();
|
||||||
|
|
||||||
|
estimate_R_and_t(R, t);
|
||||||
|
|
||||||
|
return reprojection_error(R, t);
|
||||||
|
}
|
||||||
|
|
||||||
|
double upnp::reprojection_error(const double R[3][3], const double t[3])
|
||||||
|
{
|
||||||
|
double sum2 = 0.0;
|
||||||
|
|
||||||
|
for(int i = 0; i < number_of_correspondences; i++) {
|
||||||
|
double * pw = &pws[3 * i];
|
||||||
|
double Xc = dot(R[0], pw) + t[0];
|
||||||
|
double Yc = dot(R[1], pw) + t[1];
|
||||||
|
double inv_Zc = 1.0 / (dot(R[2], pw) + t[2]);
|
||||||
|
double ue = uc + fu * Xc * inv_Zc;
|
||||||
|
double ve = vc + fv * Yc * inv_Zc;
|
||||||
|
double u = us[2 * i], v = us[2 * i + 1];
|
||||||
|
|
||||||
|
sum2 += sqrt( (u - ue) * (u - ue) + (v - ve) * (v - ve) );
|
||||||
|
}
|
||||||
|
|
||||||
|
return sum2 / number_of_correspondences;
|
||||||
|
}
|
||||||
|
|
||||||
|
void upnp::choose_control_points()
|
||||||
|
{
|
||||||
|
for (int i = 0; i < 4; ++i)
|
||||||
|
cws[i][0] = cws[i][1] = cws[i][2] = 0.0;
|
||||||
|
cws[0][0] = cws[1][1] = cws[2][2] = 1.0;
|
||||||
|
}
|
||||||
|
|
||||||
|
void upnp::compute_alphas()
|
||||||
|
{
|
||||||
|
Mat CC = Mat(4, 3, CV_64F, &cws);
|
||||||
|
Mat PC = Mat(number_of_correspondences, 3, CV_64F, &pws[0]);
|
||||||
|
Mat ALPHAS = Mat(number_of_correspondences, 4, CV_64F, &alphas[0]);
|
||||||
|
|
||||||
|
Mat CC_ = CC.clone().t();
|
||||||
|
Mat PC_ = PC.clone().t();
|
||||||
|
|
||||||
|
Mat row14 = Mat::ones(1, 4, CV_64F);
|
||||||
|
Mat row1n = Mat::ones(1, number_of_correspondences, CV_64F);
|
||||||
|
|
||||||
|
CC_.push_back(row14);
|
||||||
|
PC_.push_back(row1n);
|
||||||
|
|
||||||
|
ALPHAS = Mat( CC_.inv() * PC_ ).t();
|
||||||
|
}
|
||||||
|
|
||||||
|
void upnp::fill_M(Mat * M, const int row, const double * as, const double u, const double v)
|
||||||
|
{
|
||||||
|
double * M1 = M->ptr<double>(row);
|
||||||
|
double * M2 = M1 + 12;
|
||||||
|
|
||||||
|
for(int i = 0; i < 4; i++) {
|
||||||
|
M1[3 * i ] = as[i] * fu;
|
||||||
|
M1[3 * i + 1] = 0.0;
|
||||||
|
M1[3 * i + 2] = as[i] * (uc - u);
|
||||||
|
|
||||||
|
M2[3 * i ] = 0.0;
|
||||||
|
M2[3 * i + 1] = as[i] * fv;
|
||||||
|
M2[3 * i + 2] = as[i] * (vc - v);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
void upnp::compute_ccs(const double * betas, const double * ut)
|
||||||
|
{
|
||||||
|
for(int i = 0; i < 4; ++i)
|
||||||
|
ccs[i][0] = ccs[i][1] = ccs[i][2] = 0.0;
|
||||||
|
|
||||||
|
int N = 4;
|
||||||
|
for(int i = 0; i < N; ++i) {
|
||||||
|
const double * v = ut + 12 * (9 + i);
|
||||||
|
for(int j = 0; j < 4; ++j)
|
||||||
|
for(int k = 0; k < 3; ++k)
|
||||||
|
ccs[j][k] += betas[i] * v[3 * j + k];
|
||||||
|
}
|
||||||
|
|
||||||
|
for (int i = 0; i < 4; ++i) ccs[i][2] *= fu;
|
||||||
|
}
|
||||||
|
|
||||||
|
void upnp::compute_pcs(void)
|
||||||
|
{
|
||||||
|
for(int i = 0; i < number_of_correspondences; i++) {
|
||||||
|
double * a = &alphas[0] + 4 * i;
|
||||||
|
double * pc = &pcs[0] + 3 * i;
|
||||||
|
|
||||||
|
for(int j = 0; j < 3; j++)
|
||||||
|
pc[j] = a[0] * ccs[0][j] + a[1] * ccs[1][j] + a[2] * ccs[2][j] + a[3] * ccs[3][j];
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
void upnp::find_betas_and_focal_approx_1(Mat * Ut, Mat * Rho, double * betas, double * efs)
|
||||||
|
{
|
||||||
|
Mat Kmf1 = Mat(12, 1, CV_64F, Ut->ptr<double>(11));
|
||||||
|
Mat dsq = Mat(6, 1, CV_64F, Rho->ptr<double>(0));
|
||||||
|
|
||||||
|
Mat D = compute_constraint_distance_2param_6eq_2unk_f_unk( Kmf1 );
|
||||||
|
Mat Dt = D.t();
|
||||||
|
|
||||||
|
Mat A = Dt * D;
|
||||||
|
Mat b = Dt * dsq;
|
||||||
|
|
||||||
|
Mat x = Mat(2, 1, CV_64F);
|
||||||
|
solve(A, b, x);
|
||||||
|
|
||||||
|
betas[0] = sqrt( abs( x.at<double>(0) ) );
|
||||||
|
betas[1] = betas[2] = betas[3] = 0.0;
|
||||||
|
|
||||||
|
efs[0] = sqrt( abs( x.at<double>(1) ) ) / betas[0];
|
||||||
|
}
|
||||||
|
|
||||||
|
