itkShapeLabelMapFilter.hxx

/*=========================================================================
 *
 *  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 itkShapeLabelMapFilter_hxx
#define itkShapeLabelMapFilter_hxx

#include "itkProgressReporter.h"
#include "itkConstNeighborhoodIterator.h"
#include "itkConstShapedNeighborhoodIterator.h"
#include "itkLabelMapToLabelImageFilter.h"
#include "itkConstantBoundaryCondition.h"
#include "itkGeometryUtilities.h"
#include "itkConnectedComponentAlgorithm.h"
#include "vnl/algo/vnl_real_eigensystem.h"
#include "vnl/algo/vnl_symmetric_eigensystem.h"
#include "itkMath.h"
#include "itkLexicographicCompare.h"
#include <deque>
#include <map>

namespace itk
{
template <typename TImage, typename TLabelImage>
ShapeLabelMapFilter<TImage, TLabelImage>::ShapeLabelMapFilter()
{
  m_ComputeFeretDiameter = false;
  m_ComputePerimeter = true;
  m_ComputeOrientedBoundingBox = false;
}

template <typename TImage, typename TLabelImage>
void
ShapeLabelMapFilter<TImage, TLabelImage>::BeforeThreadedGenerateData()
{
  Superclass::BeforeThreadedGenerateData();

  // Generate the label image, if needed
  if (m_ComputeFeretDiameter)
  {
    if (!m_LabelImage)
    {
      // generate an image of the labelized image
      using LCI2IType = LabelMapToLabelImageFilter<TImage, LabelImageType>;
      auto lci2i = LCI2IType::New();
      lci2i->SetInput(this->GetOutput());
      // Respect the number of threads of the filter
      lci2i->SetNumberOfWorkUnits(this->GetNumberOfWorkUnits());
      lci2i->Update();
      m_LabelImage = lci2i->GetOutput();
    }
  }
}

template <typename TImage, typename TLabelImage>
void
ShapeLabelMapFilter<TImage, TLabelImage>::ThreadedProcessLabelObject(LabelObjectType * labelObject)
{
  ImageType * output = this->GetOutput();

  // Compute the size per pixel, to be used later
  double sizePerPixel = 1;

  for (unsigned int i = 0; i < ImageDimension; ++i)
  {
    sizePerPixel *= output->GetSpacing()[i];
  }

  typename std::vector<double> sizePerPixelPerDimension;
  for (unsigned int i = 0; i < ImageDimension; ++i)
  {
    sizePerPixelPerDimension.push_back(sizePerPixel / output->GetSpacing()[i]);
  }

  // Compute the max the index on the border of the image
  IndexType borderMin = output->GetLargestPossibleRegion().GetIndex();
  IndexType borderMax = borderMin;
  for (unsigned int i = 0; i < ImageDimension; ++i)
  {
    borderMax[i] += output->GetLargestPossibleRegion().GetSize()[i] - 1;
  }

  // Init the vars
  SizeValueType                           nbOfPixels = 0;
  ContinuousIndex<double, ImageDimension> centroid;
  centroid.Fill(0);
  IndexType mins;
  mins.Fill(NumericTraits<IndexValueType>::max());
  IndexType maxs;
  maxs.Fill(NumericTraits<IndexValueType>::NonpositiveMin());
  SizeValueType nbOfPixelsOnBorder = 0;
  double        perimeterOnBorder = 0;
  MatrixType    centralMoments;
  centralMoments.Fill(0);

  using LengthType = typename LabelObjectType::LengthType;

  // Iterate over all the lines
  typename LabelObjectType::ConstLineIterator lit(labelObject);
  while (!lit.IsAtEnd())
  {
    const IndexType & idx = lit.GetLine().GetIndex();
    LengthType        length = lit.GetLine().GetLength();

    // Update the nbOfPixels
    nbOfPixels += length;

    // Update the centroid - and report the progress
    // First, update the axes that are not 0
    for (unsigned int i = 1; i < ImageDimension; ++i)
    {
      centroid[i] += (OffsetValueType)length * idx[i];
    }
    // Then, update the axis 0
    centroid[0] += idx[0] * (OffsetValueType)length + (length * (length - 1)) / 2.0;

    // Update the mins and maxs
    for (unsigned int i = 0; i < ImageDimension; ++i)
    {
      if (idx[i] < mins[i])
      {
        mins[i] = idx[i];
      }
      if (idx[i] > maxs[i])
      {
        maxs[i] = idx[i];
      }
    }
    // Must fix the max for the axis 0
    if (idx[0] + (OffsetValueType)length > maxs[0])
    {
      maxs[0] = idx[0] + length - 1;
    }

