diff --git a/Modules/Numerics/PrincipalComponentsAnalysis/CMakeLists.txt b/Modules/Numerics/PrincipalComponentsAnalysis/CMakeLists.txt
new file mode 100644
index 00000000000..c372726e883
--- /dev/null
+++ b/Modules/Numerics/PrincipalComponentsAnalysis/CMakeLists.txt
@@ -0,0 +1,3 @@
+project(PrincipalComponentsAnalysis)
+
+itk_module_impl()
diff --git a/Modules/Numerics/PrincipalComponentsAnalysis/README.md b/Modules/Numerics/PrincipalComponentsAnalysis/README.md
new file mode 100644
index 00000000000..bbca9ec7fb7
--- /dev/null
+++ b/Modules/Numerics/PrincipalComponentsAnalysis/README.md
@@ -0,0 +1,24 @@
+# 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+URL above for historical reference (notably the `doc/` and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>
diff --git a/Modules/Numerics/PrincipalComponentsAnalysis/include/itkVectorFieldPCA.h b/Modules/Numerics/PrincipalComponentsAnalysis/include/itkVectorFieldPCA.h
new file mode 100644
index 00000000000..744989cb08e
--- /dev/null
+++ b/Modules/Numerics/PrincipalComponentsAnalysis/include/itkVectorFieldPCA.h
@@ -0,0 +1,245 @@
+/*=========================================================================
+ *
+ *  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
diff --git a/Modules/Numerics/PrincipalComponentsAnalysis/include/itkVectorFieldPCA.hxx b/Modules/Numerics/PrincipalComponentsAnalysis/include/itkVectorFieldPCA.hxx
new file mode 100644
index 00000000000..4d36b2f3064
--- /dev/null
+++ b/Modules/Numerics/PrincipalComponentsAnalysis/include/itkVectorFieldPCA.hxx
@@ -0,0 +1,332 @@
+/*=========================================================================
+ *
+ *  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_hxx
+#define itkVectorFieldPCA_hxx
+
+#include "vnl/algo/vnl_symmetric_eigensystem.h"
+#include "vnl/vnl_c_vector.h"
+#include "itkMath.h"
+
+namespace itk
+{
+
+template <typename TVectorFieldElementType,
+          typename TPCType,
+          typename TPointSetPixelType,
+          typename TPointSetCoordRepType,
+          typename KernelFunctionType,
+          class TPointSetType>
+VectorFieldPCA<TVectorFieldElementType,
+               TPCType,
+               TPointSetPixelType,
+               TPointSetCoordRepType,
+               KernelFunctionType,
+               TPointSetType>::VectorFieldPCA()
+  : m_BasisVectors(BasisSetType::New())
+
+{}
+
+template <typename TVectorFieldElementType,
+          typename TPCType,
+          typename TPointSetPixelType,
+          typename TPointSetCoordRepType,
+          typename KernelFunctionType,
+          class TPointSetType>
+void
+VectorFieldPCA<TVectorFieldElementType,
+               TPCType,
+               TPointSetPixelType,
+               TPointSetCoordRepType,
+               KernelFunctionType,
+               TPointSetType>::Compute()
+{
+  // Check parameters
+  if (!m_VectorFieldSet || !m_VectorFieldSet->Size())
+  {
+    itkExceptionMacro("Vector Field Set not specified.");
+    return;
+  }
+
+  m_SetSize = m_VectorFieldSet->Size();
+  if (m_ComponentCount <= 0 || m_ComponentCount > m_SetSize)
+  {
+    itkExceptionMacro("Component Count N must be 0 < N <= VectorFieldSetSize (" << m_VectorFieldSet->Size() << ").");
+    return;
+  }
+
+  // Get vector/point dim from the first member of the vector set
+
+  VectorFieldType & firstField = m_VectorFieldSet->ElementAt(0);
+  m_VectorDimCount = firstField.rows();
+  m_PointDim = firstField.cols();
+
+  // Check all vector dimensions in the set
+  for (unsigned int i = 1; i < m_VectorFieldSet->Size(); i++)
+  {
+    VectorFieldType & thisField = m_VectorFieldSet->ElementAt(i);
+    if (thisField.rows() != m_VectorDimCount || thisField.cols() != m_PointDim)
+    {
+      itkExceptionMacro("Vector " << i << " dimensions (" << thisField.rows() << "x" << thisField.cols()
+                                  << ") does not match other vector fields dimensions (" << m_VectorDimCount << "x"
+                                  << m_PointDim << ").");
+      return;
+    }
+  }
+
+  if (m_KernelFunction)
+  {
+    // will try Kernel PCA, so need a point set...