void upnp::find_betas_and_focal_approx_2(Mat * Ut, Mat * Rho, double * betas, double * efs)
|
||||||
|
{
|
||||||
|
double u[12*12];
|
||||||
|
Mat U = Mat(12, 12, CV_64F, u);
|
||||||
|
Ut->copyTo(U);
|
||||||
|
|
||||||
|
Mat Kmf1 = Mat(12, 1, CV_64F, Ut->ptr<double>(10));
|
||||||
|
Mat Kmf2 = Mat(12, 1, CV_64F, Ut->ptr<double>(11));
|
||||||
|
Mat dsq = Mat(6, 1, CV_64F, Rho->ptr<double>(0));
|
||||||
|
|
||||||
|
Mat D = compute_constraint_distance_3param_6eq_6unk_f_unk( Kmf1, Kmf2 );
|
||||||
|
|
||||||
|
Mat A = D;
|
||||||
|
Mat b = dsq;
|
||||||
|
|
||||||
|
double x[6];
|
||||||
|
Mat X = Mat(6, 1, CV_64F, x);
|
||||||
|
|
||||||
|
solve(A, b, X, DECOMP_QR);
|
||||||
|
|
||||||
|
double solutions[18][3];
|
||||||
|
generate_all_possible_solutions_for_f_unk(x, solutions);
|
||||||
|
|
||||||
|
// find solution with minimum reprojection error
|
||||||
|
double min_error = std::numeric_limits<double>::max();
|
||||||
|
int min_sol = 0;
|
||||||
|
for (int i = 0; i < 18; ++i) {
|
||||||
|
|
||||||
|
betas[3] = solutions[i][0];
|
||||||
|
betas[2] = solutions[i][1];
|
||||||
|
betas[1] = betas[0] = 0.0;
|
||||||
|
fu = fv = solutions[i][2];
|
||||||
|
|
||||||
|
double Rs[3][3], ts[3];
|
||||||
|
double error_i = compute_R_and_t( u, betas, Rs, ts);
|
||||||
|
|
||||||
|
if( error_i < min_error)
|
||||||
|
{
|
||||||
|
min_error = error_i;
|
||||||
|
min_sol = i;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
betas[0] = solutions[min_sol][0];
|
||||||
|
betas[1] = solutions[min_sol][1];
|
||||||
|
betas[2] = betas[3] = 0.0;
|
||||||
|
|
||||||
|
efs[0] = solutions[min_sol][2];
|
||||||
|
}
|
||||||
|
|
||||||
|
Mat upnp::compute_constraint_distance_2param_6eq_2unk_f_unk(const Mat& M1)
|
||||||
|
{
|
||||||
|
Mat P = Mat(6, 2, CV_64F);
|
||||||
|
|
||||||
|
double m[13];
|
||||||
|
for (int i = 1; i < 13; ++i) m[i] = *M1.ptr<double>(i-1);
|
||||||
|
|
||||||
|
double t1 = pow( m[4], 2 );
|
||||||
|
double t4 = pow( m[1], 2 );
|
||||||
|
double t5 = pow( m[5], 2 );
|
||||||
|
double t8 = pow( m[2], 2 );
|
||||||
|
double t10 = pow( m[6], 2 );
|
||||||
|
double t13 = pow( m[3], 2 );
|
||||||
|
double t15 = pow( m[7], 2 );
|
||||||
|
double t18 = pow( m[8], 2 );
|
||||||
|
double t22 = pow( m[9], 2 );
|
||||||
|
double t26 = pow( m[10], 2 );
|
||||||
|
double t29 = pow( m[11], 2 );
|
||||||
|
double t33 = pow( m[12], 2 );
|
||||||
|
|
||||||
|
*P.ptr<double>(0,0) = t1 - 2 * m[4] * m[1] + t4 + t5 - 2 * m[5] * m[2] + t8;
|
||||||
|
*P.ptr<double>(0,1) = t10 - 2 * m[6] * m[3] + t13;
|
||||||
|
*P.ptr<double>(1,0) = t15 - 2 * m[7] * m[1] + t4 + t18 - 2 * m[8] * m[2] + t8;
|
||||||
|
*P.ptr<double>(1,1) = t22 - 2 * m[9] * m[3] + t13;
|
||||||
|
*P.ptr<double>(2,0) = t26 - 2 * m[10] * m[1] + t4 + t29 - 2 * m[11] * m[2] + t8;
|
||||||
|
*P.ptr<double>(2,1) = t33 - 2 * m[12] * m[3] + t13;
|
||||||
|
*P.ptr<double>(3,0) = t15 - 2 * m[7] * m[4] + t1 + t18 - 2 * m[8] * m[5] + t5;
|
||||||
|
*P.ptr<double>(3,1) = t22 - 2 * m[9] * m[6] + t10;
|
||||||
|
*P.ptr<double>(4,0) = t26 - 2 * m[10] * m[4] + t1 + t29 - 2 * m[11] * m[5] + t5;
|
||||||
|
*P.ptr<double>(4,1) = t33 - 2 * m[12] * m[6] + t10;
|
||||||
|
*P.ptr<double>(5,0) = t26 - 2 * m[10] * m[7] + t15 + t29 - 2 * m[11] * m[8] + t18;
|
||||||
|
*P.ptr<double>(5,1) = t33 - 2 * m[12] * m[9] + t22;
|
||||||
|
|
||||||
|
return P;
|
||||||
|
}
|
||||||
|
|
||||||
|
Mat upnp::compute_constraint_distance_3param_6eq_6unk_f_unk(const Mat& M1, const Mat& M2)
|
||||||
|
{
|
||||||
|
Mat P = Mat(6, 6, CV_64F);
|
||||||
|
|
||||||
|
double m[3][13];
|
||||||
|
for (int i = 1; i < 13; ++i)
|
||||||
|
{
|
||||||
|
m[1][i] = *M1.ptr<double>(i-1);
|
||||||
|
m[2][i] = *M2.ptr<double>(i-1);
|
||||||
|
}
|
||||||
|
|
||||||
|
double t1 = pow( m[1][4], 2 );
|
||||||
|
double t2 = pow( m[1][1], 2 );
|
||||||
|
double t7 = pow( m[1][5], 2 );
|
||||||
|
double t8 = pow( m[1][2], 2 );
|
||||||