    // Object is on a border ?
    bool isOnBorder = false;
    for (unsigned int i = 1; i < ImageDimension; ++i)
    {
      if (idx[i] == borderMin[i] || idx[i] == borderMax[i])
      {
        isOnBorder = true;
        break;
      }
    }
    if (isOnBorder)
    {
      // The line touch a border on a dimension other than 0, so
      // all the line touch a border
      nbOfPixelsOnBorder += length;
    }
    else
    {
      // We must check for the dimension 0
      bool isOnBorder0 = false;
      if (idx[0] == borderMin[0])
      {
        // One more pixel on the border
        ++nbOfPixelsOnBorder;
        isOnBorder0 = true;
      }
      if (!isOnBorder0 || length > 1)
      {
        // We can check for the end of the line
        if (idx[0] + (OffsetValueType)length - 1 == borderMax[0])
        {
          // One more pixel on the border
          ++nbOfPixelsOnBorder;
        }
      }
    }

    // Physical size on border
    // First, the dimension 0
    if (idx[0] == borderMin[0])
    {
      // The beginning of the line
      perimeterOnBorder += sizePerPixelPerDimension[0];
    }
    if (idx[0] + (OffsetValueType)length - 1 == borderMax[0])
    {
      // And the end of the line
      perimeterOnBorder += sizePerPixelPerDimension[0];
    }
    // Then the other dimensions
    for (unsigned int i = 1; i < ImageDimension; ++i)
    {
      if (idx[i] == borderMin[i])
      {
        // one border
        perimeterOnBorder += sizePerPixelPerDimension[i] * length;
      }
      if (idx[i] == borderMax[i])
      {
        // and the other
        perimeterOnBorder += sizePerPixelPerDimension[i] * length;
      }
    }

    // moments computation
    //
    //  This computation has changed from what is documented in the
    //  original publication ( see class level documentation for
    //  reference).  It has been re derived to properly support the
    //  direction cosine matrix in the image.
    //
    // Using the same optimization of the computation and substitutions,
    // the new computation is derived with the following:
    //
    //   p_i = o_i + s_0*d_i_0 * x, where s_0 is spacing the line run, and
    //   d_i_0, it the components of the first column of the direction cosine
    //        matrix, and x is the index offset from o_i.
    //
    // Then the elements of the central moments _all_ are:
    //   S_i_j = sum_L_in_O( sum_p_in_L( p_i dot p_j ) )
    //
    // Then we follow the paper, in substituting p, expanding and
    // substituting for known summations over x. This is very similar to
    // equation 9 in the paper but with p_i dot p_j and NOT p_i dot p_i.

    if (length <= 2)
    {

      // The following code is the basic implementation. The next
      // piece of code gives the same result in an efficient way, by
      // using expended formulae allowed by the binary case instead of
      // loops.
      IndexValueType endIdx0 = idx[0] + length;
      for (IndexType iidx = idx; iidx[0] < endIdx0; iidx[0]++)
      {
        typename LabelObjectType::CentroidType pP;
        output->TransformIndexToPhysicalPoint(iidx, pP);

        for (unsigned int i = 0; i < ImageDimension; ++i)
        {
          centralMoments[i][i] += pP[i] * pP[i];
          for (unsigned int j = i + 1; j < ImageDimension; ++j)
          {
            const double cm = pP[i] * pP[j];
            centralMoments[i][j] += cm;
            centralMoments[j][i] += cm;
          }
        }
      }
    }
    else
    {
      // get the physical position and the spacing - they are used several times
      // later
      typename LabelObjectType::CentroidType physicalPosition;
      output->TransformIndexToPhysicalPoint(idx, physicalPosition);

      const typename ImageType::DirectionType & direction = output->GetDirection();
      auto                                      scale = MakeFilled<VectorType>(output->GetSpacing()[0]);
      for (unsigned int i = 0; i < ImageDimension; ++i)
      {
        scale[i] *= direction(i, 0);
      }

      const double lcoff_1 = (length - 1.0) / 2.0;
      const double lcoff_2 = (2.0 * length - 1.0) / 3.0;

      for (unsigned int i = 0; i < ImageDimension; ++i)
      {
        centralMoments[i][i] +=
          length * (physicalPosition[i] * physicalPosition[i] +
                    lcoff_1 * (2.0 * physicalPosition[i] * scale[i] + lcoff_2 * scale[i] * scale[i]));

        for (unsigned int j = i + 1; j < ImageDimension; ++j)
        {
          const double cm = length * (physicalPosition[i] * physicalPosition[j] +
                                      lcoff_1 * (physicalPosition[i] * scale[j] + scale[i] * physicalPosition[j] +
                                                 lcoff_2 * scale[i] * scale[j]));
          centralMoments[j][i] += cm;
          centralMoments[i][j] += cm;
        }
      }
    }