+    if (!m_PointSet)
+    {
+      itkExceptionMacro("KernelFunction is set but no PointSet is available.");
+      return;
+    }
+
+    //  PointSet only necessary for Kernel PCA, check that it matches.
+    if (m_PointSet->GetNumberOfPoints() != m_VectorDimCount)
+    {
+      itkExceptionMacro("Point Set count (" << m_PointSet->GetNumberOfPoints()
+                                            << ") does not match vector field count (" << m_VectorDimCount << ").");
+    }
+  }
+
+  this->ComputeMomentumSCP();
+  this->KernelPCA();
+
+  // Save only the desired eigenvalues
+  m_PCAEigenValues = m_PCAEigenValues.extract(m_ComponentCount);
+
+  // Save only the desired eigenvectors
+  m_V0 = m_V0.extract(m_V0.rows(), m_ComponentCount);
+
+  m_BasisVectors->Reserve(m_ComponentCount);
+  for (unsigned int k = 0; k < m_ComponentCount; k++)
+  {
+    MatrixType      basisVector(m_VectorDimCount, m_PointDim);
+    VectorFieldType accum(m_VectorDimCount, m_PointDim);
+    accum = 0.0;
+    basisVector = 0.0;
+    for (unsigned int j = 0; j < m_SetSize; j++)
+    {
+      vnl_c_vector<TVectorFieldElementType>::saxpy(
+        m_V0(j, k), (m_VectorFieldSet->ElementAt(j)).data_block(), accum.data_block(), accum.size());
+    }
+
+    for (unsigned int i = 0; i < accum.size(); ++i)
+      basisVector.begin()[i] = TPCType(accum.begin()[i]);
+    m_BasisVectors->SetElement(k, basisVector);
+  }
+
+  m_PCAEigenValues /= m_SetSize;
+  m_PCAEigenValues = m_PCAEigenValues.apply(sqrt);
+
+  m_PCACalculated = true;
+}
+
+template <typename TVectorFieldElementType,
+          typename TPCType,
+          typename TPointSetPixelType,
+          typename TPointSetCoordRepType,
+          typename KernelFunctionType,
+          class TPointSetType>
+void
+VectorFieldPCA<TVectorFieldElementType,
+               TPCType,
+               TPointSetPixelType,
+               TPointSetCoordRepType,
+               KernelFunctionType,
+               TPointSetType>::ComputeMomentumSCP()
+{
+  VectorFieldType accum;
+  accum.set_size(m_VectorDimCount, m_PointDim);
+  accum = 0.0;
+
+  // Determine the average of the vector field over the set
+  for (unsigned k = 0; k < m_SetSize; k++)
+  {
+    accum += m_VectorFieldSet->ElementAt(k);
+  }
+  accum /= (double)m_SetSize;
+
+  m_AveVectorField.set_size(m_VectorDimCount, m_PointDim);
+
+  for (unsigned int i = 0; i < accum.size(); ++i)
+    m_AveVectorField.begin()[i] = TPCType(accum.begin()[i]);
+
+
+  MatrixType kernelM(m_VectorDimCount, m_VectorDimCount);
+
+  // Check whether we're doing kernel PCA
+  if (!m_KernelFunction.IsNull())
+  {
+    unsigned k1, l1;
+    k1 = 0;
+    for (PointsContainerIterator kIx = m_PointSet->GetPoints()->Begin(); kIx != m_PointSet->GetPoints()->End(); kIx++)
+    {
+      l1 = 0;
+      for (PointsContainerIterator lIx = m_PointSet->GetPoints()->Begin(); lIx != m_PointSet->GetPoints()->End(); lIx++)
+      {
+        kernelM(k1, l1) = m_KernelFunction->Evaluate((kIx.Value()).SquaredEuclideanDistanceTo(lIx.Value()));
+        kernelM(l1, k1) = kernelM(k1, l1);
+        l1++;
+      }
+      k1++;
+    }
+  }
+
+  m_K.set_size(m_SetSize, m_SetSize);
+  MatrixType alphaK(m_VectorDimCount, m_PointDim);
+  MatrixType alphaL(m_VectorDimCount, m_PointDim);
+  MatrixType tmpA;
+  for (unsigned k = 0; k < m_SetSize; k++)
+  {
+    for (unsigned l = k; l < m_SetSize; l++)
+    {
+      for (unsigned int i = 0; i < alphaK.size(); ++i)
+      {
+        alphaK.begin()[i] = TPCType(m_VectorFieldSet->ElementAt(k).begin()[i]);
+      }
+      for (unsigned int i = 0; i < alphaL.size(); ++i)
+      {
+        alphaL.begin()[i] = TPCType(m_VectorFieldSet->ElementAt(l).begin()[i]);
+      }
+
+      if (m_KernelFunction)
+      {
+        tmpA = kernelM * (alphaL - m_AveVectorField);
+      }
+      else
+      {
+        tmpA = alphaL - m_AveVectorField;
+      }
+
+      MatrixType tmpB = alphaK - m_AveVectorField;
