// Copyright (c) 2009 libmv authors. // // Permission is hereby granted, free of charge, to any person obtaining a copy // of this software and associated documentation files (the "Software"), to // deal in the Software without restriction, including without limitation the // rights to use, copy, modify, merge, publish, distribute, sublicense, and/or // sell copies of the Software, and to permit persons to whom the Software is // furnished to do so, subject to the following conditions: // // The above copyright notice and this permission notice shall be included in // all copies or substantial portions of the Software. // // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS // IN THE SOFTWARE. // // Compute a 3D position of a point from several images of it. In particular, // compute the projective point X in R^4 such that x = PX. // // Algorithm is the standard DLT; for derivation see appendix of Keir's thesis. #ifndef LIBMV_MULTIVIEW_NVIEWTRIANGULATION_H #define LIBMV_MULTIVIEW_NVIEWTRIANGULATION_H #include "libmv/base/vector.h" #include "libmv/logging/logging.h" #include "libmv/numeric/numeric.h" namespace libmv { // x's are 2D coordinates (x,y,1) in each image; Ps are projective cameras. The // output, X, is a homogeneous four vectors. template<typename T> void NViewTriangulate(const Matrix<T, 2, Dynamic> &x, const vector<Matrix<T, 3, 4> > &Ps, Matrix<T, 4, 1> *X) { int nviews = x.cols(); assert(nviews == Ps.size()); Matrix<T, Dynamic, Dynamic> design(3*nviews, 4 + nviews); design.setConstant(0.0); for (int i = 0; i < nviews; i++) { design.template block<3, 4>(3*i, 0) = -Ps[i]; 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; } Matrix<T, Dynamic, 1> X_and_alphas; Nullspace(&design, &X_and_alphas); X->resize(4); *X = X_and_alphas.head(4); } // x's are 2D coordinates (x,y,1) in each image; Ps are projective cameras. The // output, X, is a homogeneous four vectors. // This method uses the algebraic distance approximation. // Note that this method works better when the 2D points are normalized // with an isotopic normalization. template<typename T> void NViewTriangulateAlgebraic(const Matrix<T, 2, Dynamic> &x, const vector<Matrix<T, 3, 4> > &Ps, Matrix<T, 4, 1> *X) { int nviews = x.cols(); assert(nviews == Ps.size()); Matrix<T, Dynamic, 4> design(2*nviews, 4); for (int i = 0; i < nviews; i++) { design.template block<2, 4>(2*i, 0) = SkewMatMinimal(x.col(i)) * Ps[i]; } X->resize(4); Nullspace(&design, X); } } // namespace libmv #endif // LIBMV_MULTIVIEW_RESECTION_H