    ++lit;
  }


  // final computation
  typename LabelObjectType::RegionType::SizeType boundingBoxSize;
  for (unsigned int i = 0; i < ImageDimension; ++i)
  {
    centroid[i] /= nbOfPixels;
    boundingBoxSize[i] = maxs[i] - mins[i] + 1;
    for (unsigned int j = 0; j < ImageDimension; ++j)
    {
      centralMoments[i][j] /= nbOfPixels;
    }
  }
  typename LabelObjectType::RegionType   boundingBox(mins, boundingBoxSize);
  typename LabelObjectType::CentroidType physicalCentroid;
  output->TransformContinuousIndexToPhysicalPoint(centroid, physicalCentroid);

  // Center the second order moments
  for (unsigned int i = 0; i < ImageDimension; ++i)
  {
    for (unsigned int j = 0; j < ImageDimension; ++j)
    {
      centralMoments[i][j] -= physicalCentroid[i] * physicalCentroid[j];
    }
  }

  // Compute principal moments and axes
  VectorType                        principalMoments;
  vnl_symmetric_eigensystem<double> eigen{ centralMoments.GetVnlMatrix().as_matrix() };
  vnl_diag_matrix<double>           pm = eigen.D;
  for (unsigned int i = 0; i < ImageDimension; ++i)
  {
    principalMoments[i] = pm(i);
  }
  MatrixType principalAxes(eigen.V.transpose());

  // Add a final reflection if needed for a proper rotation,
  // by multiplying the last row by the determinant
  vnl_real_eigensystem                  eigenrot{ principalAxes.GetVnlMatrix().as_matrix() };
  vnl_diag_matrix<std::complex<double>> eigenval{ eigenrot.D };
  std::complex<double>                  det(1.0, 0.0);

  for (unsigned int i = 0; i < ImageDimension; ++i)
  {
    det *= eigenval(i);
  }

  for (unsigned int i = 0; i < ImageDimension; ++i)
  {
    principalAxes[ImageDimension - 1][i] *= std::real(det);
  }

  double elongation = 0;
  double flatness = 0;
  if constexpr (ImageDimension < 2)
  {
    elongation = 1;
    flatness = 1;
  }
  else
  {
    if (Math::NotAlmostEquals(principalMoments[0], typename VectorType::ValueType{}))
    {
      const double flatnessRatio = principalMoments[1] / principalMoments[0];
      flatness = 0.0;
      if (flatnessRatio > 0.0)
      {
        flatness = std::sqrt(flatnessRatio);
      }
    }
    if (Math::NotAlmostEquals(principalMoments[ImageDimension - 2], typename VectorType::ValueType{}))
    {
      const double elongationRatio = principalMoments[ImageDimension - 1] / principalMoments[ImageDimension - 2];
      elongation = 0.0;
      if (elongationRatio > 0.0)
      {
        elongation = std::sqrt(elongationRatio);
      }
    }
  }

  double physicalSize = nbOfPixels * sizePerPixel;
  double equivalentRadius = GeometryUtilities::HyperSphereRadiusFromVolume(ImageDimension, physicalSize);
  double equivalentPerimeter = GeometryUtilities::HyperSpherePerimeter(ImageDimension, equivalentRadius);

  // Compute equivalent ellipsoid radius
  VectorType ellipsoidDiameter;
  double     edet = 1.0;
  for (unsigned int i = 0; i < ImageDimension; ++i)
  {
    edet *= principalMoments[i];
  }
  edet = std::pow(edet, 1.0 / ImageDimension);
  for (unsigned int i = 0; i < ImageDimension; ++i)
  {
    ellipsoidDiameter[i] = 0.0;
    if (edet != 0.0 && principalMoments[i] / edet > 0.0)
    {
      ellipsoidDiameter[i] = 2.0 * equivalentRadius * std::sqrt(principalMoments[i] / edet);
    }
  }