|
double t11 = m[1][1] * m[2][1];
|
||||||
|
double t12 = m[1][5] * m[2][5];
|
||||||
|
double t15 = m[1][2] * m[2][2];
|
||||||
|
double t16 = m[1][4] * m[2][4];
|
||||||
|
double t19 = pow( m[2][4], 2 );
|
||||||
|
double t22 = pow( m[2][2], 2 );
|
||||||
|
double t23 = pow( m[2][1], 2 );
|
||||||
|
double t24 = pow( m[2][5], 2 );
|
||||||
|
double t28 = pow( m[1][6], 2 );
|
||||||
|
double t29 = pow( m[1][3], 2 );
|
||||||
|
double t34 = pow( m[1][3], 2 );
|
||||||
|
double t36 = m[1][6] * m[2][6];
|
||||||
|
double t40 = pow( m[2][6], 2 );
|
||||||
|
double t41 = pow( m[2][3], 2 );
|
||||||
|
double t47 = pow( m[1][7], 2 );
|
||||||
|
double t48 = pow( m[1][8], 2 );
|
||||||
|
double t52 = m[1][7] * m[2][7];
|
||||||
|
double t55 = m[1][8] * m[2][8];
|
||||||
|
double t59 = pow( m[2][8], 2 );
|
||||||
|
double t62 = pow( m[2][7], 2 );
|
||||||
|
double t64 = pow( m[1][9], 2 );
|
||||||
|
double t68 = m[1][9] * m[2][9];
|
||||||
|
double t74 = pow( m[2][9], 2 );
|
||||||
|
double t78 = pow( m[1][10], 2 );
|
||||||
|
double t79 = pow( m[1][11], 2 );
|
||||||
|
double t84 = m[1][10] * m[2][10];
|
||||||
|
double t87 = m[1][11] * m[2][11];
|
||||||
|
double t90 = pow( m[2][10], 2 );
|
||||||
|
double t95 = pow( m[2][11], 2 );
|
||||||
|
double t99 = pow( m[1][12], 2 );
|
||||||
|
double t101 = m[1][12] * m[2][12];
|
||||||
|
double t105 = pow( m[2][12], 2 );
|
||||||
|
|
||||||
|
*P.ptr<double>(0,0) = t1 + t2 - 2 * m[1][4] * m[1][1] - 2 * m[1][5] * m[1][2] + t7 + t8;
|
||||||
|
*P.ptr<double>(0,1) = -2 * m[2][4] * m[1][1] + 2 * t11 + 2 * t12 - 2 * m[1][4] * m[2][1] - 2 * m[2][5] * m[1][2] + 2 * t15 + 2 * t16 - 2 * m[1][5] * m[2][2];
|
||||||
|
*P.ptr<double>(0,2) = t19 - 2 * m[2][4] * m[2][1] + t22 + t23 + t24 - 2 * m[2][5] * m[2][2];
|
||||||
|
*P.ptr<double>(0,3) = t28 + t29 - 2 * m[1][6] * m[1][3];
|
||||||
|
*P.ptr<double>(0,4) = -2 * m[2][6] * m[1][3] + 2 * t34 - 2 * m[1][6] * m[2][3] + 2 * t36;
|
||||||
|
*P.ptr<double>(0,5) = -2 * m[2][6] * m[2][3] + t40 + t41;
|
||||||
|
|
||||||
|
*P.ptr<double>(1,0) = t8 - 2 * m[1][8] * m[1][2] - 2 * m[1][7] * m[1][1] + t47 + t48 + t2;
|
||||||
|
*P.ptr<double>(1,1) = 2 * t15 - 2 * m[1][8] * m[2][2] - 2 * m[2][8] * m[1][2] + 2 * t52 - 2 * m[1][7] * m[2][1] - 2 * m[2][7] * m[1][1] + 2 * t55 + 2 * t11;
|
||||||
|
*P.ptr<double>(1,2) = -2 * m[2][8] * m[2][2] + t22 + t23 + t59 - 2 * m[2][7] * m[2][1] + t62;
|
||||||
|
*P.ptr<double>(1,3) = t29 + t64 - 2 * m[1][9] * m[1][3];
|
||||||
|
*P.ptr<double>(1,4) = 2 * t34 + 2 * t68 - 2 * m[2][9] * m[1][3] - 2 * m[1][9] * m[2][3];
|
||||||
|
*P.ptr<double>(1,5) = -2 * m[2][9] * m[2][3] + t74 + t41;
|
||||||
|
|
||||||
|
*P.ptr<double>(2,0) = -2 * m[1][11] * m[1][2] + t2 + t8 + t78 + t79 - 2 * m[1][10] * m[1][1];
|
||||||
|
*P.ptr<double>(2,1) = 2 * t15 - 2 * m[1][11] * m[2][2] + 2 * t84 - 2 * m[1][10] * m[2][1] - 2 * m[2][10] * m[1][1] + 2 * t87 - 2 * m[2][11] * m[1][2]+ 2 * t11;
|
||||||
|
*P.ptr<double>(2,2) = t90 + t22 - 2 * m[2][10] * m[2][1] + t23 - 2 * m[2][11] * m[2][2] + t95;
|
||||||
|
*P.ptr<double>(2,3) = -2 * m[1][12] * m[1][3] + t99 + t29;
|
||||||
|
*P.ptr<double>(2,4) = 2 * t34 + 2 * t101 - 2 * m[2][12] * m[1][3] - 2 * m[1][12] * m[2][3];
|
||||||
|
*P.ptr<double>(2,5) = t41 + t105 - 2 * m[2][12] * m[2][3];
|
||||||
|
|
||||||
|
*P.ptr<double>(3,0) = t48 + t1 - 2 * m[1][8] * m[1][5] + t7 - 2 * m[1][7] * m[1][4] + t47;
|
||||||
|
*P.ptr<double>(3,1) = 2 * t16 - 2 * m[1][7] * m[2][4] + 2 * t55 + 2 * t52 - 2 * m[1][8] * m[2][5] - 2 * m[2][8] * m[1][5] - 2 * m[2][7] * m[1][4] + 2 * t12;
|
||||||
|
*P.ptr<double>(3,2) = t24 - 2 * m[2][8] * m[2][5] + t19 - 2 * m[2][7] * m[2][4] + t62 + t59;
|
||||||
|
*P.ptr<double>(3,3) = -2 * m[1][9] * m[1][6] + t64 + t28;
|
||||||
|
*P.ptr<double>(3,4) = 2 * t68 + 2 * t36 - 2 * m[2][9] * m[1][6] - 2 * m[1][9] * m[2][6];
|
||||||
|
*P.ptr<double>(3,5) = t40 + t74 - 2 * m[2][9] * m[2][6];
