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struct SimilarityTransform3D
class Procrustes3D

Source code

#pragma once

#include <vnl/vnl_matrix.h>
#include <vnl/vnl_matrix_fixed.h>
#include <vnl/vnl_vector_fixed.h>

#include <vector>

struct SimilarityTransform3D {
  vnl_matrix_fixed<double, 3, 3> rotation;
  double scale;
  vnl_vector_fixed<double, 3> translation;

class Procrustes3D {
  typedef double RealType;
  typedef vnl_vector_fixed<double, 3> PointType;
  typedef std::vector<PointType> ShapeType;
  typedef ShapeType::iterator ShapeIteratorType;

  typedef std::vector<ShapeType> ShapeListType;
  typedef ShapeListType::iterator ShapeListIteratorType;

  typedef std::vector<SimilarityTransform3D> SimilarityTransformListType;
  typedef SimilarityTransformListType::iterator SimilarityTransformListIteratorType;

  typedef vnl_matrix_fixed<double, 3 + 1, 3 + 1> TransformMatrixType;
  typedef std::vector<TransformMatrixType> TransformMatrixListType;
  typedef TransformMatrixListType::iterator TransformMatrixIteratorType;

  Procrustes3D() : m_Scaling(true), m_RotationTranslation(true) {}
  Procrustes3D(bool do_scaling, bool do_rotation_translation)
      : m_Scaling(do_scaling), m_RotationTranslation(do_rotation_translation) {}

  bool GetScaling() const { return m_Scaling; }
  void ScalingOn() { m_Scaling = true; }
  void ScalingOff() { m_Scaling = false; }

  bool GetRotationTranslation() const { return m_RotationTranslation; }
  void RotationTranslationOn() { m_RotationTranslation = true; }
  void RotationTranslationOff() { m_RotationTranslation = false; }

  // Align a list of shapes using Generalized Procrustes Analysis
  void AlignShapes(SimilarityTransformListType& transforms, ShapeListType& shapes);

  void RemoveTranslation(SimilarityTransformListType& transforms, ShapeListType& shapes);

  // Helper function to transform a shape by a similarity transform
  static void TransformShape(ShapeType& shape, SimilarityTransform3D& transform);

  // Helper function to transform a list of shapes by a list of transforms
  static void TransformShapes(ShapeListType& shapes, SimilarityTransformListType& transforms);

  static RealType ComputeSumOfSquares(ShapeListType& shapes);

  // Transform from Configuration space to Procrustes space.  Translation
  // followed by rotation and scaling.
  void ConstructTransformMatrices(SimilarityTransformListType& transforms, TransformMatrixListType& transformMatrices);
  void ConstructTransformMatrix(SimilarityTransform3D& transform, TransformMatrixType& transformMatrix);

  void ComputeMeanShape(ShapeType& mean, ShapeListType& shapeList);
  void ComputeCenterOfMass(ShapeType& shape, PointType& center);
  void CenterShape(ShapeType& shape);

  // this is the center which needed for translation of the shapes to coincide on the image origin
  // so that the whole object is in the image and won't go outside
  void ComputeCommonCenter(SimilarityTransformListType& transforms, PointType& center);

  // Align source shape to target using Ordinary Procrustes Analysis (translation, scaling and rotation)
  // the target shape is assumed to be centered at the origin
  void AlignSourceToTarget(SimilarityTransform3D& transform, ShapeType& target, ShapeType& source);

  /* The median shape is
       defined as the shape with the minimum sum of Euclidean L1 norms to all
       other shapes in that group.  */
  int ComputeMedianShape(ShapeListType& shapeList);

  // Align two shapes (rotation & scale) using Ordinary Procrustes Analysis
  void AlignTwoShapes(SimilarityTransform3D& transform, ShapeType& shape1, ShapeType& shape2);

  bool m_Scaling;              // a flag to factor out scaling
  bool m_RotationTranslation;  // a flag for rotation + translation + (scale depending on m_Scaling), if false, the
                               // transformation will only be scaling

Updated on 2022-07-23 at 17:50:04 -0600