  // Set the values in the object
  labelObject->SetNumberOfPixels(nbOfPixels);
  labelObject->SetPhysicalSize(physicalSize);
  labelObject->SetBoundingBox(boundingBox);
  labelObject->SetCentroid(physicalCentroid);
  labelObject->SetNumberOfPixelsOnBorder(nbOfPixelsOnBorder);
  labelObject->SetPerimeterOnBorder(perimeterOnBorder);
  labelObject->SetPrincipalMoments(principalMoments);
  labelObject->SetPrincipalAxes(principalAxes);
  labelObject->SetElongation(elongation);
  labelObject->SetEquivalentSphericalRadius(equivalentRadius);
  labelObject->SetEquivalentSphericalPerimeter(equivalentPerimeter);
  labelObject->SetEquivalentEllipsoidDiameter(ellipsoidDiameter);
  labelObject->SetFlatness(flatness);

  if (m_ComputeFeretDiameter)
  {
    this->ComputeFeretDiameter(labelObject);
  }

  if (m_ComputePerimeter)
  {
    this->ComputePerimeter(labelObject);
  }

  if (m_ComputeOrientedBoundingBox)
  {
    this->ComputeOrientedBoundingBox(labelObject);
  }
}

template <typename TImage, typename TLabelImage>
void
ShapeLabelMapFilter<TImage, TLabelImage>::ComputeFeretDiameter(LabelObjectType * labelObject)
{
  const LabelPixelType & label = labelObject->GetLabel();

  using IndexListType = typename std::deque<IndexType>;
  IndexListType idxList;

  using NeighborIteratorType = typename itk::ConstNeighborhoodIterator<LabelImageType>;
  SizeType neighborHoodRadius;
  neighborHoodRadius.Fill(1);
  NeighborIteratorType                      it(neighborHoodRadius, m_LabelImage, m_LabelImage->GetBufferedRegion());
  ConstantBoundaryCondition<LabelImageType> lcbc;
  // Use label + 1 to have a label different of the current label on the border
  lcbc.SetConstant(label + 1);
  it.OverrideBoundaryCondition(&lcbc);
  it.GoToBegin();

  using NeighborIndexType = typename NeighborIteratorType::NeighborIndexType;

  // Iterate over all the indexes
  typename LabelObjectType::ConstIndexIterator iit(labelObject);
  while (!iit.IsAtEnd())
  {
    // Move the iterator to the new location
    it += iit.GetIndex() - it.GetIndex();

    // Push the pixel in the list if it is on the border of the object
    for (NeighborIndexType i = 0; i < it.Size(); ++i)
    {
      if (it.GetPixel(i) != label)
      {
        idxList.push_back(iit.GetIndex());
        break;
      }
    }
    ++iit;
  }

  ImageType * output = this->GetOutput();

  const typename ImageType::SpacingType & spacing = output->GetSpacing();

  // We can now search the feret diameter
  double feretDiameter = 0;
  for (typename IndexListType::const_iterator iIt1 = idxList.begin(); iIt1 != idxList.end(); ++iIt1)
  {
    auto iIt2 = iIt1;
    for (iIt2++; iIt2 != idxList.end(); ++iIt2)
    {
      // Compute the length between the 2 indexes
      double length = 0;
      for (unsigned int i = 0; i < ImageDimension; ++i)
      {
        const OffsetValueType indexDifference = (iIt1->operator[](i) - iIt2->operator[](i));
        length += std::pow(indexDifference * spacing[i], 2);
      }
      if (feretDiameter < length)
      {
        feretDiameter = length;
      }
    }
  }
  // Final computation
  feretDiameter = std::sqrt(feretDiameter);

  // Finally put the values in the label object
  labelObject->SetFeretDiameter(feretDiameter);
}

template <typename TImage, typename TLabelImage>
void
ShapeLabelMapFilter<TImage, TLabelImage>::ComputePerimeter(LabelObjectType * labelObject)
{
  // store the lines in a N-1D image of vectors
  using VectorLineType = std::deque<typename LabelObjectType::LineType>;
  using LineImageType = itk::Image<VectorLineType, ImageDimension - 1>;
  auto                              lineImage = LineImageType::New();
  typename LineImageType::IndexType lIdx;
  typename LineImageType::SizeType  lSize;
  RegionType                        boundingBox = labelObject->GetBoundingBox();
  for (unsigned int i = 0; i < ImageDimension - 1; ++i)
  {
    lIdx[i] = boundingBox.GetIndex()[i + 1];
    lSize[i] = boundingBox.GetSize()[i + 1];
  }
  const typename LineImageType::RegionType lRegion(lIdx, lSize);
  // enlarge the region a bit to avoid boundary problems
  typename LineImageType::RegionType elRegion(lRegion);
  lSize.Fill(1);
  elRegion.PadByRadius(lSize);
  // std::cout << boundingBox << "  " << lRegion << "  " << elRegion << std::endl;
  // now initialize the image
  lineImage->SetRegions(elRegion);
  lineImage->AllocateInitialized();

