Path: blob/master/modules/calib3d/src/five-point.cpp
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/* This is a 5-point algorithm contributed to OpenCV by the author, Bo Li.1It implements the 5-point algorithm solver from Nister's paper:2Nister, An efficient solution to the five-point relative pose problem, PAMI, 2004.3*/45/* Copyright (c) 2013, Bo Li ([email protected]), ETH Zurich6All rights reserved.78Redistribution and use in source and binary forms, with or without9modification, are permitted provided that the following conditions are met:10* Redistributions of source code must retain the above copyright11notice, this list of conditions and the following disclaimer.12* Redistributions in binary form must reproduce the above copyright13notice, this list of conditions and the following disclaimer in the14documentation and/or other materials provided with the distribution.15* Neither the name of the copyright holder nor the16names of its contributors may be used to endorse or promote products17derived from this software without specific prior written permission.1819THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND20ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED21WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE22DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE FOR ANY23DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES24(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;25LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND26ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT27(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS28SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.29*/3031#include "precomp.hpp"3233namespace cv34{3536class EMEstimatorCallback CV_FINAL : public PointSetRegistrator::Callback37{38public:39int runKernel( InputArray _m1, InputArray _m2, OutputArray _model ) const CV_OVERRIDE40{41Mat q1 = _m1.getMat(), q2 = _m2.getMat();42Mat Q1 = q1.reshape(1, (int)q1.total());43Mat Q2 = q2.reshape(1, (int)q2.total());4445int n = Q1.rows;46Mat Q(n, 9, CV_64F);47Q.col(0) = Q1.col(0).mul( Q2.col(0) );48Q.col(1) = Q1.col(1).mul( Q2.col(0) );49Q.col(2) = Q2.col(0) * 1.0;50Q.col(3) = Q1.col(0).mul( Q2.col(1) );51Q.col(4) = Q1.col(1).mul( Q2.col(1) );52Q.col(5) = Q2.col(1) * 1.0;53Q.col(6) = Q1.col(0) * 1.0;54Q.col(7) = Q1.col(1) * 1.0;55Q.col(8) = 1.0;5657Mat U, W, Vt;58SVD::compute(Q, W, U, Vt, SVD::MODIFY_A | SVD::FULL_UV);5960Mat EE = Mat(Vt.t()).colRange(5, 9) * 1.0;61Mat A(10, 20, CV_64F);62EE = EE.t();63getCoeffMat(EE.ptr<double>(), A.ptr<double>());64EE = EE.t();6566A = A.colRange(0, 10).inv() * A.colRange(10, 20);6768double b[3 * 13];69Mat B(3, 13, CV_64F, b);70for (int i = 0; i < 3; i++)71{72Mat arow1 = A.row(i * 2 + 4) * 1.0;73Mat arow2 = A.row(i * 2 + 5) * 1.0;74Mat row1(1, 13, CV_64F, Scalar(0.0));75Mat