+      m_K(k, l) = vnl_c_vector<TPCType>::dot_product(tmpA.data_block(), tmpB.data_block(), tmpA.size());
+      m_K(l, k) = m_K(k, l);
+    }
+  }
+}
+
+template <typename TVectorFieldElementType,
+          typename TPCType,
+          typename TPointSetPixelType,
+          typename TPointSetCoordRepType,
+          typename KernelFunctionType,
+          class TPointSetType>
+void
+VectorFieldPCA<TVectorFieldElementType,
+               TPCType,
+               TPointSetPixelType,
+               TPointSetCoordRepType,
+               KernelFunctionType,
+               TPointSetType>::KernelPCA()
+{
+  VectorType rowMeans(m_SetSize);
+
+  for (unsigned int k = 0; k < m_SetSize; k++)
+  {
+    rowMeans(k) = m_K.get_row(k).mean();
+  }
+
+  TPCType    meanOfMeans = rowMeans.mean();
+  MatrixType K0(m_K - meanOfMeans);
+  for (unsigned int k = 0; k < m_SetSize; k++)
+  {
+    for (unsigned int l = 0; l < m_SetSize; l++)
+    {
+      K0(k, l) -= rowMeans(k) + rowMeans(l);
+    }
+  }
+
+  vnl_symmetric_eigensystem<TPCType> eigs(K0);
+
+  m_PCAEigenValues = eigs.D.diagonal();
+
+  // Eigenvalues come out in ascending order, reorder them
+  m_PCAEigenValues.flip();
+
+  // Reorder eigenvectors
+  m_V0 = eigs.V;
+  m_V0.fliplr();
+
+  const double eigenvalue_epsilon = 1.0e-10;
+  for (unsigned int k = 0; k < m_SetSize; k++)
+  {
+    m_V0.scale_column(k, 1.0 / std::sqrt(m_PCAEigenValues(k) + eigenvalue_epsilon));
+  }
+}
+
+template <typename TVectorFieldElementType,
+          typename TPCType,
+          typename TPointSetPixelType,
+          typename TPointSetCoordRepType,
+          typename KernelFunctionType,
+          class TPointSetType>
+void
+VectorFieldPCA<TVectorFieldElementType,
+               TPCType,
+               TPointSetPixelType,
+               TPointSetCoordRepType,
+               KernelFunctionType,
+               TPointSetType>::PrintSelf(std::ostream & os, Indent indent) const
+{
+  Superclass::PrintSelf(os, indent);
+
+  os << indent << "PCAEigenvalues: " << this->m_PCAEigenValues << std::endl;
+
+  if (this->m_BasisVectors.IsNotNull())
+  {
+    os << indent << "Basis Vector count: " << this->m_BasisVectors->Size() << std::endl;
+    if (this->m_BasisVectors->Size())
+    {
+      MatrixType & thisBasis = this->m_BasisVectors->ElementAt(0);
+      os << indent << "Basis Vector dimensions: " << thisBasis.rows() << "x" << thisBasis.cols() << std::endl;
+    }
+  }
+  itkPrintSelfObjectMacro(BasisVectors);
+
+  if (this->m_VectorFieldSet.IsNotNull())
+  {
+    os << indent << "Vector Field Set count: " << this->m_VectorFieldSet->Size() << std::endl;
+  }
+  itkPrintSelfObjectMacro(VectorFieldSet);
+
+  if (this->m_PointSet.IsNotNull())
+  {
+    os << indent << "PointSet dimensions: " << m_PointSet->GetNumberOfPoints() << "x"
+       << this->m_PointSet->PointDimension << std::endl;
+  }
+  itkPrintSelfObjectMacro(PointSet);
+
+  itkPrintSelfObjectMacro(KernelFunction);
+
+  os << indent << "ComponentCount: " << this->m_ComponentCount << std::endl;
+  os << indent << "SetSize: " << this->m_SetSize << std::endl;
+  os << indent << "VectorDimCount: " << this->m_VectorDimCount << std::endl;
+  os << indent << "PointDim: " << this->m_PointDim << std::endl;
+
+  os << indent << "V0 : " << this->m_V0 << std::endl;
+  os << indent << "AveVectorField: " << this->m_AveVectorField << std::endl;
+  os << indent << "K: " << this->m_K << std::endl;
+
+  os << indent << "PCACalculated: " << this->m_PCACalculated << std::endl;
+}
+} // end namespace itk
+
+#endif
diff --git a/Modules/Numerics/PrincipalComponentsAnalysis/itk-module.cmake b/Modules/Numerics/PrincipalComponentsAnalysis/itk-module.cmake
new file mode 100644
index 00000000000..3d76265b276
--- /dev/null
+++ b/Modules/Numerics/PrincipalComponentsAnalysis/itk-module.cmake
@@ -0,0 +1,18 @@
+set(
+  DOCUMENTATION
+  "This module contains an implementation of the
+principal component analysis for the ITK toolkit."
