ENH: Ingest ITKPrincipalComponentsAnalysis into Modules/Numerics

Modules/Numerics/PrincipalComponentsAnalysis/CMakeLists.txt

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+project(PrincipalComponentsAnalysis)
+
+itk_module_impl()

Modules/Numerics/PrincipalComponentsAnalysis/README.md

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+# PrincipalComponentsAnalysis
+
+In-tree ITK module providing a principal component analysis filter for
+scalar, vector, and mesh-vertex data. The flagship class is
+`itk::VectorFieldPCA`, which computes the principal components of an
+ensemble of vector fields defined on a common mesh, useful for
+shape-modeling and multivariate statistics workflows.
+
+## Origin
+
+Ingested from the standalone remote module
+[**InsightSoftwareConsortium/ITKPrincipalComponentsAnalysis**](https://github.com/InsightSoftwareConsortium/ITKPrincipalComponentsAnalysis)
+on 2026-05-08, following the v4 ingestion guidelines defined in
+InsightSoftwareConsortium/ITK#6204. The upstream repository will be
+archived read-only after this PR merges; it remains reachable at the
+URL above for historical reference (notably the `doc/` and
+`examples/` directories, which were intentionally left in the
+upstream archive).
+
+## References
+
+- Bowers M., Younes L. *Principal Components Analysis of Scalar,
+  Vector, and Mesh Vertex Data.* The Insight Journal. August, 2013.
+  <https://doi.org/10.54294/loekqj>