row2(1, 13, CV_64F, Scalar(0.0));7677row1.colRange(1, 4) = arow1.colRange(0, 3) * 1.0;78row1.colRange(5, 8) = arow1.colRange(3, 6) * 1.0;79row1.colRange(9, 13) = arow1.colRange(6, 10) * 1.0;8081row2.colRange(0, 3) = arow2.colRange(0, 3) * 1.0;82row2.colRange(4, 7) = arow2.colRange(3, 6) * 1.0;83row2.colRange(8, 12) = arow2.colRange(6, 10) * 1.0;8485B.row(i) = row1 - row2;86}8788double c[11];89Mat coeffs(1, 11, CV_64F, c);90c[10] = (b[0]*b[17]*b[34]+b[26]*b[4]*b[21]-b[26]*b[17]*b[8]-b[13]*b[4]*b[34]-b[0]*b[21]*b[30]+b[13]*b[30]*b[8]);91c[9] = (b[26]*b[4]*b[22]+b[14]*b[30]*b[8]+b[13]*b[31]*b[8]+b[1]*b[17]*b[34]-b[13]*b[5]*b[34]+b[26]*b[5]*b[21]-b[0]*b[21]*b[31]-b[26]*b[17]*b[9]-b[1]*b[21]*b[30]+b[27]*b[4]*b[21]+b[0]*b[17]*b[35]-b[0]*b[22]*b[30]+b[13]*b[30]*b[9]+b[0]*b[18]*b[34]-b[27]*b[17]*b[8]-b[14]*b[4]*b[34]-b[13]*b[4]*b[35]-b[26]*b[18]*b[8]);92c[8] = (b[14]*b[30]*b[9]+b[14]*b[31]*b[8]+b[13]*b[31]*b[9]-b[13]*b[4]*b[36]-b[13]*b[5]*b[35]+b[15]*b[30]*b[8]-b[13]*b[6]*b[34]+b[13]*b[30]*b[10]+b[13]*b[32]*b[8]-b[14]*b[4]*b[35]-b[14]*b[5]*b[34]+b[26]*b[4]*b[23]+b[26]*b[5]*b[22]+b[26]*b[6]*b[21]-b[26]*b[17]*b[10]-b[15]*b[4]*b[34]-b[26]*b[18]*b[9]-b[26]*b[19]*b[8]+b[27]*b[4]*b[22]+b[27]*b[5]*b[21]-b[27]*b[17]*b[9]-b[27]*b[18]*b[8]-b[1]*b[21]*b[31]-b[0]*b[23]*b[30]-b[0]*b[21]*b[32]+b[28]*b[4]*b[21]-b[28]*b[17]*b[8]+b[2]*b[17]*b[34]+b[0]*b[18]*b[35]-b[0]*b[22]*b[31]+b[0]*b[17]*b[36]+b[0]*b[19]*b[34]-b[1]*b[22]*b[30]+b[1]*b[18]*b[34]+b[1]*b[17]*b[35]-b[2]*b[21]*b[30]);93c[7] = (b[14]*b[30]*b[10]+b[14]*b[32]*b[8]-b[3]*b[21]*b[30]+b[3]*b[17]*b[34]+b[13]*b[32]*b[9]+b[13]*b[33]*b[8]-b[13]*b[4]*b[37]-b[13]*b[5]*b[36]+b[15]*b[30]*b[9]+b[15]*b[31]*b[8]-b[16]*b[4]*b[34]-b[13]*b[6]*b[35]-b[13]*b[7]*b[34]+b[13]*b[30]*b[11]+b[13]*b[31]*b[10]+b[14]*b[31]*b[9]-b[14]*b[4]*b[36]-b[14]*b[5]*b[35]-b[14]*b[6]*b[34]+b[16]*b[30]*b[8]-b[26]*b[20]*b[8]+b[26]*b[4]*b[24]+b[26]*b[5]*b[23]+b[26]*b[6]*b[22]+b[26]*b[7]*b[21]-b[26]*b[17]*b[11]-b[15]*b[4]*b[35]-b[15]*b[5]*b[34]-b[26]*b[18]*b[10]-b[26]*b[19]*b[9]+b[27]*b[4]*b[23]+b[27]*b[5]*b[22]+b[27]*b[6]*b[21]-b[27]*b[17]*b[10]-b[27]*b[18]*b[9]-b[27]*b[19]*b[8]+b[0]*b[17]*b[37]-b[0]*b[23]*b[31]-b[0]*b[24]*b[30]-b[0]*b[21]*b[33]-b[29]*b[17]*b[8]+b[28]*b[4]*b[22]+b[28]*b[5]*b[21]-b[28]*b[17]*b[9]-b[28]*b[18]*b[8]+b[29]*b[4]*b[21]+b[1]*b[19]*b[34]-b[2]*b[21]*b[31]+b[0]*b[20]*b[34]+b[0]*b[19]*b[35]+b[0]*b[18]*b[36]-b[0]*b[22]*b[32]-b[1]*b[23]*b[30]-b[1]*b[21]*b[32]+b[1]*b[18]*b[35]-b[1]*b[22]*b[31]-b[2]*b[22]*b[30]+b[2]*b[17]*b[35]+b[1]*b[17]*b[36]+b[2]*b[18]*b[34]);94c[6] = (-b[14]*b[6]*b[35]-b[14]*b[7]*b[34]-b[3]*b[22]*b[30]-b[3]*b[21]*b[31]+b[3]*b[17]*b[35]+b[3]*b[18]*b[34]+b[13]*b[32]*b[10]+b[13]*b[33]*b[9]-b[13]*b[4]*b[38]-b[13]*b[5]*b[37]-b[15]*b[6]*b[34]+b[15]*b[30]*b[10]+b[15]*b[32]*b[8]-b[16]*b[4]*b[35]-b[13]*b[6]*b[36]-b[13]*b[7]*b[35]+b[