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Diffstat (limited to 'src/Eigen/src/Geometry/Umeyama.h')
-rw-r--r-- | src/Eigen/src/Geometry/Umeyama.h | 177 |
1 files changed, 177 insertions, 0 deletions
diff --git a/src/Eigen/src/Geometry/Umeyama.h b/src/Eigen/src/Geometry/Umeyama.h new file mode 100644 index 0000000..5e20662 --- /dev/null +++ b/src/Eigen/src/Geometry/Umeyama.h @@ -0,0 +1,177 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009 Hauke Heibel <hauke.heibel@gmail.com> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_UMEYAMA_H +#define EIGEN_UMEYAMA_H + +// This file requires the user to include +// * Eigen/Core +// * Eigen/LU +// * Eigen/SVD +// * Eigen/Array + +namespace Eigen { + +#ifndef EIGEN_PARSED_BY_DOXYGEN + +// These helpers are required since it allows to use mixed types as parameters +// for the Umeyama. The problem with mixed parameters is that the return type +// cannot trivially be deduced when float and double types are mixed. +namespace internal { + +// Compile time return type deduction for different MatrixBase types. +// Different means here different alignment and parameters but the same underlying +// real scalar type. +template<typename MatrixType, typename OtherMatrixType> +struct umeyama_transform_matrix_type +{ + enum { + MinRowsAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(MatrixType::RowsAtCompileTime, OtherMatrixType::RowsAtCompileTime), + + // When possible we want to choose some small fixed size value since the result + // is likely to fit on the stack. So here, EIGEN_SIZE_MIN_PREFER_DYNAMIC is not what we want. + HomogeneousDimension = int(MinRowsAtCompileTime) == Dynamic ? Dynamic : int(MinRowsAtCompileTime)+1 + }; + + typedef Matrix<typename traits<MatrixType>::Scalar, + HomogeneousDimension, + HomogeneousDimension, + AutoAlign | (traits<MatrixType>::Flags & RowMajorBit ? RowMajor : ColMajor), + HomogeneousDimension, + HomogeneousDimension + > type; +}; + +} + +#endif + +/** +* \geometry_module \ingroup Geometry_Module +* +* \brief Returns the transformation between two point sets. +* +* The algorithm is based on: +* "Least-squares estimation of transformation parameters between two point patterns", +* Shinji Umeyama, PAMI 1991, DOI: 10.1109/34.88573 +* +* It estimates parameters \f$ c, \mathbf{R}, \f$ and \f$ \mathbf{t} \f$ such that +* \f{align*} +* \frac{1}{n} \sum_{i=1}^n \vert\vert y_i - (c\mathbf{R}x_i + \mathbf{t}) \vert\vert_2^2 +* \f} +* is minimized. +* +* The algorithm is based on the analysis of the covariance matrix +* \f$ \Sigma_{\mathbf{x}\mathbf{y}} \in \mathbb{R}^{d \times d} \f$ +* of the input point sets \f$ \mathbf{x} \f$ and \f$ \mathbf{y} \f$ where +* \f$d\f$ is corresponding to the dimension (which is typically small). +* The analysis is involving the SVD having a complexity of \f$O(d^3)\f$ +* though the actual computational effort lies in the covariance +* matrix computation which has an asymptotic lower bound of \f$O(dm)\f$ when +* the input point sets have dimension \f$d \times m\f$. +* +* Currently the method is working only for floating point matrices. +* +* \todo Should the return type of umeyama() become a Transform? +* +* \param src Source points \f$ \mathbf{x} = \left( x_1, \hdots, x_n \right) \f$. +* \param dst Destination points \f$ \mathbf{y} = \left( y_1, \hdots, y_n \right) \f$. +* \param with_scaling Sets \f$ c=1 \f$ when <code>false</code> is passed. +* \return The homogeneous transformation +* \f{align*} +* T = \begin{bmatrix} c\mathbf{R} & \mathbf{t} \\ \mathbf{0} & 1 \end{bmatrix} +* \f} +* minimizing the resudiual above. This transformation is always returned as an +* Eigen::Matrix. +*/ +template <typename Derived, typename OtherDerived> +typename internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type +umeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& dst, bool with_scaling = true) +{ + typedef typename internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type TransformationMatrixType; + typedef typename internal::traits<TransformationMatrixType>::Scalar Scalar; + typedef typename NumTraits<Scalar>::Real RealScalar; + typedef typename Derived::Index Index; + + EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL) + EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename internal::traits<OtherDerived>::Scalar>::value), + YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY) + + enum { Dimension = EIGEN_SIZE_MIN_PREFER_DYNAMIC(Derived::RowsAtCompileTime, OtherDerived::RowsAtCompileTime) }; + + typedef Matrix<Scalar, Dimension, 1> VectorType; + typedef Matrix<Scalar, Dimension, Dimension> MatrixType; + typedef typename internal::plain_matrix_type_row_major<Derived>::type RowMajorMatrixType; + + const Index m = src.rows(); // dimension + const Index n = src.cols(); // number of measurements + + // required for demeaning ... + const RealScalar one_over_n = RealScalar(1) / static_cast<RealScalar>(n); + + // computation of mean + const VectorType src_mean = src.rowwise().sum() * one_over_n; + const VectorType dst_mean = dst.rowwise().sum() * one_over_n; + + // demeaning of src and dst points + const RowMajorMatrixType src_demean = src.colwise() - src_mean; + const RowMajorMatrixType dst_demean = dst.colwise() - dst_mean; + + // Eq. (36)-(37) + const Scalar src_var = src_demean.rowwise().squaredNorm().sum() * one_over_n; + + // Eq. (38) + const MatrixType sigma = one_over_n * dst_demean * src_demean.transpose(); + + JacobiSVD<MatrixType> svd(sigma, ComputeFullU | ComputeFullV); + + // Initialize the resulting transformation with an identity matrix... + TransformationMatrixType Rt = TransformationMatrixType::Identity(m+1,m+1); + + // Eq. (39) + VectorType S = VectorType::Ones(m); + if (sigma.determinant()<Scalar(0)) S(m-1) = Scalar(-1); + + // Eq. (40) and (43) + const VectorType& d = svd.singularValues(); + Index rank = 0; for (Index i=0; i<m; ++i) if (!internal::isMuchSmallerThan(d.coeff(i),d.coeff(0))) ++rank; + if (rank == m-1) { + if ( svd.matrixU().determinant() * svd.matrixV().determinant() > Scalar(0) ) { + Rt.block(0,0,m,m).noalias() = svd.matrixU()*svd.matrixV().transpose(); + } else { + const Scalar s = S(m-1); S(m-1) = Scalar(-1); + Rt.block(0,0,m,m).noalias() = svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose(); + S(m-1) = s; + } + } else { + Rt.block(0,0,m,m).noalias() = svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose(); + } + + if (with_scaling) + { + // Eq. (42) + const Scalar c = Scalar(1)/src_var * svd.singularValues().dot(S); + + // Eq. (41) + Rt.col(m).head(m) = dst_mean; + Rt.col(m).head(m).noalias() -= c*Rt.topLeftCorner(m,m)*src_mean; + Rt.block(0,0,m,m) *= c; + } + else + { + Rt.col(m).head(m) = dst_mean; + Rt.col(m).head(m).noalias() -= Rt.topLeftCorner(m,m)*src_mean; + } + + return Rt; +} + +} // end namespace Eigen + +#endif // EIGEN_UMEYAMA_H |