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/*
* Software License Agreement (BSD License)
*
* Copyright (c) 2009, Willow Garage, Inc.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials provided
* with the distribution.
* * Neither the name of Willow Garage, Inc. 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 OWNER 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"
// Eigen
#include <Eigen/Core>
// OpenCV
#include <opencv2/core/eigen.hpp>
#include <opencv2/sfm/triangulation.hpp>
#include <opencv2/sfm/projection.hpp>
// libmv headers
#include "libmv/multiview/twoviewtriangulation.h"
#include "libmv/multiview/fundamental.h"
using namespace cv;
using namespace std;
namespace cv
{
namespace sfm
{
/** @brief Triangulates the a 3d position between two 2d correspondences, using the DLT.
@param xl Input vector with first 2d point.
@param xr Input vector with second 2d point.
@param Pl Input 3x4 first projection matrix.
@param Pr Input 3x4 second projection matrix.
@param objectPoint Output vector with computed 3d point.
Reference: @cite HartleyZ00 12.2 pag.312
*/
void
triangulateDLT( const Vec2d &xl, const Vec2d &xr,
const Matx34d &Pl, const Matx34d &Pr,
Vec3d &point3d )
{
Matx44d design;
for (int i = 0; i < 4; ++i)
{
design(0,i) = xl(0) * Pl(2,i) - Pl(0,i);
design(1,i) = xl(1) * Pl(2,i) - Pl(1,i);
design(2,i) = xr(0) * Pr(2,i) - Pr(0,i);
design(3,i) = xr(1) * Pr(2,i) - Pr(1,i);
}
Vec4d XHomogeneous;
cv::SVD::solveZ(design, XHomogeneous);
homogeneousToEuclidean(XHomogeneous, point3d);
}
/** @brief Triangulates the 3d position of 2d correspondences between n images, using the DLT
* @param x Input vectors of 2d points (the inner vector is per image). Has to be 2xN
* @param Ps Input vector with 3x4 projections matrices of each image.
* @param X Output vector with computed 3d point.
* Reference: it is the standard DLT; for derivation see appendix of Keir's thesis
*/
void
triangulateNViews(const Mat_<double> &x, const std::vector<Matx34d> &Ps, Vec3d &X)
{
CV_Assert(x.rows == 2);
unsigned nviews = x.cols;
CV_Assert(nviews == Ps.size());
cv::Mat_<double> design = cv::Mat_<double>::zeros(3*nviews, 4 + nviews);
for (unsigned i=0; i < nviews; ++i) {
for(char jj=0; jj<3; ++jj)
for(char ii=0; ii<4; ++ii)
design(3*i+jj, ii) = -Ps[i](jj, ii);
design(3*i + 0, 4 + i) = x(0, i);
design(3*i + 1, 4 + i) = x(1, i);
design(3*i + 2, 4 + i) = 1.0;
}
Mat X_and_alphas;
cv::SVD::solveZ(design, X_and_alphas);
homogeneousToEuclidean(X_and_alphas.rowRange(0, 4), X);
}
void
triangulatePoints(InputArrayOfArrays _points2d, InputArrayOfArrays _projection_matrices,
OutputArray _points3d)
{
// check
size_t nviews = (unsigned) _points2d.total();
CV_Assert(nviews >= 2 && nviews == _projection_matrices.total());
// inputs
size_t n_points;
std::vector<Mat_<double> > points2d(nviews);
std::vector<Matx34d> projection_matrices(nviews);
{
std::vector<Mat> points2d_tmp;
_points2d.getMatVector(points2d_tmp);
n_points = points2d_tmp[0].cols;
std::vector<Mat> projection_matrices_tmp;
_projection_matrices.getMatVector(projection_matrices_tmp);
// Make sure the dimensions are right
for(size_t i=0; i<nviews; ++i) {
CV_Assert(points2d_tmp[i].rows == 2 && points2d_tmp[i].cols == n_points);
if (points2d_tmp[i].type() == CV_64F)
points2d[i] = points2d_tmp[i];
else
points2d_tmp[i].convertTo(points2d[i], CV_64F);
CV_Assert(projection_matrices_tmp[i].rows == 3 && projection_matrices_tmp[i].cols == 4);
if (projection_matrices_tmp[i].type() == CV_64F)
projection_matrices[i] = projection_matrices_tmp[i];
else
projection_matrices_tmp[i].convertTo(projection_matrices[i], CV_64F);
}
}
// output
_points3d.create(3, n_points, CV_64F);
cv::Mat points3d = _points3d.getMat();
// Two view
if( nviews == 2 )
{
const Mat_<double> &xl = points2d[0], &xr = points2d[1];
const Matx34d & Pl = projection_matrices[0]; // left matrix projection
const Matx34d & Pr = projection_matrices[1]; // right matrix projection
// triangulate
for( unsigned i = 0; i < n_points; ++i )
{
Vec3d point3d;
triangulateDLT( Vec2d(xl(0,i), xl(1,i)), Vec2d(xr(0,i), xr(1,i)), Pl, Pr, point3d );
for(char j=0; j<3; ++j)
points3d.at<double>(j, i) = point3d[j];
}
}
else if( nviews > 2 )
{
// triangulate
for( unsigned i=0; i < n_points; ++i )
{
// build x matrix (one point per view)
Mat_<double> x( 2, nviews );
for( unsigned k=0; k < nviews; ++k )
{
points2d.at(k).col(i).copyTo( x.col(k) );
}
Vec3d point3d;
triangulateNViews( x, projection_matrices, point3d );
for(char j=0; j<3; ++j)
points3d.at<double>(j, i) = point3d[j];
}
}
}
} /* namespace sfm */
} /* namespace cv */