+)
+
+itk_module(
+  PrincipalComponentsAnalysis
+  DEPENDS
+    ITKCommon
+    ITKMesh
+    ITKIOMesh
+    ITKIOImageBase
+  TEST_DEPENDS
+    ITKTestKernel
+  EXCLUDE_FROM_DEFAULT
+  DESCRIPTION "${DOCUMENTATION}"
+)
diff --git a/Modules/Numerics/PrincipalComponentsAnalysis/test/CMakeLists.txt b/Modules/Numerics/PrincipalComponentsAnalysis/test/CMakeLists.txt
new file mode 100644
index 00000000000..9f691f972c4
--- /dev/null
+++ b/Modules/Numerics/PrincipalComponentsAnalysis/test/CMakeLists.txt
@@ -0,0 +1,54 @@
+itk_module_test()
+
+set(PCA PrincipalComponentsAnalysis)
+set(${PCA}Tests itkVectorKernelPCATest.cxx)
+
+createtestdriver(${PCA} "${${PCA}-Test_LIBRARIES}" "${${PCA}Tests}")
+
+itk_add_test(
+  NAME itkVectorKernelPCATest
+  COMMAND
+    ${PCA}TestDriver
+    itkVectorKernelPCATest
+    DATA{Input/PCATestSurface.vtk}
+    DATA{Input/PCATestSurface_alpha0_01.vtk}
+    DATA{Input/PCATestSurface_alpha0_02.vtk}
+    DATA{Input/PCATestSurface_alpha0_03.vtk}
+    DATA{Input/PCATestSurface_alpha0_04.vtk}
+    DATA{Input/PCATestSurface_alpha0_05.vtk}
+    DATA{Input/PCATestSurface_alpha0_06.vtk}
+    DATA{Input/PCATestSurface_alpha0_07.vtk}
+    DATA{Input/PCATestSurface_alpha0_08.vtk}
+    DATA{Input/PCATestSurface_alpha0_09.vtk}
+    DATA{Input/PCATestSurface_alpha0_10.vtk}
+    DATA{Input/PCATestSurface_alpha0_11.vtk}
+    DATA{Input/PCATestSurface_alpha0_12.vtk}
+    DATA{Input/PCATestSurface_alpha0_13.vtk}
+    DATA{Input/PCATestSurface_alpha0_14.vtk}
+    DATA{Input/PCATestSurface_alpha0_15.vtk}
+    DATA{Input/PCATestSurface_alpha0_16.vtk}
+    DATA{Input/PCATestSurface_alpha0_17.vtk}
+    DATA{Input/PCATestSurface_alpha0_18.vtk}
+    DATA{Input/PCATestSurface_alpha0_19.vtk}
+    DATA{Input/PCATestSurface_alpha0_20.vtk}
+    DATA{Input/PCATestSurface_alpha0_21.vtk}
+    DATA{Input/PCATestSurface_alpha0_22.vtk}
+    DATA{Input/PCATestSurface_alpha0_23.vtk}
+    DATA{Input/PCATestSurface_alpha0_24.vtk}
+    DATA{Input/PCATestSurface_alpha0_25.vtk}
+    DATA{Input/PCATestSurface_alpha0_26.vtk}
+    DATA{Input/PCATestSurface_alpha0_27.vtk}
+    DATA{Input/PCATestSurface_alpha0_28.vtk}
+    DATA{Input/PCATestSurface_alpha0_29.vtk}
+    DATA{Input/PCATestSurface_alpha0_30.vtk}
+    DATA{Input/PCATestSurface_alpha0_31.vtk}
+    DATA{Input/PCATestSurface_alpha0_32.vtk}
+    DATA{Input/PCATestSurface_alpha0_33.vtk}
+    DATA{Input/PCATestSurface_alpha0_34.vtk}
+    DATA{Input/PCATestSurface_alpha0_35.vtk}
+    DATA{Input/PCATestSurface_alpha0_36.vtk}
+    DATA{Input/PCATestSurface_alpha0_37.vtk}
+    DATA{Input/PCATestSurface_alpha0_38.vtk}
+    DATA{Input/PCATestSurface_alpha0_39.vtk}
+    DATA{Input/PCATestSurface_alpha0_40.vtk}
+)
diff --git a/Modules/Numerics/PrincipalComponentsAnalysis/test/Input/PCATestSurface.vtk.cid b/Modules/Numerics/PrincipalComponentsAnalysis/test/Input/PCATestSurface.vtk.cid
new file mode 100644
index 00000000000..1add67feb28
--- /dev/null
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new file mode 100644
index 00000000000..804f52cbdca
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new file mode 100644
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new file mode 100644
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new file mode 100644
index 00000000000..c6144c6cf5c
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new file mode 100644
index 00000000000..ad244938ba5
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new file mode 100644
index 00000000000..bc1238493d2
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new file mode 100644
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new file mode 100644
index 00000000000..49da6db2fc1
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new file mode 100644
index 00000000000..65989cc8bec
