EIC code displayed by LXR master/​include/​eigen3/​Eigen/​src/​Geometry/​Umeyama.h	Source navigation Diff markup Identifier search General search
	Version: master test Revert   Change

Warning, file /include/eigen3/Eigen/src/Geometry/Umeyama.h was not indexed or was modified since last indexation (in which case cross-reference links may be missing, inaccurate or erroneous).

 // 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 residual 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;
 
   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  ( svd.matrixU().determinant() * svd.matrixV().determinant() < 0 )
     S(m-1) = -1;
 
   // Eq. (40) and (43)
   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

This page was automatically generated by the 2.3.7 LXR engine. The LXR team