|
||||||
|
|
||||||
|
*P.ptr<double>(4,0) = t1 - 2 * m[1][10] * m[1][4] + t7 + t78 + t79 - 2 * m[1][11] * m[1][5];
|
||||||
|
*P.ptr<double>(4,1) = 2 * t84 - 2 * m[1][11] * m[2][5] - 2 * m[1][10] * m[2][4] + 2 * t16 - 2 * m[2][11] * m[1][5] + 2 * t87 - 2 * m[2][10] * m[1][4] + 2 * t12;
|
||||||
|
*P.ptr<double>(4,2) = t19 + t24 - 2 * m[2][10] * m[2][4] - 2 * m[2][11] * m[2][5] + t95 + t90;
|
||||||
|
*P.ptr<double>(4,3) = t28 - 2 * m[1][12] * m[1][6] + t99;
|
||||||
|
*P.ptr<double>(4,4) = 2 * t101 + 2 * t36 - 2 * m[2][12] * m[1][6] - 2 * m[1][12] * m[2][6];
|
||||||
|
*P.ptr<double>(4,5) = t105 - 2 * m[2][12] * m[2][6] + t40;
|
||||||
|
|
||||||
|
*P.ptr<double>(5,0) = -2 * m[1][10] * m[1][7] + t47 + t48 + t78 + t79 - 2 * m[1][11] * m[1][8];
|
||||||
|
*P.ptr<double>(5,1) = 2 * t84 + 2 * t87 - 2 * m[2][11] * m[1][8] - 2 * m[1][10] * m[2][7] - 2 * m[2][10] * m[1][7] + 2 * t55 + 2 * t52 - 2 * m[1][11] * m[2][8];
|
||||||
|
*P.ptr<double>(5,2) = -2 * m[2][10] * m[2][7] - 2 * m[2][11] * m[2][8] + t62 + t59 + t90 + t95;
|
||||||
|
*P.ptr<double>(5,3) = t64 - 2 * m[1][12] * m[1][9] + t99;
|
||||||
|
*P.ptr<double>(5,4) = 2 * t68 - 2 * m[2][12] * m[1][9] - 2 * m[1][12] * m[2][9] + 2 * t101;
|
||||||
|
*P.ptr<double>(5,5) = t105 - 2 * m[2][12] * m[2][9] + t74;
|
||||||
|
|
||||||
|
return P;
|
||||||
|
}
|
||||||
|
|
||||||
|
void upnp::generate_all_possible_solutions_for_f_unk(const double betas[5], double solutions[18][3])
|
||||||
|
{
|
||||||
|
int matrix_to_resolve[18][9] = {
|
||||||
|
{ 2, 0, 0, 1, 1, 0, 2, 0, 2 }, { 2, 0, 0, 1, 1, 0, 1, 1, 2 },
|
||||||
|
{ 2, 0, 0, 1, 1, 0, 0, 2, 2 }, { 2, 0, 0, 0, 2, 0, 2, 0, 2 },
|
||||||
|
{ 2, 0, 0, 0, 2, 0, 1, 1, 2 }, { 2, 0, 0, 0, 2, 0, 0, 2, 2 },
|
||||||
|
{ 2, 0, 0, 2, 0, 2, 1, 1, 2 }, { 2, 0, 0, 2, 0, 2, 0, 2, 2 },
|
||||||
|
{ 2, 0, 0, 1, 1, 2, 0, 2, 2 }, { 1, 1, 0, 0, 2, 0, 2, 0, 2 },
|
||||||
|
{ 1, 1, 0, 0, 2, 0, 1, 1, 2 }, { 1, 1, 0, 2, 0, 2, 0, 2, 2 },
|
||||||
|
{ 1, 1, 0, 2, 0, 2, 1, 1, 2 }, { 1, 1, 0, 2, 0, 2, 0, 2, 2 },
|
||||||
|
{ 1, 1, 0, 1, 1, 2, 0, 2, 2 }, { 0, 2, 0, 2, 0, 2, 1, 1, 2 },
|
||||||
|
{ 0, 2, 0, 2, 0, 2, 0, 2, 2 }, { 0, 2, 0, 1, 1, 2, 0, 2, 2 }
|
||||||
|
};
|
||||||
|
|
||||||
|
int combination[18][3] = {
|
||||||
|
{ 1, 2, 4 }, { 1, 2, 5 }, { 1, 2, 6 }, { 1, 3, 4 },
|
||||||
|
{ 1, 3, 5 }, { 1, 3, 6 }, { 1, 4, 5 }, { 1, 4, 6 },
|
||||||
|
{ 1, 5, 6 }, { 2, 3, 4 }, { 2, 3, 5 }, { 2, 3, 6 },
|
||||||
|
{ 2, 4, 5 }, { 2, 4, 6 }, { 2, 5, 6 }, { 3, 4, 5 },
|
||||||
|
{ 3, 4, 6 }, { 3, 5, 6 }
|
||||||
|
};
|
||||||
|
|
||||||
|
for (int i = 0; i < 18; ++i) {
|
||||||
|
double matrix[9], independent_term[3];
|
||||||
|
Mat M = Mat(3, 3, CV_64F, matrix);
|
||||||
|
Mat I = Mat(3, 1, CV_64F, independent_term);
|
||||||
|
Mat S = Mat(1, 3, CV_64F);
|
||||||
|
|
||||||
|
for (int j = 0; j < 9; ++j) matrix[j] = (double)matrix_to_resolve[i][j];
|
||||||
|
|
||||||
|
independent_term[0] = log( abs( betas[ combination[i][0]-1 ] ) );
|
||||||
|
independent_term[1] = log( abs( betas[ combination[i][1]-1 ] ) );
|
||||||
|
independent_term[2] = log( abs( betas[ combination[i][2]-1 ] ) );
|
||||||
|
|
||||||
|
exp( Mat(M.inv() * I), S);
|
||||||
|
|
||||||
|
solutions[i][0] = S.at<double>(0);
|
||||||
|
solutions[i][1] = S.at<double>(1) * sign( betas[1] );
|
||||||
|
solutions[i][2] = abs( S.at<double>(2) );
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
void upnp::gauss_newton(const Mat * L_6x12, const Mat * Rho, double betas[4], double * f)
|
||||||
|
{
|
||||||
|
const int iterations_number = 50;
|
||||||
|
|
||||||
|
double a[6*4], b[6], x[4];
|
||||||
|
Mat * A = new Mat(6, 4, CV_64F, a);
|
||||||
|
Mat * B = new Mat(6, 1, CV_64F, b);
|
||||||
|
Mat * X = new Mat(4, 1, CV_64F, x);
|
||||||
|
|
||||||
|
for(int k = 0; k < iterations_number; k++)
|
||||||
|
{
|
||||||
|
compute_A_and_b_gauss_newton(L_6x12->ptr<double>(0), Rho->ptr<double>(0), betas, A, B, f[0]);