  // std::cout << "lineContainer.size(): " << lineContainer.size() << std::endl;

  // Iterate over all the lines and fill the image of lines
  typename LabelObjectType::ConstLineIterator lit(labelObject);
  while (!lit.IsAtEnd())
  {
    const IndexType & idx = lit.GetLine().GetIndex();
    for (unsigned int i = 0; i < ImageDimension - 1; ++i)
    {
      lIdx[i] = idx[i + 1];
    }
    lineImage->GetPixel(lIdx).push_back(lit.GetLine());
    ++lit;
  }

  // a data structure to store the number of intercepts on each direction
  using MapInterceptType = typename std::map<OffsetType, SizeValueType, Functor::LexicographicCompare>;
  MapInterceptType intercepts;
  // int nbOfDirections = static_cast<int>(std::pow(2.0, static_cast<int>(ImageDimension))) - 1;
  // intercepts.resize(nbOfDirections + 1);  // code begins at position 1

  // now iterate over the vectors of lines
  using LineImageIteratorType = ConstShapedNeighborhoodIterator<LineImageType>;
  LineImageIteratorType lIt(lSize, lineImage, lRegion); // the original, non padded region
  setConnectivity(&lIt, true);
  for (lIt.GoToBegin(); !lIt.IsAtEnd(); ++lIt)
  {
    const VectorLineType & ls = lIt.GetCenterPixel();

    // there are two intercepts on the 0 axis for each line
    OffsetType no;
    no.Fill(0);
    no[0] = 1;
    // std::cout << no << "-> " << 2 * ls.size() << std::endl;
    intercepts[no] += 2 * static_cast<SizeValueType>(ls.size());

    // and look at the neighbors
    typename LineImageIteratorType::ConstIterator ci;
    for (ci = lIt.Begin(); ci != lIt.End(); ++ci)
    {
      // std::cout << "-------------" << std::endl;
      // the vector of lines in the neighbor
      const VectorLineType & ns = ci.Get();
      // prepare the offset to be stored in the intercepts map
      typename LineImageType::OffsetType lno = ci.GetNeighborhoodOffset();
      no[0] = 0;
      for (unsigned int i = 0; i < ImageDimension - 1; ++i)
      {
        no[i + 1] = itk::Math::abs(lno[i]);
      }
      OffsetType dno = no; // offset for the diagonal
      dno[0] = 1;

      // now process the two lines to search the pixels on the contour of the object
      if (ls.empty())
      {
        // std::cout << "ls.empty()" << std::endl;
        // nothing to do
      }
      if (ns.empty())
      {
        // no line in the neighbors - all the lines in ls are on the contour
        for (auto li = ls.begin(); li != ls.end(); ++li)
        {
          // std::cout << "ns.empty()" << std::endl;
          const typename LabelObjectType::LineType & l = *li;
          // add as much intercepts as the line size
          intercepts[no] += l.GetLength();
          // and 2 times as much diagonal intercepts as the line size
          intercepts[dno] += l.GetLength() * 2;
        }
      }
      else
      {
        // std::cout << "else" << std::endl;
        // TODO - fix the code when the line starts at  NumericTraits<IndexValueType>::NonpositiveMin()
        // or end at  NumericTraits<IndexValueType>::max()
        auto li = ls.begin();
        auto ni = ns.begin();

        IndexValueType lZero = 0;
        IndexValueType lMin = 0;
        IndexValueType lMax = 0;

        IndexValueType nMin = NumericTraits<IndexValueType>::NonpositiveMin() + 1;
        IndexValueType nMax = ni->GetIndex()[0] - 1;

        while (li != ls.end())
        {
          // update the current line min and max. Neighbor line data is already up to date.
          lMin = li->GetIndex()[0];
          lMax = lMin + li->GetLength() - 1;

