Umeyama.h
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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2009 Hauke Heibel <hauke.heibel@gmail.com>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #ifndef EIGEN_UMEYAMA_H
11 #define EIGEN_UMEYAMA_H
12 
13 // This file requires the user to include
14 // * Eigen/Core
15 // * Eigen/LU
16 // * Eigen/SVD
17 // * Eigen/Array
18 
19 namespace Eigen {
20 
21 #ifndef EIGEN_PARSED_BY_DOXYGEN
22 
23 // These helpers are required since it allows to use mixed types as parameters
24 // for the Umeyama. The problem with mixed parameters is that the return type
25 // cannot trivially be deduced when float and double types are mixed.
26 namespace internal {
27 
28 // Compile time return type deduction for different MatrixBase types.
29 // Different means here different alignment and parameters but the same underlying
30 // real scalar type.
31 template<typename MatrixType, typename OtherMatrixType>
33 {
34  enum {
35  MinRowsAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(MatrixType::RowsAtCompileTime, OtherMatrixType::RowsAtCompileTime),
36 
37  // When possible we want to choose some small fixed size value since the result
38  // is likely to fit on the stack. So here, EIGEN_SIZE_MIN_PREFER_DYNAMIC is not what we want.
40  };
41 
46  HomogeneousDimension,
47  HomogeneousDimension
48  > type;
49 };
50 
51 }
52 
53 #endif
54 
93 template <typename Derived, typename OtherDerived>
95 umeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& dst, bool with_scaling = true)
96 {
97  typedef typename internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type TransformationMatrixType;
99  typedef typename NumTraits<Scalar>::Real RealScalar;
100 
101  EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)
103  YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
104 
105  enum { Dimension = EIGEN_SIZE_MIN_PREFER_DYNAMIC(Derived::RowsAtCompileTime, OtherDerived::RowsAtCompileTime) };
106 
109  typedef typename internal::plain_matrix_type_row_major<Derived>::type RowMajorMatrixType;
110 
111  const Index m = src.rows(); // dimension
112  const Index n = src.cols(); // number of measurements
113 
114  // required for demeaning ...
115  const RealScalar one_over_n = RealScalar(1) / static_cast<RealScalar>(n);
116 
117  // computation of mean
118  const VectorType src_mean = src.rowwise().sum() * one_over_n;
119  const VectorType dst_mean = dst.rowwise().sum() * one_over_n;
120 
121  // demeaning of src and dst points
122  const RowMajorMatrixType src_demean = src.colwise() - src_mean;
123  const RowMajorMatrixType dst_demean = dst.colwise() - dst_mean;
124 
125  // Eq. (36)-(37)
126  const Scalar src_var = src_demean.rowwise().squaredNorm().sum() * one_over_n;
127 
128  // Eq. (38)
129  const MatrixType sigma = one_over_n * dst_demean * src_demean.transpose();
130 
132 
133  // Initialize the resulting transformation with an identity matrix...
134  TransformationMatrixType Rt = TransformationMatrixType::Identity(m+1,m+1);
135 
136  // Eq. (39)
137  VectorType S = VectorType::Ones(m);
138 
139  if ( svd.matrixU().determinant() * svd.matrixV().determinant() < 0 )
140  S(m-1) = -1;
141 
142  // Eq. (40) and (43)
143  Rt.block(0,0,m,m).noalias() = svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose();
144 
145  if (with_scaling)
146  {
147  // Eq. (42)
148  const Scalar c = Scalar(1)/src_var * svd.singularValues().dot(S);
149 
150  // Eq. (41)
151  Rt.col(m).head(m) = dst_mean;
152  Rt.col(m).head(m).noalias() -= c*Rt.topLeftCorner(m,m)*src_mean;
153  Rt.block(0,0,m,m) *= c;
154  }
155  else
156  {
157  Rt.col(m).head(m) = dst_mean;
158  Rt.col(m).head(m).noalias() -= Rt.topLeftCorner(m,m)*src_mean;
159  }
160 
161  return Rt;
162 }
163 
164 } // end namespace Eigen
165 
166 #endif // EIGEN_UMEYAMA_H
Matrix3f m
SCALAR Scalar
Definition: bench_gemm.cpp:46
cout<< "Here is the matrix m:"<< endl<< m<< endl;JacobiSVD< MatrixXf > svd(m, ComputeThinU|ComputeThinV)
EIGEN_DEVICE_FUNC ConstColwiseReturnType colwise() const
Definition: DenseBase.h:562
int n
Scalar Scalar * c
Definition: benchVecAdd.cpp:17
Namespace containing all symbols from the Eigen library.
Definition: jet.h:637
MatrixXf MatrixType
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:232
#define EIGEN_STATIC_ASSERT(CONDITION, MSG)
Definition: StaticAssert.h:127
DiscreteKey S(1, 2)
const unsigned int RowMajorBit
Definition: Constants.h:66
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
EIGEN_DEVICE_FUNC ConstRowwiseReturnType rowwise() const
Definition: DenseBase.h:550
internal::umeyama_transform_matrix_type< Derived, OtherDerived >::type umeyama(const MatrixBase< Derived > &src, const MatrixBase< OtherDerived > &dst, bool with_scaling=true)
Returns the transformation between two point sets.
Definition: Umeyama.h:95
NumTraits< Scalar >::Real RealScalar
Definition: bench_gemm.cpp:47
Two-sided Jacobi SVD decomposition of a rectangular matrix.
const SingularValuesType & singularValues() const
Definition: SVDBase.h:129
static const double sigma
const int Dynamic
Definition: Constants.h:22
The matrix class, also used for vectors and row-vectors.
#define EIGEN_SIZE_MIN_PREFER_DYNAMIC(a, b)
Definition: Macros.h:1294
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48


gtsam
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autogenerated on Tue Jul 4 2023 02:40:39