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diff --git a/Modules/Numerics/PrincipalComponentsAnalysis/test/Input/PCATestSurface_alpha0_12.vtk.cid b/Modules/Numerics/PrincipalComponentsAnalysis/test/Input/PCATestSurface_alpha0_12.vtk.cid
new file mode 100644
index 00000000000..46ab0d1edf1
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new file mode 100644
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new file mode 100644
index 00000000000..815f9d5d35c
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new file mode 100644
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diff --git a/Modules/Numerics/PrincipalComponentsAnalysis/test/itkVectorKernelPCATest.cxx b/Modules/Numerics/PrincipalComponentsAnalysis/test/itkVectorKernelPCATest.cxx
new file mode 100644
index 00000000000..b140df074e5
--- /dev/null
+++ b/Modules/Numerics/PrincipalComponentsAnalysis/test/itkVectorKernelPCATest.cxx
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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.
+ *
+=========================================================================*/
+
+#include "itkMesh.h"
+#include "itkMeshFileReader.h"
+#include "itkVectorFieldPCA.h"
+#include "itkTestingMacros.h"
+#include "vnl/vnl_vector.h"
+
+
+template <typename TPixel, typename TMesh, typename TVectorContainer>
+int
+ParseVectorFields(std::vector<std::string> vectorFieldFilenames, typename TVectorContainer::Pointer vectorFieldSet)
+{
+  int testStatus = EXIT_SUCCESS;
+
+  using ReaderType = itk::MeshFileReader<TMesh>;
+  typename ReaderType::Pointer meshReader = ReaderType::New();
+
+  unsigned int fieldSetCount = vectorFieldFilenames.size();
+  vectorFieldSet->Reserve(fieldSetCount);
+
+
+  typename TVectorContainer::Element vectorField;
+
+  unsigned int vectorFieldDim = 0;
+  unsigned int vectorFieldCount = 0;
+
+  unsigned int setIx = 0;
+  for (unsigned int i = 0; i < fieldSetCount; i++)
+  {
+    std::string vectorFieldName = vectorFieldFilenames[i];
+
+    meshReader->SetFileName(vectorFieldName);
+
+    ITK_TRY_EXPECT_NO_EXCEPTION(meshReader->Update());
+
+    // Get the objects
+    typename TMesh::Pointer meshWithField = meshReader->GetOutput();
+
+    typename TMesh::PointDataContainerPointer pointData = meshWithField->GetPointData();
+    if (setIx == 0)
+    {
+      vectorFieldCount = pointData->Size();
+      if (vectorFieldCount)
+      {
+        TPixel oneDataSetVal = pointData->GetElement(0);
+        vectorFieldDim = oneDataSetVal.size();
+      }
+      if (vectorFieldCount != meshWithField->GetNumberOfPoints())
+      {
+        std::cerr << "Test failed!" << std::endl;
+        std::cerr << "Vector field count (" << vectorFieldCount << ") doesn't match mesh vertext count ("
+                  << meshWithField->GetNumberOfPoints() << ")." << std::endl;
+        testStatus = EXIT_FAILURE;
+      }
+      vectorField.set_size(vectorFieldCount, vectorFieldDim);
+    }
+    else
+    {
+      if (vectorFieldDim != vectorField.cols() || vectorFieldCount != meshWithField->GetNumberOfPoints())
+      {
+        std::cerr << "Test failed!" << std::endl;
+        std::cerr << "Unexpected dimensions in vector field file " << vectorFieldName << std::endl;
+        std::cerr << "Expected: " << vectorFieldCount << " x " << vectorFieldDim << ", but got "
+                  << meshWithField->GetNumberOfPoints() << " x " << vectorField.cols() << std::endl;
+        testStatus = EXIT_FAILURE;
+      }
+    }
+
+    for (unsigned int k = 0; k < pointData->Size(); k++)
+    {
+      TPixel oneDataSetVal = pointData->GetElement(k);
+      vectorField.set_row(k, oneDataSetVal);
+    }
+
+    vectorFieldSet->SetElement(setIx++, vectorField);
+  }
+
+  return testStatus;
+}
+
+
+int