Modules/Numerics/PrincipalComponentsAnalysis/include/itkVectorFieldPCA.h

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+/*=========================================================================
+ *
+ *  Copyright NumFOCUS
+ *
+ *  Licensed under the Apache License, Version 2.0 (the "License");
+ *  you may not use this file except in compliance with the License.
+ *  You may obtain a copy of the License at
+ *
+ *         https://www.apache.org/licenses/LICENSE-2.0.txt
+ *
+ *  Unless required by applicable law or agreed to in writing, software
+ *  distributed under the License is distributed on an "AS IS" BASIS,
+ *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ *  See the License for the specific language governing permissions and
+ *  limitations under the License.
+ *
+=========================================================================*/
+
+#ifndef itkVectorFieldPCA_h
+#define itkVectorFieldPCA_h
+
+#include "itkObject.h"
+#include "itkPointSet.h"
+#include "itkKernelFunctionBase.h"
+#include "vnl/vnl_vector.h"
+#include "vnl/vnl_matrix.h"
+
+namespace itk
+{
+
+/** \class VectorFieldPCA
+ * \brief Produce the principle components of a vector valued function.
+ *
+ * This calculator produces a set of basis functions composed of the
+ * principal components of a set of vector valued functions.
+ *
+ * Specify an itk::KernelFunction for Kernel PCA.  The Kernel Function
+ * can take as input an optional point set.
+ *
+ * This class is templated over the types of the vector valued functions,
+ * the output point types, and optionally the point set type.
+ *
+ * \author Michael Bowers, Laurent Younes
+ *
+ * This code was contributed in the Insight Journal paper:
+ *
+ * "Principal Components Analysis of Scalar, Vector, and Mesh Vertex Data"
+ * https://www.insight-journal.org/browse/publication/878
+ *
+ * \ingroup ITKStatistics
+ * \ingroup PrincipalComponentsAnalysis
+ */
+
+template <typename TRealValueType = double>
+class ITK_TEMPLATE_EXPORT GaussianDistanceKernel : public KernelFunctionBase<TRealValueType>
+{
+public:
+  /** Standard class type alias. */
+  using Self = GaussianDistanceKernel;
+  using Superclass = KernelFunctionBase<TRealValueType>;
+  using Pointer = SmartPointer<Self>;
+  using ConstPointer = SmartPointer<const Self>;
+
+  /** Run-time type information (and related methods). */
+  itkTypeMacro(GaussianDistanceKernel, KernelFunction);
+
+  /** Method for creation through the object factory. */
+  itkNewMacro(Self);
+
+  /**
+   * \brief Set and get the Kernel sigma.
+   */
+  void
+  SetKernelSigma(double s)
+  {
+    m_KernelSigma = s;
+    m_OneOverMinusTwoSigmaSqr = -1.0 / (2.0 * s * s);
+  }
+  itkGetMacro(KernelSigma, double);
+
+  /**
+   * \brief Evaluate the function. Input is the squared distance
+   */
+  inline TRealValueType
+  Evaluate(const TRealValueType & u) const override
+  {
+    return (std::exp(u * m_OneOverMinusTwoSigmaSqr));
+  }
+
+protected:
+  GaussianDistanceKernel() = default;
+  ~GaussianDistanceKernel() override = default;
+  void
+  PrintSelf(std::ostream & os, Indent indent) const override
+  {
+    Superclass::PrintSelf(os, indent);
+  }
+
+private:
+  double m_KernelSigma{ 1.0 };
+  double m_OneOverMinusTwoSigmaSqr{ -0.5 };
+};
+
+template <typename TVectorFieldElementType,
+          typename TPCType,
+          typename TPointSetPixelType = float,
+          typename TPointSetCoordRepType = float,
+          typename KernelFunctionType = KernelFunctionBase<TPointSetCoordRepType>,
+          class TPointSetType =
+            PointSet<TPointSetPixelType, 3, DefaultStaticMeshTraits<TPointSetPixelType, 3, 3, TPointSetCoordRepType>>>
+class ITK_TEMPLATE_EXPORT VectorFieldPCA : public Object
+{
+public:
+  ITK_DISALLOW_COPY_AND_MOVE(VectorFieldPCA);
+
+  /** Standard class type alias. */
+  using Self = VectorFieldPCA;
+  using Superclass = Object;
+  using Pointer = SmartPointer<Self>;
+  using ConstPointer = SmartPointer<const Self>;
+
+  /** Method for creation through the object factory. */
+  itkNewMacro(Self);
+
+  /** Run-time type information (and related methods). */
+  itkTypeMacro(VectorFieldPCA, Object);
+
+  /** Type definitions for the PointSet. */
+  using InputPointSetType = TPointSetType;
+
+  /** Definitions for points of the PointSet. */
+  using InputPointType = typename InputPointSetType::PointType;
+
+  /** Definitions for the PointsContainer. */
+  using PointsContainer = typename InputPointSetType::PointsContainer;
+  using PointsContainerIterator = typename PointsContainer::Iterator;
+
+  /** Pointer types for the PointSet. */
+  using InputPointSetPointer = typename InputPointSetType::Pointer;
+
+  /** Const Pointer type for the PointSet. */
+  using InputPointSetConstPointer = typename InputPointSetType::ConstPointer;
+
+  /**
+   * \brief Input PointSet dimension
+   */
+  itkStaticConstMacro(InputMeshDimension, unsigned int, TPointSetType::PointDimension);
+
+  /** type for the vector fields. */
+  using VectorFieldType = vnl_matrix<TVectorFieldElementType>;
+  using VectorFieldSetType = VectorContainer<unsigned int, VectorFieldType>;
+
+  using VectorFieldSetTypePointer = typename VectorFieldSetType::Pointer;
+  using VectorFieldSetTypeConstPointer = typename VectorFieldSetType::ConstPointer;
+
+  /** types for the output. */
+  using MatrixType = vnl_matrix<TPCType>;
+  using VectorType = vnl_vector<TPCType>;
+
+  using BasisSetType = VectorContainer<unsigned int, MatrixType>;
+  using ResSetType = VectorContainer<unsigned int, VectorType>;
+
+  using BasisSetTypePointer = typename BasisSetType::Pointer;
+  using KernelFunctionPointer = typename KernelFunctionType::Pointer;
+
+  /**
+   * \brief Set and get the input point set.
+   */
+  itkSetMacro(PointSet, InputPointSetPointer);
+  itkGetMacro(PointSet, InputPointSetPointer);
+
+  /**
+   * \brief Set and get the vector fields for the analysis.
+   */
+  itkSetMacro(VectorFieldSet, VectorFieldSetTypePointer);
+  itkGetMacro(VectorFieldSet, VectorFieldSetTypePointer);
+
+  /**
+   * \brief Set and get the PCA count.
+   */
+  itkSetMacro(ComponentCount, unsigned int);
+  itkGetMacro(ComponentCount, unsigned int);
+
+  /**
+   * \brief Set pointer to the Kernel object.
+   */
+  itkSetMacro(KernelFunction, KernelFunctionPointer);
+
+  /**
+  * \brief Compute the PCA decomposition of the input point set.
+      If a Kernel and a Kernel Sigma are set ,
+      the calculator will perform Kernel PCA.
+  */
+  void
+  Compute();
+
+  /**
+   * \brief Return the results.
+   */
+  itkGetConstReferenceMacro(AveVectorField, MatrixType);
+  itkGetConstReferenceMacro(PCAEigenValues, VectorType);
+  itkGetConstObjectMacro(BasisVectors, BasisSetType);
+
+protected:
+  VectorFieldPCA();
+  ~VectorFieldPCA() override = default;
+  void
+  PrintSelf(std::ostream & os, Indent indent) const override;
+
+  /** Kernel PCA. */
+  void
+  KernelPCA();
+
+  /** Compute Momentum SCP. */
+  void
+  ComputeMomentumSCP();
+
+private:
+  VectorType m_PCAEigenValues;
+
+  BasisSetTypePointer       m_BasisVectors;
+  VectorFieldSetTypePointer m_VectorFieldSet;
+  InputPointSetPointer      m_PointSet;
+  KernelFunctionPointer     m_KernelFunction;
+
+  // Problem dimensions
+  unsigned int m_ComponentCount{ 0 };
+  unsigned int m_SetSize{ 0 };
+  unsigned int m_VectorDimCount{ 0 };
+  unsigned int m_PointDim{ 0 };
+
+  MatrixType m_V0;
+  MatrixType m_AveVectorField;
+  MatrixType m_K;
+
+  bool m_PCACalculated{ false };
+};
+
+} // end namespace itk
+
+#ifndef ITK_MANUAL_INSTANTIATION
+#  include "itkVectorFieldPCA.hxx"
+#endif
+
+#endif