          // add as much intercepts as intersections of the 2 lines
          intercepts[no] += std::max(lZero, std::min(lMax, nMax) - std::max(lMin, nMin) + 1);
          // std::cout << "============" << std::endl;
          // std::cout << "  lMin:" << lMin << " lMax:" << lMax << " nMin:" << nMin << " nMax:" << nMax;
          // std::cout << " count: " << std::max( 0l, std::min(lMax, nMax) - std::max(lMin, nMin) + 1 ) << std::endl;
          // std::cout << "  " << no << ": " << intercepts[no] << std::endl;
          // std::cout << std::max( lZero, std::min(lMax, nMax+1) - std::max(lMin, nMin+1) + 1 ) << std::endl;
          // std::cout << std::max( lZero, std::min(lMax, nMax-1) - std::max(lMin, nMin-1) + 1 ) << std::endl;
          // left diagonal intercepts
          intercepts[dno] += std::max(lZero, std::min(lMax, nMax + 1) - std::max(lMin, nMin + 1) + 1);
          // right diagonal intercepts
          intercepts[dno] += std::max(lZero, std::min(lMax, nMax - 1) - std::max(lMin, nMin - 1) + 1);

          // go to the next line or the next neighbor depending on where we are
          if (nMax <= lMax)
          {
            // go to next neighbor
            nMin = ni->GetIndex()[0] + ni->GetLength();
            ++ni;

            if (ni != ns.end())
            {
              nMax = ni->GetIndex()[0] - 1;
            }
            else
            {
              nMax = NumericTraits<IndexValueType>::max() - 1;
            }
          }
          else
          {
            // go to next line
            ++li;
          }
        }
      }
    }
  }

  // compute the perimeter based on the intercept counts
  double perimeter = PerimeterFromInterceptCount(intercepts, this->GetOutput()->GetSpacing());
  labelObject->SetPerimeter(perimeter);
  labelObject->SetRoundness(labelObject->GetEquivalentSphericalPerimeter() / perimeter);
  labelObject->SetPerimeterOnBorderRatio(labelObject->GetPerimeterOnBorder() / perimeter);
}

template <typename TImage, typename TLabelImage>
template <typename TMapIntercept, typename TSpacing>
double
ShapeLabelMapFilter<TImage, TLabelImage>::PerimeterFromInterceptCount(TMapIntercept &  intercepts,
                                                                      const TSpacing & spacing)
{
  // std::cout << "PerimeterFromInterceptCount<>" << std::endl;
  double perimeter = 0.0;
  double pixelSize = 1.0;
  int    dim = TSpacing::GetVectorDimension();
  for (int i = 0; i < dim; ++i)
  {
    pixelSize *= spacing[i];
  }

  for (int i = 0; i < dim; ++i)
  {
    OffsetType no;
    no.Fill(0);
    no[i] = 1;
    // std::cout << no << ": " << intercepts[no] << std::endl;
    perimeter += pixelSize / spacing[i] * intercepts[no] / 2.0;
  }

  // Crofton's constant
  perimeter *= GeometryUtilities::HyperSphereVolume(dim, 1.0) / GeometryUtilities::HyperSphereVolume(dim - 1, 1.0);
  return perimeter;
}

#if !defined(ITK_DO_NOT_USE_PERIMETER_SPECIALIZATION)
template <typename TImage, typename TLabelImage>
double
ShapeLabelMapFilter<TImage, TLabelImage>::PerimeterFromInterceptCount(MapIntercept2Type & intercepts,
                                                                      const Spacing2Type  spacing)
{
  // std::cout << "PerimeterFromInterceptCount2" << std::endl;
  double dx = spacing[0];
  double dy = spacing[1];

  Offset2Type nx = { { 1, 0 } };
  Offset2Type ny = { { 0, 1 } };
  Offset2Type nxy = { { 1, 1 } };

  // std::cout << "nx: " << intercepts[nx] << std::endl;
  // std::cout << "ny: " << intercepts[ny] << std::endl;
  // std::cout << "nxy: " << intercepts[nxy] << std::endl;

  double perimeter = 0.0;
  perimeter += dy * intercepts[nx] / 2.0;
  perimeter += dx * intercepts[ny] / 2.0;
  perimeter += dx * dy / spacing.GetNorm() * intercepts[nxy] / 2.0;
  perimeter *= itk::Math::pi / 4.0;
  return perimeter;
}

template <typename TImage, typename TLabelImage>
double
ShapeLabelMapFilter<TImage, TLabelImage>::PerimeterFromInterceptCount(MapIntercept3Type & intercepts,
                                                                      const Spacing3Type  spacing)
{
  // std::cout << "PerimeterFromInterceptCount3" << std::endl;
  double dx = spacing[0];
  double dy = spacing[1];
  double dz = spacing[2];
  double dxy = std::sqrt(spacing[0] * spacing[0] + spacing[1] * spacing[1]);
  double dxz = std::sqrt(spacing[0] * spacing[0] + spacing[2] * spacing[2]);
  double dyz = std::sqrt(spacing[1] * spacing[1] + spacing[2] * spacing[2]);
  double dxyz = std::sqrt(spacing[0] * spacing[0] + spacing[1] * spacing[1] + spacing[2] * spacing[2]);
  double vol = spacing[0] * spacing[1] * spacing[2];