13]*b[31]*b[11]+b[13]*b[30]*b[12]+b[14]*b[32]*b[9]+b[14]*b[33]*b[8]-b[14]*b[4]*b[37]-b[14]*b[5]*b[36]+b[16]*b[30]*b[9]+b[16]*b[31]*b[8]-b[26]*b[20]*b[9]+b[26]*b[4]*b[25]+b[26]*b[5]*b[24]+b[26]*b[6]*b[23]+b[26]*b[7]*b[22]-b[26]*b[17]*b[12]+b[14]*b[30]*b[11]+b[14]*b[31]*b[10]+b[15]*b[31]*b[9]-b[15]*b[4]*b[36]-b[15]*b[5]*b[35]-b[26]*b[18]*b[11]-b[26]*b[19]*b[10]-b[27]*b[20]*b[8]+b[27]*b[4]*b[24]+b[27]*b[5]*b[23]+b[27]*b[6]*b[22]+b[27]*b[7]*b[21]-b[27]*b[17]*b[11]-b[27]*b[18]*b[10]-b[27]*b[19]*b[9]-b[16]*b[5]*b[34]-b[29]*b[17]*b[9]-b[29]*b[18]*b[8]+b[28]*b[4]*b[23]+b[28]*b[5]*b[22]+b[28]*b[6]*b[21]-b[28]*b[17]*b[10]-b[28]*b[18]*b[9]-b[28]*b[19]*b[8]+b[29]*b[4]*b[22]+b[29]*b[5]*b[21]-b[2]*b[23]*b[30]+b[2]*b[18]*b[35]-b[1]*b[22]*b[32]-b[2]*b[21]*b[32]+b[2]*b[19]*b[34]+b[0]*b[19]*b[36]-b[0]*b[22]*b[33]+b[0]*b[20]*b[35]-b[0]*b[23]*b[32]-b[0]*b[25]*b[30]+b[0]*b[17]*b[38]+b[0]*b[18]*b[37]-b[0]*b[24]*b[31]+b[1]*b[17]*b[37]-b[1]*b[23]*b[31]-b[1]*b[24]*b[30]-b[1]*b[21]*b[33]+b[1]*b[20]*b[34]+b[1]*b[19]*b[35]+b[1]*b[18]*b[36]+b[2]*b[17]*b[36]-b[2]*b[22]*b[31]);95c[5] = (-b[14]*b[6]*b[36]-b[14]*b[7]*b[35]+b[14]*b[31]*b[11]-b[3]*b[23]*b[30]-b[3]*b[21]*b[32]+b[3]*b[18]*b[35]-b[3]*b[22]*b[31]+b[3]*b[17]*b[36]+b[3]*b[19]*b[34]+b[13]*b[32]*b[11]+b[13]*b[33]*b[10]-b[13]*b[5]*b[38]-b[15]*b[6]*b[35]-b[15]*b[7]*b[34]+b[15]*b[30]*b[11]+b[15]*b[31]*b[10]+b[16]*b[31]*b[9]-b[13]*b[6]*b[37]-b[13]*b[7]*b[36]+b[13]*b[31]*b[12]+b[14]*b[32]*b[10]+b[14]*b[33]*b[9]-b[14]*b[4]*b[38]-b[14]*b[5]*b[37]-b[16]*b[6]*b[34]+b[16]*b[30]*b[10]+b[16]*b[32]*b[8]-b[26]*b[20]*b[10]+b[26]*b[5]*b[25]+b[26]*b[6]*b[24]+b[26]*b[7]*b[23]+b[14]*b[30]*b[12]+b[15]*b[32]*b[9]+b[15]*b[33]*b[8]-b[15]*b[4]*b[37]-b[15]*b[5]*b[36]+b[29]*b[5]*b[22]+b[29]*b[6]*b[21]-b[26]*b[18]*b[12]-b[26]*b[19]*b[11]-b[27]*b[20]*b[9]+b[27]*b[4]*b[25]+b[27]*b[5]*b[24]+b[27]*b[6]*b[23]+b[27]*b[7]*b[22]-b[27]*b[17]*b[12]-b[27]*b[18]*b[11]-b[27]*b[19]*b[10]-b[28]*b[20]*b[8]-b[16]*b[4]*b[36]-b[16]*b[5]*b[35]-b[29]*b[17]*b[10]-b[29]*b[18]*b[9]-b[29]*b[19]*b[8]+b[28]*b[4]*b[24]+b[28]*b[5]*b[23]+b[28]*b[6]*b[22]+b[28]*b[7]*b[21]-b[28]*b[17]*b[11]-b[28]*b[18]*b[10]-b[28]*b[19]*b[9]+b[29]*b[4]*b[23]-b[2]*b[22]*b[32]-b[2]*b[21]*b[33]-b[1]*b[24]*b[31]+b[0]*b[18]*b[38]-b[0]*b[24]*b[32]+b[0]*b[19]*b[37]+b[0]*b[20]*b[36]-b[0]*b[25]*b[31]-b[0]*b[23]*b[33]+b[1]*b[19]*b[36]-b[1]*b[22]*b[33]+b[1]*b[20]*b[35]+b[2]*b[19]*b[35]-b[2]*b[24]*b[30]-b[2]*b[23]*b[31]+b[2]*b[20]*b[34]+b[2]*b[17]*b[37]-b[1]*b[25]*b[30]+b[1]*b[18]*b[37]+b[1]*b[17]*b[38]-b[1]*b[23]*b[32]+b[2]*b[18]*b[36]);96c[4] = (-b[14]*b[6]*b[37]-b[14]*b[7]*b[36]+b[14]*b[31]*b[12]+b[3]*b[17]*b[37]-b[3]*b[23]*b[31]-b[3]*b[24]*b[30]-b[3]*b[21]*b[33]+b[3]*b[20]*b[34]+b[3]*b[19]*b[35]+b[3]*b[18]*b[36]-b[3]*b[22]*b[32]+b[13]*b[32]*b[12]+b[13]*b[33]*b[11]-b[15]*b[6]*b[36]-b[15]*b[7]*b[35]+b[15]*b[31]*b[11]+b[15]*b[30