|
||||||
|
qr_solve(A, B, X);
|
||||||
|
for(int i = 0; i < 3; i++)
|
||||||
|
betas[i] += x[i];
|
||||||
|
f[0] += x[3];
|
||||||
|
}
|
||||||
|
|
||||||
|
if (f[0] < 0) f[0] = -f[0];
|
||||||
|
fu = fv = f[0];
|
||||||
|
|
||||||
|
}
|
||||||
|
|
||||||
|
void upnp::compute_A_and_b_gauss_newton(const double * l_6x12, const double * rho,
|
||||||
|
const double betas[4], Mat * A, Mat * b, double const f)
|
||||||
|
{
|
||||||
|
|
||||||
|
for(int i = 0; i < 6; i++) {
|
||||||
|
const double * rowL = l_6x12 + i * 12;
|
||||||
|
double * rowA = A->ptr<double>(i);
|
||||||
|
|
||||||
|
rowA[0] = 2 * rowL[0] * betas[0] + rowL[1] * betas[1] + rowL[2] * betas[2] + f*f * ( 2 * rowL[6]*betas[0] + rowL[7]*betas[1] + rowL[8]*betas[2] );
|
||||||
|
rowA[1] = rowL[1] * betas[0] + 2 * rowL[3] * betas[1] + rowL[4] * betas[2] + f*f * ( rowL[7]*betas[0] + 2 * rowL[9]*betas[1] + rowL[10]*betas[2] );
|
||||||
|
rowA[2] = rowL[2] * betas[0] + rowL[4] * betas[1] + 2 * rowL[5] * betas[2] + f*f * ( rowL[8]*betas[0] + rowL[10]*betas[1] + 2 * rowL[11]*betas[2] );
|
||||||
|
rowA[3] = 2*f * ( rowL[6]*betas[0]*betas[0] + rowL[7]*betas[0]*betas[1] + rowL[8]*betas[0]*betas[2] + rowL[9]*betas[1]*betas[1] + rowL[10]*betas[1]*betas[2] + rowL[11]*betas[2]*betas[2] ) ;
|
||||||
|
|
||||||
|
*b->ptr<double>(i) = rho[i] -
|
||||||
|
(
|
||||||
|
rowL[0] * betas[0] * betas[0] +
|
||||||
|
rowL[1] * betas[0] * betas[1] +
|
||||||
|
rowL[2] * betas[0] * betas[2] +
|
||||||
|
rowL[3] * betas[1] * betas[1] +
|
||||||
|
rowL[4] * betas[1] * betas[2] +
|
||||||
|
rowL[5] * betas[2] * betas[2] +
|
||||||
|
f*f * rowL[6] * betas[0] * betas[0] +
|
||||||
|
f*f * rowL[7] * betas[0] * betas[1] +
|
||||||
|
f*f * rowL[8] * betas[0] * betas[2] +
|
||||||
|
f*f * rowL[9] * betas[1] * betas[1] +
|
||||||
|
f*f * rowL[10] * betas[1] * betas[2] +
|
||||||
|
f*f * rowL[11] * betas[2] * betas[2]
|
||||||
|
);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
void upnp::compute_L_6x12(const double * ut, double * l_6x12)
|
||||||
|
{
|
||||||
|
const double * v[3];
|
||||||
|
|
||||||
|
v[0] = ut + 12 * 9;
|
||||||
|
v[1] = ut + 12 * 10;
|
||||||
|
v[2] = ut + 12 * 11;
|
||||||
|
|
||||||
|
double dv[3][6][3];
|
||||||
|
|
||||||
|
for(int i = 0; i < 3; i++) {
|
||||||
|
int a = 0, b = 1;
|
||||||
|
for(int j = 0; j < 6; j++) {
|
||||||
|
dv[i][j][0] = v[i][3 * a ] - v[i][3 * b];
|
||||||
|
dv[i][j][1] = v[i][3 * a + 1] - v[i][3 * b + 1];
|
||||||
|
dv[i][j][2] = v[i][3 * a + 2] - v[i][3 * b + 2];
|
||||||
|
|
||||||
|
b++;
|
||||||
|
if (b > 3) {
|
||||||
|
a++;
|
||||||
|
b = a + 1;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
for(int i = 0; i < 6; i++) {
|
||||||
|
double * row = l_6x12 + 12 * i;
|
||||||
|
|
||||||
|
row[0] = dotXY(dv[0][i], dv[0][i]);
|
||||||
|
row[1] = 2.0f * dotXY(dv[0][i], dv[1][i]);
|
||||||
|
row[2] = dotXY(dv[1][i], dv[1][i]);
|
||||||
|
row[3] = 2.0f * dotXY(dv[0][i], dv[2][i]);
|
||||||
|
row[4] = 2.0f * dotXY(dv[1][i], dv[2][i]);
|
||||||
|
row[5] = dotXY(dv[2][i], dv[2][i]);
|
||||||
|
|
||||||
|
row[6] = dotZ(dv[0][i], dv[0][i]);
|
||||||
|
row[7] = 2.0f * dotZ(dv[0][i], dv[1][i]);
|
||||||
|
row[8] = 2.0f * dotZ(dv[0][i], dv[2][i]);
|
||||||
|
row[9] = dotZ(dv[1][i], dv[1][i]);
|
||||||
|
row[10] = 2.0f * dotZ(dv[1][i], dv[2][i]);
|
||||||
|
row[11] = dotZ(dv[2][i], dv[2][i]);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
void upnp::compute_rho(double * rho)
|
||||||
|
{
|
||||||
|
rho[0] = dist2(cws[0], cws[1]);
|
||||||
|
rho[1] = dist2(cws[0], cws[2]);
|
||||||
|
rho[2] = dist2(cws[0], cws[3]);
|
||||||
|
rho[3] = dist2(cws[1], cws[2]);
|
||||||
|
rho[4] = dist2(cws[1], cws[3]);
|
||||||
|
rho[5] = dist2(cws[2], cws[3]);
|
||||||
|
}
|
||||||
|
|
||||||
|
double upnp::dist2(const double * p1, const double * p2)
|
||||||
|
{
|
||||||
|
return
|
||||||
|