  // 'magical numbers', corresponding to area of voronoi partition on the
  // unit sphere, when germs are the 26 directions on the unit cube
  // Sum of (c1+c2+c3 + c4*2+c5*2+c6*2 + c7*4) equals 1.
  double c1 = 0.04577789120476 * 2; // Ox
  double c2 = 0.04577789120476 * 2; // Oy
  double c3 = 0.04577789120476 * 2; // Oz
  double c4 = 0.03698062787608 * 2; // Oxy
  double c5 = 0.03698062787608 * 2; // Oxz
  double c6 = 0.03698062787608 * 2; // Oyz
  double c7 = 0.03519563978232 * 2; // Oxyz
  // TODO - recompute those values if the spacing is non isotropic

  Offset3Type nx = { { 1, 0, 0 } };
  Offset3Type ny = { { 0, 1, 0 } };
  Offset3Type nz = { { 0, 0, 1 } };
  Offset3Type nxy = { { 1, 1, 0 } };
  Offset3Type nxz = { { 1, 0, 1 } };
  Offset3Type nyz = { { 0, 1, 1 } };
  Offset3Type nxyz = { { 1, 1, 1 } };

  // std::cout << "nx: " << intercepts[nx] << std::endl;
  // std::cout << "ny: " << intercepts[ny] << std::endl;
  // std::cout << "nz: " << intercepts[nz] << std::endl;
  // std::cout << "nxy: " << intercepts[nxy] << std::endl;
  // std::cout << "nxz: " << intercepts[nxz] << std::endl;
  // std::cout << "nyz: " << intercepts[nyz] << std::endl;
  // std::cout << "nxyz: " << intercepts[nxyz] << std::endl;

  double perimeter = 0.0;
  perimeter += vol / dx * intercepts[nx] / 2.0 * c1;
  perimeter += vol / dy * intercepts[ny] / 2.0 * c2;
  perimeter += vol / dz * intercepts[nz] / 2.0 * c3;
  perimeter += vol / dxy * intercepts[nxy] / 2.0 * c4;
  perimeter += vol / dxz * intercepts[nxz] / 2.0 * c5;
  perimeter += vol / dyz * intercepts[nyz] / 2.0 * c6;
  perimeter += vol / dxyz * intercepts[nxyz] / 2.0 * c7;
  perimeter *= 4;
  return perimeter;
}
#endif


template <typename TImage, typename TLabelImage>
void
ShapeLabelMapFilter<TImage, TLabelImage>::ComputeOrientedBoundingBox(LabelObjectType * labelObject)
{

  using VNLMatrixType = vnl_matrix<double>;
  using VNLVectorType = vnl_vector<double>;

  const ImageType * output = this->GetOutput();

  VNLMatrixType principalAxesBasisMatrix{ labelObject->GetPrincipalAxes().GetVnlMatrix().as_matrix() };

  const typename LabelObjectType::CentroidType centroid = labelObject->GetCentroid();
  const unsigned int                           numLines = labelObject->GetNumberOfLines();

  // Create a matrix where the columns are the physical points of the
  // start and end of each RLE line from the label map, relative to
  // the centroid
  VNLMatrixType pixelLocations(ImageDimension, labelObject->GetNumberOfLines() * 2);
  for (unsigned int l = 0; l < numLines; ++l)
  {
    typename LabelObjectType::LineType line = labelObject->GetLine(l);

    // add start index of line as physical point relative to centroid
    IndexType                     idx = line.GetIndex();
    typename ImageType::PointType pt;
    output->TransformIndexToPhysicalPoint(idx, pt);
    for (unsigned int j = 0; j < ImageDimension; ++j)
    {
      pixelLocations(j, l * 2) = pt[j] - centroid[j];
    }

    // add end index of line as physical point relative to centroid
    idx[0] += line.GetLength() - 1;
    output->TransformIndexToPhysicalPoint(idx, pt);
    for (unsigned int j = 0; j < ImageDimension; ++j)
    {
      pixelLocations(j, l * 2 + 1) = pt[j] - centroid[j];
    }
  }