]*b[12]+b[16]*b[32]*b[9]+b[16]*b[33]*b[8]-b[13]*b[6]*b[38]-b[13]*b[7]*b[37]+b[14]*b[32]*b[11]+b[14]*b[33]*b[10]-b[14]*b[5]*b[38]-b[16]*b[6]*b[35]-b[16]*b[7]*b[34]+b[16]*b[30]*b[11]+b[16]*b[31]*b[10]-b[26]*b[19]*b[12]-b[26]*b[20]*b[11]+b[26]*b[6]*b[25]+b[26]*b[7]*b[24]+b[15]*b[32]*b[10]+b[15]*b[33]*b[9]-b[15]*b[4]*b[38]-b[15]*b[5]*b[37]+b[29]*b[5]*b[23]+b[29]*b[6]*b[22]+b[29]*b[7]*b[21]-b[27]*b[20]*b[10]+b[27]*b[5]*b[25]+b[27]*b[6]*b[24]+b[27]*b[7]*b[23]-b[27]*b[18]*b[12]-b[27]*b[19]*b[11]-b[28]*b[20]*b[9]-b[16]*b[4]*b[37]-b[16]*b[5]*b[36]+b[0]*b[19]*b[38]-b[0]*b[24]*b[33]+b[0]*b[20]*b[37]-b[29]*b[17]*b[11]-b[29]*b[18]*b[10]-b[29]*b[19]*b[9]+b[28]*b[4]*b[25]+b[28]*b[5]*b[24]+b[28]*b[6]*b[23]+b[28]*b[7]*b[22]-b[28]*b[17]*b[12]-b[28]*b[18]*b[11]-b[28]*b[19]*b[10]-b[29]*b[20]*b[8]+b[29]*b[4]*b[24]+b[2]*b[18]*b[37]-b[0]*b[25]*b[32]+b[1]*b[18]*b[38]-b[1]*b[24]*b[32]+b[1]*b[19]*b[37]+b[1]*b[20]*b[36]-b[1]*b[25]*b[31]+b[2]*b[17]*b[38]+b[2]*b[19]*b[36]-b[2]*b[24]*b[31]-b[2]*b[22]*b[33]-b[2]*b[23]*b[32]+b[2]*b[20]*b[35]-b[1]*b[23]*b[33]-b[2]*b[25]*b[30]);97c[3] = (-b[14]*b[6]*b[38]-b[14]*b[7]*b[37]+b[3]*b[19]*b[36]-b[3]*b[22]*b[33]+b[3]*b[20]*b[35]-b[3]*b[23]*b[32]-b[3]*b[25]*b[30]+b[3]*b[17]*b[38]+b[3]*b[18]*b[37]-b[3]*b[24]*b[31]-b[15]*b[6]*b[37]-b[15]*b[7]*b[36]+b[15]*b[31]*b[12]+b[16]*b[32]*b[10]+b[16]*b[33]*b[9]+b[13]*b[33]*b[12]-b[13]*b[7]*b[38]+b[14]*b[32]*b[12]+b[14]*b[33]*b[11]-b[16]*b[6]*b[36]-b[16]*b[7]*b[35]+b[16]*b[31]*b[11]+b[16]*b[30]*b[12]+b[15]*b[32]*b[11]+b[15]*b[33]*b[10]-b[15]*b[5]*b[38]+b[29]*b[5]*b[24]+b[29]*b[6]*b[23]-b[26]*b[20]*b[12]+b[26]*b[7]*b[25]-b[27]*b[19]*b[12]-b[27]*b[20]*b[11]+b[27]*b[6]*b[25]+b[27]*b[7]*b[24]-b[28]*b[20]*b[10]-b[16]*b[4]*b[38]-b[16]*b[5]*b[37]+b[29]*b[7]*b[22]-b[29]*b[17]*b[12]-b[29]*b[18]*b[11]-b[29]*b[19]*b[10]+b[28]*b[5]*b[25]+b[28]*b[6]*b[24]+b[28]*b[7]*b[23]-b[28]*b[18]*b[12]-b[28]*b[19]*b[11]-b[29]*b[20]*b[9]+b[29]*b[4]*b[25]-b[2]*b[24]*b[32]+b[0]*b[20]*b[38]-b[0]*b[25]*b[33]+b[1]*b[19]*b[38]-b[1]*b[24]*b[33]+b[1]*b[20]*b[37]-b[2]*b[25]*b[31]+b[2]*b[20]*b[36]-b[1]*b[25]*b[32]+b[2]*b[19]*b[37]+b[2]*b[18]*b[38]-b[2]*b[23]*b[33]);98c[2] = (b[3]*b[18]*b[38]-b[3]*b[24]*b[32]+b[3]*b[19]*b[37]+b[3]*b[20]*b[36]-b[3]*b[25]*b[31]-b[3]*b[23]*b[33]-b[15]*b[6]*b[38]-b[15]*b[7]*b[37]+b[16]*b[32]*b[11]+b[16]*b[33]*b[10]-b[16]*b[5]*b[38]-b[16]*b[6]*b[37]-b[16]*b[7]*b[36]+b[16]*b[31]*b[12]+b[14]*b[33]*b[12]-b[14]*b[7]*b[38]+b[15]*b[32]*b[12]+b[15]*b[33]*b[11]+b[29]*b[5]*b[25]+b[29]*b[6]*b[24]-b[27]*b[20]*b[12]+b[27]*b[7]*b[25]-b[28]*b[19]*b[12]-b[28]*b[20]*b[11]+b[29]*b[7]*b[23]-b[29]*b[18]*b[12]-b[29]*b[19]*b[11]+b[28]*b[6]*b[25]+b[28]*b[7]*b[24]-b[29]*b[20]*b[10]+b[2]*b[19]*b[38]-b[1]*b[25]*b[33]+b[2]*b[20]*b[37]-b[2]*b[24]*b[33]-b[2]*b[25]*b[32]+b[1]*b[20]*b[38]);99c[1] = (b[29]*b[7]*b[24]-b[29]*b[20]*b[11]+b[2]*b[20]*b[38]-b[2]*b[25]*