(p1[0] - p2[0]) * (p1[0] - p2[0]) +
|
||||||
|
(p1[1] - p2[1]) * (p1[1] - p2[1]) +
|
||||||
|
(p1[2] - p2[2]) * (p1[2] - p2[2]);
|
||||||
|
}
|
||||||
|
|
||||||
|
double upnp::dot(const double * v1, const double * v2)
|
||||||
|
{
|
||||||
|
return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
|
||||||
|
}
|
||||||
|
|
||||||
|
double upnp::dotXY(const double * v1, const double * v2)
|
||||||
|
{
|
||||||
|
return v1[0] * v2[0] + v1[1] * v2[1];
|
||||||
|
}
|
||||||
|
|
||||||
|
double upnp::dotZ(const double * v1, const double * v2)
|
||||||
|
{
|
||||||
|
return v1[2] * v2[2];
|
||||||
|
}
|
||||||
|
|
||||||
|
double upnp::sign(const double v)
|
||||||
|
{
|
||||||
|
return ( v < 0.0 ) ? -1.0 : ( v > 0.0 ) ? 1.0 : 0.0;
|
||||||
|
}
|
||||||
|
|
||||||
|
void upnp::qr_solve(Mat * A, Mat * b, Mat * X)
|
||||||
|
{
|
||||||
|
const int nr = A->rows;
|
||||||
|
const int nc = A->cols;
|
||||||
|
|
||||||
|
if (max_nr != 0 && max_nr < nr)
|
||||||
|
{
|
||||||
|
delete [] A1;
|
||||||
|
delete [] A2;
|
||||||
|
}
|
||||||
|
if (max_nr < nr)
|
||||||
|
{
|
||||||
|
max_nr = nr;
|
||||||
|
A1 = new double[nr];
|
||||||
|
A2 = new double[nr];
|
||||||
|
}
|
||||||
|
|
||||||
|
double * pA = A->ptr<double>(0), * ppAkk = pA;
|
||||||
|
for(int k = 0; k < nc; k++)
|
||||||
|
{
|
||||||
|
double * ppAik1 = ppAkk, eta = fabs(*ppAik1);
|
||||||
|
for(int i = k + 1; i < nr; i++)
|
||||||
|
{
|
||||||
|
double elt = fabs(*ppAik1);
|
||||||
|
if (eta < elt) eta = elt;
|
||||||
|
ppAik1 += nc;
|
||||||
|
}
|
||||||
|
if (eta == 0)
|
||||||
|
{
|
||||||
|
A1[k] = A2[k] = 0.0;
|
||||||
|
//cerr << "God damnit, A is singular, this shouldn't happen." << endl;
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
double * ppAik2 = ppAkk, sum2 = 0.0, inv_eta = 1. / eta;
|
||||||
|
for(int i = k; i < nr; i++)
|
||||||
|
{
|
||||||
|
*ppAik2 *= inv_eta;
|
||||||
|
sum2 += *ppAik2 * *ppAik2;
|
||||||
|
ppAik2 += nc;
|
||||||
|
}
|
||||||
|
double sigma = sqrt(sum2);
|
||||||
|
if (*ppAkk < 0)
|
||||||
|
sigma = -sigma;
|
||||||
|
*ppAkk += sigma;
|
||||||
|
A1[k] = sigma * *ppAkk;
|
||||||
|
A2[k] = -eta * sigma;
|
||||||
|
for(int j = k + 1; j < nc; j++)
|
||||||
|
{
|
||||||
|
double * ppAik = ppAkk, sum = 0;
|
||||||
|
for(int i = k; i < nr; i++)
|
||||||
|
{
|
||||||
|
sum += *ppAik * ppAik[j - k];
|
||||||
|
ppAik += nc;
|
||||||
|
}
|
||||||
|
double tau = sum / A1[k];
|
||||||
|
ppAik = ppAkk;
|
||||||
|
for(int i = k; i < nr; i++)
|
||||||
|
{
|
||||||
|
ppAik[j - k] -= tau * *ppAik;
|
||||||
|
ppAik += nc;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
ppAkk += nc + 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
// b <- Qt b
|
||||||
|
double * ppAjj = pA, * pb = b->ptr<double>(0);
|
||||||
|
for(int j = 0; j < nc; j++)
|
||||||
|
{
|
||||||
|
double * ppAij = ppAjj, tau = 0;
|
||||||
|
for(int i = j; i < nr; i++)
|
||||||
|
{
|
||||||
|
tau += *ppAij * pb[i];
|
||||||
|
ppAij += nc;
|
||||||
|
}
|
||||||
|
tau /= A1[j];
|
||||||
|
ppAij = ppAjj;
|
||||||
|
for(int i = j; i < nr; i++)
|
||||||
|
{
|
||||||
|
pb[i] -= tau * *ppAij;
|
||||||
|
ppAij += nc;
|
||||||
|
}
|
||||||
|
ppAjj += nc + 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
// X = R-1 b
|
||||||
|
double * pX = X->ptr<double>(0);
|
||||||
|
pX[nc - 1] = pb[nc - 1] / A2[nc - 1];
|
||||||
|
for(int i = nc - 2; i >= 0; i--)
|
||||||
|
{
|
||||||
|
double * ppAij = pA + i * nc + (i + 1), sum = 0;
|
||||||
|
|
||||||
|
for(int j = i + 1; j < nc; j++)
|
||||||
|
{
|
||||||
|
sum += *ppAij * pX[j];
|
||||||
|
ppAij++;
|
||||||
|
}
|
||||||
|
pX[i] = (pb[i] - sum) / A2[i];
|
||||||
|
}
|
||||||
|
}
|
||||||
134
modules/calib3d/src/upnp.h
Normal file
134
modules/calib3d/src/upnp.h
Normal file
@ -0,0 +1,134 @@
|
|||||||
|
//M*//////////////////////////////////////////////////////////////////////////////////////
|
||||||
|
//
|
||||||
|
// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
|
||||||
|
//
|
||||||
|
// By downloading, copying, installing or using the software you agree to this license.
|
||||||
|
// If you do not agree to this license, do not download, install,
|
||||||
|
// copy or use the software.
|
||||||
|
//
|
||||||
|
//
|
||||||
|
// License Agreement
|
||||||
|
// For Open Source Computer Vision Library
|
||||||
|
//
|
||||||
|
// Copyright (C) 2000, Intel Corporation, all rights reserved.
|
||||||
|
// Copyright (C) 2013, OpenCV Foundation, all rights reserved.
|
||||||
|
// Third party copyrights are property of their respective owners.
|
||||||
|
//
|
||||||
|
// Redistribution and use in source and binary forms, with or without modification,
|
||||||
|
// are permitted provided that the following conditions are met:
|
||||||
|
//
|
||||||
|
// * Redistribution's of source code must retain the above copyright notice,
|
||||||
|
// this list of conditions and the following disclaimer.
|
||||||
|
//
|
||||||
|
// * Redistribution's 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.
|
||||||
|
//
|
||||||
|
// * The name of the copyright holders may not 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 Intel Corporation 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.
|
||||||
|
//
|
||||||
|
//M*/
|
||||||
|
|
||||||
|
/****************************************************************************************\
|
||||||
|
* Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation.
|
||||||
|
* Contributed by Edgar Riba
|
||||||
|
\****************************************************************************************/
|
||||||
|
|
||||||
|
#ifndef OPENCV_CALIB3D_UPNP_H_
|
||||||
|
#define OPENCV_CALIB3D_UPNP_H_
|
||||||
|
|
||||||
|
#include "precomp.hpp"
|
||||||
|
#include "opencv2/core/core_c.h"
|
||||||
|
#include <iostream>
|
||||||
|
|
||||||
|
class upnp
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
upnp(const cv::Mat& cameraMatrix, const cv::Mat& opoints, const cv::Mat& ipoints);
|
||||||
|
~upnp();
|
||||||
|
|
||||||
|
double compute_pose(cv::Mat& R, cv::Mat& t);
|
||||||
|
private:
|
||||||
|
template <typename T>
|
||||||
|
void init_camera_parameters(const cv::Mat& cameraMatrix)
|
||||||
|
{
|
||||||
|
uc = cameraMatrix.at<T> (0, 2);
|
||||||
|
vc = cameraMatrix.at<T> (1, 2);
|
||||||
|
fu = 1;
|
||||||
|
fv = 1;
|
||||||
|
}
|
||||||
|
template <typename OpointType, typename IpointType>
|
||||||
|
void init_points(const cv::Mat& opoints, const cv::Mat& ipoints)
|
||||||
|
{
|
||||||
|
for(int i = 0; i < number_of_correspondences; i++)
|
||||||
|
{
|
||||||
|
pws[3 * i ] = opoints.at<OpointType>(0,i).x;
|
||||||
|
pws[3 * i + 1] = opoints.at<OpointType>(0,i).y;
|
||||||
|
pws[3 * i + 2] = opoints.at<OpointType>(0,i).z;
|
||||||
|
|
||||||
|
us[2 * i ] = ipoints.at<IpointType>(0,i).x;
|
||||||
|
us[2 * i + 1] = ipoints.at<IpointType>(0,i).y;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
double reprojection_error(const double R[3][3], const double t[3]);
|
||||||
|
void choose_control_points();
|
||||||
|
void compute_alphas();
|
||||||
|
void fill_M(cv::Mat * M, const int row, const double * alphas, const double u, const double v);
|
||||||
|
void compute_ccs(const double * betas, const double * ut);
|
||||||
|
void compute_pcs(void);
|
||||||
|
|
||||||
|
void solve_for_sign(void);
|
||||||
|
|
||||||
|
void find_betas_and_focal_approx_1(cv::Mat * Ut, cv::Mat * Rho, double * betas, double * efs);
|
||||||
|
void find_betas_and_focal_approx_2(cv::Mat * Ut, cv::Mat * Rho, double * betas, double * efs);
|
||||||
|
void qr_solve(cv::Mat * A, cv::Mat * b, cv::Mat * X);
|
||||||
|
|
||||||
|
cv::Mat compute_constraint_distance_2param_6eq_2unk_f_unk(const cv::Mat& M1);
|
||||||
|
cv::Mat compute_constraint_distance_3param_6eq_6unk_f_unk(const cv::Mat& M1, const cv::Mat& M2);
|
||||||
|