+itkVectorKernelPCATest(int argc, char * argv[])
+{
+  if (argc < 6)
+  {
+    std::cerr << "Missing parameters." << std::endl;
+    std::cerr << "Usage: " << argv[0] << "<vtkMeshFile> <vectorField1> ... <vectorFieldN> " << std::endl;
+    std::cerr << "where N must be greater than 3" << std::endl;
+    return EXIT_FAILURE;
+  }
+
+
+  int testStatus = EXIT_SUCCESS;
+
+  const unsigned int Dimension = 3;
+
+  using PointDataType = double;
+  using PointDataVectorType = itk::Array<PointDataType>;
+  using PixelType = PointDataVectorType;
+  using CoordRep = double;
+
+  using PCAResultsType = double;
+
+  // Declare the type of the input mesh
+  using MeshType = itk::Mesh<PixelType, Dimension>;
+
+  // Declare the type of the kernel function class
+  using KernelType = itk::GaussianDistanceKernel<CoordRep>;
+
+  // Declare the type of the PCA calculator
+  using PCACalculatorType =
+    itk::VectorFieldPCA<PointDataType, PCAResultsType, PixelType, CoordRep, KernelType, MeshType>;
+
+  // Instantiate the reader
+  using ReaderType = itk::MeshFileReader<MeshType>;
+  ReaderType::Pointer meshReader = ReaderType::New();
+
+  meshReader->SetFileName(argv[1]);
+
+  ITK_TRY_EXPECT_NO_EXCEPTION(meshReader->Update());
+
+
+  // Get the input mesh
+  MeshType::Pointer mesh = meshReader->GetOutput();
+
+
+  PCACalculatorType::Pointer pcaCalc = PCACalculatorType::New();
+
+  ITK_EXERCISE_BASIC_OBJECT_METHODS(pcaCalc, VectorFieldPCA, Object);
+
+  // Test exception when trying to compute before setting much of anything
+  ITK_TRY_EXPECT_EXCEPTION(pcaCalc->Compute());
+
+
+  // Set user variables
+  unsigned int pcaCount = 3;
+  pcaCalc->SetComponentCount(pcaCount);
+
+  // Connect the input
+  pcaCalc->SetPointSet(mesh);
+  ITK_TEST_SET_GET_VALUE(mesh, pcaCalc->GetPointSet());
+
+  // Set vector fields
+
+  PCACalculatorType::VectorFieldType vectorField;
+
+  // Should know vector field dimensions now
+  unsigned int vectorFieldDim = 0;
+
+  // how many vector field sets?
+  std::vector<std::string> vectorFieldFilenames;
+  unsigned int             firstVectorFieldIdx = 2;
+  unsigned int             fieldSetCount = argc - firstVectorFieldIdx;
+  for (unsigned int i = firstVectorFieldIdx; i < firstVectorFieldIdx + fieldSetCount; i++)
+  {
+    vectorFieldFilenames.emplace_back(argv[i]);
+  }
+
+  PCACalculatorType::VectorFieldSetTypePointer vectorFieldSet = PCACalculatorType::VectorFieldSetType::New();
+
+  testStatus =
+    ParseVectorFields<PixelType, MeshType, PCACalculatorType::VectorFieldSetType>(vectorFieldFilenames, vectorFieldSet);
+
+  pcaCalc->SetVectorFieldSet(vectorFieldSet);
+  ITK_TEST_SET_GET_VALUE(vectorFieldSet, pcaCalc->GetVectorFieldSet());
+
+  // Execute the PCA calculator
+  ITK_TRY_EXPECT_NO_EXCEPTION(pcaCalc->Compute());
+
+  double              kernelSigma = 6.25;
+  KernelType::Pointer distKernel = KernelType::New();
+  distKernel->SetKernelSigma(kernelSigma);
+  pcaCalc->SetKernelFunction(distKernel);
+
+
+  // Get the output and perform basic checks
+  unsigned int computedNumberOfAverageVectorFieldCols = pcaCalc->GetAveVectorField().cols();
+
+  unsigned int computedNumberOfAverageVectorFieldRows = pcaCalc->GetAveVectorField().rows();
+
+  for (unsigned int j = 0; j < pcaCalc->GetComponentCount(); j++)
+  {
+    unsigned int expectedBasisVectorCols = pcaCalc->GetVectorFieldSet()->GetElement(j).cols();
+    unsigned int computedBasisVectorCols = pcaCalc->GetBasisVectors()->GetElement(j).cols();
+    if (computedBasisVectorCols != expectedBasisVectorCols)
+    {
+      std::cout << "Test failed!" << std::endl;
+      std::cout << "Error in GetBasisVectors() dimension check at index [" << j << "]" << std::endl;
+      std::cout << "Expected: " << expectedBasisVectorCols << " columns, but got: " << computedBasisVectorCols