b[33]-b[28]*b[20]*b[12]+b[28]*b[7]*b[25]-b[29]*b[19]*b[12]-b[3]*b[24]*b[33]+b[15]*b[33]*b[12]+b[3]*b[19]*b[38]-b[16]*b[6]*b[38]+b[3]*b[20]*b[37]+b[16]*b[32]*b[12]+b[29]*b[6]*b[25]-b[16]*b[7]*b[37]-b[3]*b[25]*b[32]-b[15]*b[7]*b[38]+b[16]*b[33]*b[11]);100c[0] = -b[29]*b[20]*b[12]+b[29]*b[7]*b[25]+b[16]*b[33]*b[12]-b[16]*b[7]*b[38]+b[3]*b[20]*b[38]-b[3]*b[25]*b[33];101102std::vector<Complex<double> > roots;103solvePoly(coeffs, roots);104105std::vector<double> xs, ys, zs;106int count = 0;107108Mat ematrix(10*3, 3, CV_64F);109double* e = ematrix.ptr<double>();110for (size_t i = 0; i < roots.size(); i++)111{112if (fabs(roots[i].im) > 1e-10) continue;113double z1 = roots[i].re;114double z2 = z1 * z1;115double z3 = z2 * z1;116double z4 = z3 * z1;117118double bz[3][3];119for (int j = 0; j < 3; j++)120{121const double * br = b + j * 13;122bz[j][0] = br[0] * z3 + br[1] * z2 + br[2] * z1 + br[3];123bz[j][1] = br[4] * z3 + br[5] * z2 + br[6] * z1 + br[7];124bz[j][2] = br[8] * z4 + br[9] * z3 + br[10] * z2 + br[11] * z1 + br[12];125}126127Mat Bz(3, 3, CV_64F, bz);128cv::Mat xy1;129SVD::solveZ(Bz, xy1);130131if (fabs(xy1.at<double>(2)) < 1e-10) continue;132xs.push_back(xy1.at<double>(0) / xy1.at<double>(2));133ys.push_back(xy1.at<double>(1) / xy1.at<double>(2));134zs.push_back(z1);135136cv::Mat Evec = EE.col(0) * xs.back() + EE.col(1) * ys.back() + EE.col(2) * zs.back() + EE.col(3);137Evec /= norm(Evec);138139memcpy(e + count * 9, Evec.ptr(), 9 * sizeof(double));140count++;141}142143ematrix.rowRange(0, count*3).copyTo(_model);144return count;145}146147protected:148void getCoeffMat(double *e, double *A) const149{150double ep2[36], ep3[36];151for (int i = 0; i < 36; i++)152{153ep2[i] = e[i] * e[i];154ep3[i] = ep2[i] * 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perm[20] = {6, 8, 18, 15, 12, 5, 14, 7, 4, 11, 19, 13, 1, 16, 17, 3, 10, 9, 2, 0};359double AA[200];360for (int i = 0; i < 20; i++)361{362for (int j = 0; j < 10; j++) AA[i + j * 20] = A[perm[i] + j * 20];363}364365for (int i = 0; i < 200; i++)366{367A[i] = AA[i];368}369}370371372void computeError( InputArray _m1, InputArray _m2, InputArray _model, OutputArray _err ) const CV_OVERRIDE373{374Mat X1 = _m1.getMat(), X2 = _m2.getMat(), model = _model.getMat();375const Point2d* x1ptr = X1.ptr<Point2d>();376const Point2d* x2ptr = X2.ptr<Point2d>();377int n = X1.checkVector(2);378Matx33d E(model.ptr<double>());379380_err.create(n, 1, CV_32F);381Mat err = _err.getMat();382383for (int i = 0; i < n; i++)384{385Vec3d x1(x1ptr[i].x, x1ptr[i].y, 1.);386Vec3d x2(x2ptr[i].x, x2ptr[i].y, 1.);387Vec3d Ex1 = E * x1;388Vec3d Etx2 = E.t() * x2;389double x2tEx1 = x2.dot(Ex1);390391double a = Ex1[0] * Ex1[0];392double b = Ex1[1] * Ex1[1];393double c = Etx2[0] * Etx2[0];394double d = Etx2[1] * Etx2[1];395396err.at<float>(i) = (float)(x2tEx1 * x2tEx1 / (a + b + c + d));397}398}399};400401}402403// Input should be a vector of n 2D points or a Nx2 matrix404cv::Mat cv::findEssentialMat( InputArray _points1, InputArray _points2, InputArray _cameraMatrix,405int method, double prob, double threshold, OutputArray _mask)406{407CV_INSTRUMENT_REGION();408409Mat points1, points2, cameraMatrix;410_points1.getMat().convertTo(points1, CV_64F);411_points2.getMat().convertTo(points2, CV_64F);412_cameraMatrix.getMat().convertTo(cameraMatrix, CV_64F);413414int npoints = points1.checkVector(2);415CV_Assert( npoints >= 0 && points2.checkVector(2) == npoints &&416points1.type() == points2.type());417418CV_Assert(cameraMatrix.rows == 3 && cameraMatrix.cols == 3 && cameraMatrix.channels() == 1);419420if (points1.channels() > 1)421{422points1 = points1.reshape(1, npoints);423points2 = points2.reshape(1, npoints);424}425426double fx = cameraMatrix.at<double>(0,0);427double fy = cameraMatrix.at<double>(1,1);428double cx = cameraMatrix.at<double>(0,2);429double cy = cameraMatrix.at<double>(1,2);430431points1.col(0) = (points1.col(0) - cx) / fx;432points2.col(0) = (points2.col(0) - cx) / fx;433points1.col(1) = (points1.col(1) - cy) / fy;434points2.col(1) = (points2.col(1) - cy) / fy;435436// Reshape data to fit opencv ransac function437points1 = points1.reshape(2, npoints);438points2 = points2.reshape(2, npoints);439440threshold /= (fx+fy)/2;441442Mat E;443if( method == RANSAC )444createRANSACPointSetRegistrator(makePtr<EMEstimatorCallback>(), 5, threshold, prob)->run(points1, points2, E, _mask);445else446createLMeDSPointSetRegistrator(makePtr<EMEstimatorCallback>(), 5, prob)->run(points1, points2, E, _mask);447448return E;449}450451cv::Mat cv::findEssentialMat( InputArray _points1, InputArray _points2, double focal, Point2d pp,452int method, double prob, double threshold, OutputArray _mask)453{454CV_INSTRUMENT_REGION();455456Mat cameraMatrix = (Mat_<double>(3,3) << focal, 0, pp.x, 0, focal, pp.y, 0, 0, 1);457return cv::findEssentialMat(_points1, _points2, cameraMatrix, method, prob, threshold, _mask);458}459460int cv::recoverPose( InputArray E, InputArray _points1, InputArray _points2,461InputArray _cameraMatrix, OutputArray _R, OutputArray _t, double distanceThresh,462InputOutputArray _mask, OutputArray triangulatedPoints)463{464CV_INSTRUMENT_REGION();465466Mat points1, points2, cameraMatrix;467_points1.getMat().convertTo(points1, CV_64F);468_points2.getMat().convertTo(points2, CV_64F);469_cameraMatrix.getMat().convertTo(cameraMatrix, CV_64F);470471int npoints = points1.checkVector(2);472CV_Assert( npoints >= 0 && points2.checkVector(2) == npoints &&473points1.type() == points2.type());474475CV_Assert(cameraMatrix.rows == 3 && cameraMatrix.cols == 3 && cameraMatrix.channels() == 1);476477if (points1.channels() > 1)478{479points1 = points1.reshape(1, npoints);480points2 = points2.reshape(1, npoints);481}482483double fx = cameraMatrix.at<double>(0,0);484double fy = cameraMatrix.at<double>(1,1);485double cx = cameraMatrix.at<double>(0,2);486double cy = cameraMatrix.at<double>(1,2);487488points1.col(0) = (points1.col(0) - cx) / fx;489points2.col(0) = (points2.col(0) - cx) / fx;490points1.col(1) = (points1.col(1) - cy) / fy;491points2.col(1) = (points2.col(1) - cy) / fy;492493points1 = points1.t();494points2 = points2.t();495496Mat R1, R2, t;497decomposeEssentialMat(E, R1, R2, t);498Mat P0 = Mat::eye(3, 4, R1.type());499Mat P1(3, 4, R1.type()), P2(3, 4, R1.type()), P3(3, 4, R1.type()), P4(3, 4, R1.type());500P1(Range::all(), Range(0, 3)) = R1 * 1.0; P1.col(3) = t * 1.0;501P2(Range::all(), Range(0, 3)) = R2 * 1.0; P2.col(3) = t * 1.0;502P3(Range::all(), Range(0, 3)) = R1 * 1.0; P3.col(3) = -t * 1.0;503P4(Range::all(), Range(0, 3)) = R2 * 1.0; P4.col(3) = -t * 1.0;504505// Do the cheirality check.506// Notice here a threshold dist is used to filter507// out far away points (i.e. infinite points) since508// their depth may vary between positive and negtive.509std::vector<Mat> allTriangulations(4);510Mat Q;511512triangulatePoints(P0, P1, points1, points2, Q);513if(triangulatedPoints.needed())514Q.copyTo(allTriangulations[0]);515Mat mask1 = Q.row(2).mul(Q.row(3)) > 0;516Q.row(0) /= Q.row(3);517Q.row(1) /= Q.row(3);518Q.row(2) /= Q.row(3);519Q.row(3) /= Q.row(3);520mask1 = (Q.row(2) < distanceThresh) & mask1;521Q = P1 * Q;522mask1 = (Q.row(2) > 0) & mask1;523mask1 = (Q.row(2) < distanceThresh) & mask1;524525triangulatePoints(P0, P2, points1, points2, Q);526if(triangulatedPoints.needed())527Q.copyTo(allTriangulations[1]);528Mat mask2 = Q.row(2).mul(Q.row(3)) > 0;529Q.row(0) /= Q.row(3);530Q.row(1) /= Q.row(3);531Q.row(2) /= Q.row(3);532Q.row(3) /= Q.row(3);533mask2 = (Q.row(2) < distanceThresh) & mask2;534Q = P2 * Q;535mask2 = (Q.row(2) > 0) & mask2;536mask2 = (Q.row(2) < distanceThresh) & mask2;537538triangulatePoints(P0, P3, points1, points2, Q);539if(triangulatedPoints.needed())540Q.copyTo(allTriangulations[2]);541Mat mask3 = Q.row(2).mul(Q.row(3)) > 0;542Q.row(0) /= Q.row(3);543Q.row(1) /= Q.row(3);544Q.row(2) /= Q.row(3);545Q.row(3) /= Q.row(3);546mask3 = (Q.row(2) < distanceThresh) & mask3;547Q = P3 * Q;548mask3 = (Q.row(2) > 0) & mask3;549mask3 = (Q.row(2) < distanceThresh) & mask3;550551triangulatePoints(P0, P4, points1, points2, Q);552if(triangulatedPoints.needed())553Q.copyTo(allTriangulations[3]);554Mat mask4 = Q.row(2).mul(Q.row(3)) > 0;555Q.row(0) /= Q.row(3);556Q.row(1) /= Q.row(3);557Q.row(2) /= Q.row(3);558Q.row(3) /= Q.row(3);559mask4 = (Q.row(2) < distanceThresh) & mask4;560Q = P4 * Q;561mask4 = (Q.row(2) > 0) & mask4;562mask4 = (Q.row(2) < distanceThresh) & mask4;563564mask1 = mask1.t();565mask2 = mask2.t();566mask3 = mask3.t();567mask4 = mask4.t();568569// If _mask is given, then use it to filter outliers.570if (!