void generate_all_possible_solutions_for_f_unk(const double betas[5], double solutions[18][3]);
|
||||||
|
|
||||||
|
double sign(const double v);
|
||||||
|
double dot(const double * v1, const double * v2);
|
||||||
|
double dotXY(const double * v1, const double * v2);
|
||||||
|
double dotZ(const double * v1, const double * v2);
|
||||||
|
double dist2(const double * p1, const double * p2);
|
||||||
|
|
||||||
|
void compute_rho(double * rho);
|
||||||
|
void compute_L_6x12(const double * ut, double * l_6x12);
|
||||||
|
|
||||||
|
void gauss_newton(const cv::Mat * L_6x12, const cv::Mat * Rho, double current_betas[4], double * efs);
|
||||||
|
void compute_A_and_b_gauss_newton(const double * l_6x12, const double * rho,
|
||||||
|
const double cb[4], cv::Mat * A, cv::Mat * b, double const f);
|
||||||
|
|
||||||
|
double compute_R_and_t(const double * ut, const double * betas,
|
||||||
|
double R[3][3], double t[3]);
|
||||||
|
|
||||||
|
void estimate_R_and_t(double R[3][3], double t[3]);
|
||||||
|
|
||||||
|
void copy_R_and_t(const double R_dst[3][3], const double t_dst[3],
|
||||||
|
double R_src[3][3], double t_src[3]);
|
||||||
|
|
||||||
|
|
||||||
|
double uc, vc, fu, fv;
|
||||||
|
|
||||||
|
std::vector<double> pws, us, alphas, pcs;
|
||||||
|
int number_of_correspondences;
|
||||||
|
|
||||||
|
double cws[4][3], ccs[4][3];
|
||||||
|
int max_nr;
|
||||||
|
double * A1, * A2;
|
||||||
|
};
|
||||||
|
|
||||||
|
#endif // OPENCV_CALIB3D_UPNP_H_
|
||||||
@ -58,6 +58,7 @@ public:
|
|||||||
eps[SOLVEPNP_EPNP] = 1.0e-2;
|
eps[SOLVEPNP_EPNP] = 1.0e-2;
|
||||||
eps[SOLVEPNP_P3P] = 1.0e-2;
|
eps[SOLVEPNP_P3P] = 1.0e-2;
|
||||||
eps[SOLVEPNP_DLS] = 1.0e-2;
|
eps[SOLVEPNP_DLS] = 1.0e-2;
|
||||||
|
eps[SOLVEPNP_UPNP] = 1.0e-2;
|
||||||
totalTestsCount = 10;
|
totalTestsCount = 10;
|
||||||
}
|
}
|
||||||
~CV_solvePnPRansac_Test() {}
|
~CV_solvePnPRansac_Test() {}
|
||||||
@ -118,6 +119,7 @@ protected:
|
|||||||
Mat trueRvec, trueTvec;
|
Mat trueRvec, trueTvec;
|
||||||
Mat intrinsics, distCoeffs;
|
Mat intrinsics, distCoeffs;
|
||||||
generateCameraMatrix(intrinsics, rng);
|
generateCameraMatrix(intrinsics, rng);
|
||||||
|
if (method == 4) intrinsics.at<double>(1,1) = intrinsics.at<double>(0,0);
|
||||||
if (mode == 0)
|
if (mode == 0)
|
||||||
distCoeffs = Mat::zeros(4, 1, CV_64FC1);
|
distCoeffs = Mat::zeros(4, 1, CV_64FC1);
|
||||||
else
|
else
|
||||||
@ -159,7 +161,7 @@ protected:
|
|||||||
points.resize(pointsCount);
|
points.resize(pointsCount);
|
||||||
generate3DPointCloud(points);
|
generate3DPointCloud(points);
|
||||||
|
|
||||||
const int methodsCount = 4;
|
const int methodsCount = 5;
|
||||||
RNG rng = ts->get_rng();
|
RNG rng = ts->get_rng();
|
||||||
|
|
||||||
|
|
||||||
@ -184,7 +186,7 @@ protected:
|
|||||||
}
|
}
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
double eps[4];
|
double eps[5];
|
||||||
int totalTestsCount;
|
int totalTestsCount;
|
||||||
};
|
};
|
||||||
|
|
||||||
@ -197,6 +199,7 @@ public:
|
|||||||
eps[SOLVEPNP_EPNP] = 1.0e-6;
|
eps[SOLVEPNP_EPNP] = 1.0e-6;
|
||||||
eps[SOLVEPNP_P3P] = 1.0e-4;
|
eps[SOLVEPNP_P3P] = 1.0e-4;
|
||||||
eps[SOLVEPNP_DLS] = 1.0e-4;
|
eps[SOLVEPNP_DLS] = 1.0e-4;
|
||||||
|
eps[SOLVEPNP_UPNP] = 1.0e-4;
|
||||||
totalTestsCount = 1000;
|
totalTestsCount = 1000;
|
||||||
}
|
}
|
||||||
|
|
||||||
@ -208,6 +211,7 @@ protected:
|
|||||||
Mat trueRvec, trueTvec;
|
Mat trueRvec, trueTvec;
|
||||||
Mat intrinsics, distCoeffs;
|
Mat intrinsics, distCoeffs;
|
||||||
generateCameraMatrix(intrinsics, rng);
|
generateCameraMatrix(intrinsics, rng);
|
||||||
|
if (method == 4) intrinsics.at<double>(1,1) = intrinsics.at<double>(0,0);
|
||||||
if (mode == 0)
|
if (mode == 0)
|
||||||
distCoeffs = Mat::zeros(4, 1, CV_64FC1);
|
distCoeffs = Mat::zeros(4, 1, CV_64FC1);
|
||||||
else
|
else
|
||||||
|
|||||||
Loading…
x
Reference in New Issue
Block a user