+                << std::endl;
+      testStatus = EXIT_FAILURE;
+    }
+
+    unsigned int expectedBasisVectorRows = pcaCalc->GetVectorFieldSet()->GetElement(j).rows();
+    unsigned int computedBasisVectorRows = pcaCalc->GetBasisVectors()->GetElement(j).rows();
+    if (computedBasisVectorRows != expectedBasisVectorRows)
+    {
+      std::cout << "Test failed!" << std::endl;
+      std::cout << "Error in GetBasisVectors() dimension check at index [" << j << "]" << std::endl;
+      std::cout << "Expected: " << expectedBasisVectorRows << " row, but got: " << computedBasisVectorRows << std::endl;
+      testStatus = EXIT_FAILURE;
+    }
+
+    if (computedNumberOfAverageVectorFieldCols != expectedBasisVectorCols)
+    {
+      std::cout << "Test failed!" << std::endl;
+      std::cout << "Error in GetAveVectorField() dimension check at index [" << j << "]" << std::endl;
+      std::cout << "Expected: " << vectorFieldDim << " columns, but got: " << computedNumberOfAverageVectorFieldCols
+                << std::endl;
+      testStatus = EXIT_FAILURE;
+    }
+
+    if (computedNumberOfAverageVectorFieldRows != expectedBasisVectorRows)
+    {
+      std::cout << "Test failed!" << std::endl;
+      std::cout << "Error in GetAveVectorField() dimension check at index [" << j << "]" << std::endl;
+      std::cout << "Expected: " << vectorFieldDim << " rows, but got: " << computedNumberOfAverageVectorFieldRows
+                << std::endl;
+      testStatus = EXIT_FAILURE;
+    }
+  }
+
+  unsigned int computedNumberOfEigenValueVectors = pcaCalc->GetPCAEigenValues().size();
+  if (computedNumberOfEigenValueVectors != pcaCount)
+  {
+    std::cout << "Test failed!" << std::endl;
+    std::cout << "Error in GetPCAEigenValues() dimension check." << std::endl;
+    std::cout << "Expected: " << pcaCount << ", but got: " << computedNumberOfEigenValueVectors << std::endl;
+    testStatus = EXIT_FAILURE;
+  }
+
+  // Test exception when trying to compute with a requested input count greater
+  // than the number of vector field sets
+  pcaCalc->SetComponentCount(fieldSetCount + 1);
+
+  ITK_TRY_EXPECT_EXCEPTION(pcaCalc->Compute());
+
+  std::cout << "Test finished." << std::endl;
+  return testStatus;
+}
diff --git a/Modules/Numerics/PrincipalComponentsAnalysis/wrapping/CMakeLists.txt b/Modules/Numerics/PrincipalComponentsAnalysis/wrapping/CMakeLists.txt
new file mode 100644
index 00000000000..de38eb1e8bd
--- /dev/null
+++ b/Modules/Numerics/PrincipalComponentsAnalysis/wrapping/CMakeLists.txt
@@ -0,0 +1,4 @@
+itk_wrap_module(PrincipalComponentsAnalysis)
+set(WRAPPER_SUBMODULE_ORDER)
+itk_auto_load_submodules()
+itk_end_wrap_module()
diff --git a/Modules/Numerics/PrincipalComponentsAnalysis/wrapping/itkGaussianDistanceKernel.wrap b/Modules/Numerics/PrincipalComponentsAnalysis/wrapping/itkGaussianDistanceKernel.wrap
new file mode 100644
index 00000000000..3277fd74733
--- /dev/null
+++ b/Modules/Numerics/PrincipalComponentsAnalysis/wrapping/itkGaussianDistanceKernel.wrap
@@ -0,0 +1,7 @@
+set(WRAPPER_AUTO_INCLUDE_HEADERS OFF)
+itk_wrap_include("itkVectorFieldPCA.h")
+itk_wrap_class("itk::GaussianDistanceKernel" POINTER)
+foreach(r ${WRAP_ITK_REAL})
+  itk_wrap_template("${ITKM_${r}}" "${ITKT_${r}}")
+endforeach()
+itk_end_wrap_class()
diff --git a/Modules/Remote/PrincipalComponentsAnalysis.remote.cmake b/Modules/Remote/PrincipalComponentsAnalysis.remote.cmake
deleted file mode 100644
index 4c15f7e3d2c..00000000000
--- a/Modules/Remote/PrincipalComponentsAnalysis.remote.cmake
+++ /dev/null
@@ -1,56 +0,0 @@
-#-- # Grading Level Criteria Report
-#-- EVALUATION DATE: 2020-03-01
-#-- EVALUATORS: [<<NO EVALUATOR>>,<<NO EVALUATOR>>]
-#--
-#-- ## Compliance level 5 star (AKA ITK main modules, or remote modules that could become core modules)