_mask.empty())571{572Mat mask = _mask.getMat();573CV_Assert(mask.size() == mask1.size());574bitwise_and(mask, mask1, mask1);575bitwise_and(mask, mask2, mask2);576bitwise_and(mask, mask3, mask3);577bitwise_and(mask, mask4, mask4);578}579if (_mask.empty() && _mask.needed())580{581_mask.create(mask1.size(), CV_8U);582}583584CV_Assert(_R.needed() && _t.needed());585_R.create(3, 3, R1.type());586_t.create(3, 1, t.type());587588int good1 = countNonZero(mask1);589int good2 = countNonZero(mask2);590int good3 = countNonZero(mask3);591int good4 = countNonZero(mask4);592593if (good1 >= good2 && good1 >= good3 && good1 >= good4)594{595if(triangulatedPoints.needed()) allTriangulations[0].copyTo(triangulatedPoints);596R1.copyTo(_R);597t.copyTo(_t);598if (_mask.needed()) mask1.copyTo(_mask);599return good1;600}601else if (good2 >= good1 && good2 >= good3 && good2 >= good4)602{603if(triangulatedPoints.needed()) allTriangulations[1].copyTo(triangulatedPoints);604R2.copyTo(_R);605t.copyTo(_t);606if (_mask.needed()) mask2.copyTo(_mask);607return good2;608}609else if (good3 >= good1 && good3 >= good2 && good3 >= good4)610{611if(triangulatedPoints.needed()) allTriangulations[2].copyTo(triangulatedPoints);612t = -t;613R1.copyTo(_R);614t.copyTo(_t);615if (_mask.needed()) mask3.copyTo(_mask);616return good3;617}618else619{620if(triangulatedPoints.needed()) allTriangulations[3].copyTo(triangulatedPoints);621t = -t;622R2.copyTo(_R);623t.copyTo(_t);624if (_mask.needed()) mask4.copyTo(_mask);625return good4;626}627}628629int cv::recoverPose( InputArray E, InputArray _points1, InputArray _points2, InputArray _cameraMatrix,630OutputArray _R, OutputArray _t, InputOutputArray _mask)631{632return cv::recoverPose(E, _points1, _points2, _cameraMatrix, _R, _t, 50, _mask);633}634635int cv::recoverPose( InputArray E, InputArray _points1, InputArray _points2, OutputArray _R,636OutputArray _t, double focal, Point2d pp, InputOutputArray _mask)637{638Mat cameraMatrix = (Mat_<double>(3,3) << focal, 0, pp.x, 0, focal, pp.y, 0, 0, 1);639return cv::recoverPose(E, _points1, _points2, cameraMatrix, _R, _t, _mask);640}641642void cv::decomposeEssentialMat( InputArray _E, OutputArray _R1, OutputArray _R2, OutputArray _t )643{644CV_INSTRUMENT_REGION();645646Mat E = _E.getMat().reshape(1, 3);647CV_Assert(E.cols == 3 && E.rows == 3);648649Mat D, U, Vt;650SVD::compute(E, D, U, Vt);651652if (determinant(U) < 0) U *= -1.;653if (determinant(Vt) < 0) Vt *= -1.;654655Mat W = (Mat_<double>(3, 3) << 0, 1, 0, -1, 0, 0, 0, 0, 1);656W.convertTo(W, E.type());657658Mat R1, R2, t;659R1 = U * W * Vt;660R2 = U * W.t() * Vt;661t = U.col(2) * 1.0;662663R1.copyTo(_R1);664R2.copyTo(_R2);665t.copyTo(_t);666}667668669