  // Project the physical points onto principal axes
  VNLMatrixType transformedPixelLocations = principalAxesBasisMatrix * pixelLocations;

  // find the bounds in the projected domain
  assert(transformedPixelLocations.columns() != 0);
  VNLVectorType minimumPrincipalAxis = transformedPixelLocations.get_column(0);
  VNLVectorType maximumPrincipalAxis = transformedPixelLocations.get_column(0);

  for (unsigned int column = 1; column < transformedPixelLocations.columns(); ++column)
  {
    for (unsigned int i = 0; i < ImageDimension; ++i)
    {
      const double value = transformedPixelLocations(i, column);
      minimumPrincipalAxis[i] = std::min(minimumPrincipalAxis[i], value);
      maximumPrincipalAxis[i] = std::max(maximumPrincipalAxis[i], value);
    }
  }

  // The minimumPrincipalAxis/maximumPrincipalAxis is from center of pixel to center of pixel
  // in the principal axis basis. The full extent of the pixels needs
  // to include the offset bits from the center of the pixel to the
  // corners. The extrema of the OBB is increased by checking all
  // corners of the pixels, via computing the offset vector from the
  // center to the corner in the principal axis basis.

  VNLVectorType adjusted_minimumPrincipalAxis = minimumPrincipalAxis;
  VNLVectorType adjusted_maximumPrincipalAxis = maximumPrincipalAxis;

  const typename ImageType::SpacingType & spacing = output->GetSpacing();

  // iterate over all corners (2^D) of the pixel
  for (unsigned int p = 0; p < 1u << ImageDimension; ++p)
  {
    Vector<double, ImageDimension> spacingAxis(0.5 * spacing);

    // permute signs of spacing vector components, based on a bit of p
    // to component of spacingAxis mapping
    for (unsigned int i = 0; i < ImageDimension; ++i)
    {
      if (p & 1u << i)
      {
        spacingAxis[i] *= -1;
      }
    }

    const auto    physicalOffset = output->TransformLocalVectorToPhysicalVector(spacingAxis);
    VNLVectorType paOffset = principalAxesBasisMatrix * physicalOffset.GetVnlVector();

    for (unsigned int i = 0; i < ImageDimension; ++i)
    {
      adjusted_minimumPrincipalAxis[i] =
        std::min(adjusted_minimumPrincipalAxis[i], minimumPrincipalAxis[i] + paOffset[i]);
      adjusted_maximumPrincipalAxis[i] =
        std::max(adjusted_maximumPrincipalAxis[i], maximumPrincipalAxis[i] + paOffset[i]);
    }
  }

  minimumPrincipalAxis = adjusted_minimumPrincipalAxis;
  maximumPrincipalAxis = adjusted_maximumPrincipalAxis;

  // real physical size, in basis space
  Vector<double, ImageDimension> rsize;
  for (unsigned int i = 0; i < ImageDimension; ++i)
  {
    rsize[i] = itk::Math::abs(maximumPrincipalAxis[i] - minimumPrincipalAxis[i]);
  }


  //
  // Invert rotation matrix, we will now convert points from the
  // projected space back to the physical one, for the origin
  //
  principalAxesBasisMatrix.inplace_transpose();

  typename LabelObjectType::OrientedBoundingBoxPointType origin;
  VNLVectorType                                          min = principalAxesBasisMatrix * minimumPrincipalAxis;

  for (unsigned int i = 0; i < ImageDimension; ++i)
  {
    origin[i] = min[i] + centroid[i];
  }

  labelObject->SetOrientedBoundingBoxSize(rsize);
  labelObject->SetOrientedBoundingBoxOrigin(origin);
}

template <typename TImage, typename TLabelImage>
void
ShapeLabelMapFilter<TImage, TLabelImage>::AfterThreadedGenerateData()
{
  Superclass::AfterThreadedGenerateData();

  // Release the label image
  m_LabelImage = nullptr;
}

template <typename TImage, typename TLabelImage>
void
ShapeLabelMapFilter<TImage, TLabelImage>::PrintSelf(std::ostream & os, Indent indent) const
{
  Superclass::PrintSelf(os, indent);

  os << indent << "ComputeFeretDiameter: " << m_ComputeFeretDiameter << std::endl;
  os << indent << "ComputePerimeter: " << m_ComputePerimeter << std::endl;
  os << indent << "ComputeOrientedBoundingBox: " << m_ComputeOrientedBoundingBox << std::endl;
}

} // end namespace itk
#endif