-#--   - [ ] Widespread community dependance
-#--   - [ ] Above 90% code coverage
-#--   - [ ] CI dashboards and testing monitored rigorously
-#--   - [ ] Key API features are exposed in wrapping interface
-#--   - [ ] All requirements of Levels 4,3,2,1
-#--
-#-- ## Compliance Level 4 star (Very high-quality code, perhaps small community dependance)
-#--   - [ ] Meets all ITK code style standards
-#--   - [ ] No external requirements beyond those needed by ITK proper
-#--   - [ ] Builds and passes tests on all supported platforms within 1 month of each core tagged release
-#--            - [ ] Windows Shared Library Build with Visual Studio
-#--            - [ ] Mac with clang compiller
-#--            - [ ] Linux with gcc compiler
-#--   - [ ] Active developer community dedicated to maintaining code-base
-#--   - [ ] 75% code coverage demonstrated for testing suite
-#--   - [ ] Continuous integration testing performed
-#--   - [ ] All requirements of Levels 3,2,1
-#--
-#-- ## Compliance Level 3 star (Quality beta code)
-#--   - [ ] API | executable interface is considered mostly stable and feature complete
-#--   - [ ] 10% C0-code coverage demonstrated for testing suite
-#--   - [ ] Some tests exist and pass on at least some platform
-#--   - [X] All requirements of Levels 2,1
-#--
-#-- ## Compliance Level 2 star (Alpha code feature API development or niche community/execution environment dependance )
-#--   - [X] Compiles for at least 1 niche set of execution envirionments, and perhaps others
-#--         (may depend on specific external tools like a java environment, or specific external libraries to work )
-#--   - [X] All requirements of Levels 1
-#--
-#-- ## Compliance Level 1 star (Pre-alpha features under development and code of unknown quality)
-#--   - [X] Code complies on at least 1 platform
-#--
-#-- ## Compliance Level 0 star ( Code/Feature of known poor-quality or deprecated status )
-#--   - [ ] Code reviewed and explicitly identified as not recommended for use
-#--
-#-- ### Please document here any justification for the criteria above
-#       Code style enforced by clang-format on 2020-02-19, and clang-tidy modernizations completed
-
-# Contact: Johan Andruejol <johan.andruejol@kitware.com>
-itk_fetch_module(
-  PrincipalComponentsAnalysis
-  "An ITK_-based implementation of principal components analysis.
-A more detailed description can be found in the Insight Journal article:
-  Bowers M., Younes L. ''Principal Components Analysis of Scalar, Vector, and Mesh Vertex Data.''
-    https://doi.org/10.54294/loekqj
-    August, 2013.
-"
-  MODULE_COMPLIANCE_LEVEL 2
-  GIT_REPOSITORY https://github.com/InsightSoftwareConsortium/ITKPrincipalComponentsAnalysis.git
-  GIT_TAG 88e3f65aabdc9cf2c11f03907975a4e605676504
-  )
diff --git a/Utilities/Maintenance/RemoteModuleIngest/whitelists/PrincipalComponentsAnalysis.list b/Utilities/Maintenance/RemoteModuleIngest/whitelists/PrincipalComponentsAnalysis.list
new file mode 100644
index 00000000000..1297ab5fe37
--- /dev/null
+++ b/Utilities/Maintenance/RemoteModuleIngest/whitelists/PrincipalComponentsAnalysis.list
@@ -0,0 +1,8 @@
+# PrincipalComponentsAnalysis — files that migrate into ITK at
+# Modules/Numerics/PrincipalComponentsAnalysis/
+include
+test
+wrapping
+CMakeLists.txt
+itk-module.cmake
+LICENSE
diff --git a/pyproject.toml b/pyproject.toml
index c73ae38c83d..00f4f39346e 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -62,6 +62,7 @@ cmd = '''cmake \
   -DModule_MeshNoise:BOOL=ON \
   -DModule_MGHIO:BOOL=ON \
   -DModule_PolarTransform:BOOL=ON \
+  -DModule_PrincipalComponentsAnalysis:BOOL=ON \
   -DModule_SplitComponents:BOOL=ON \
   -DModule_IOMeshMZ3:BOOL=ON \
   -DModule_IOFDF:BOOL=ON \