itk::PSMProcrustesFunction< VDimension > Class Template Reference

Generalized Procrustes Analysis is the rigid registration between different input shapes represented by point correspondences to produce an optimal mean shape. One transformation per shape is computed using the PSMProcrustesFunction. The point sets are registered by translation, rotation and uniform scaling. Scaling can be turned off if required. More...

#include <itkPSMProcrustesFunction.h>

Inheritance diagram for itk::PSMProcrustesFunction< VDimension >:

Collaboration diagram for itk::PSMProcrustesFunction< VDimension >:

Public Types
typedef double	RealType
typedef vnl_vector_fixed< double, VDimension >	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 PSMProcrustesFunction	Self
typedef Object	Superclass
typedef SmartPointer< Self >	Pointer
typedef SmartPointer< const Self >	ConstPointer

Public Member Functions
	itkNewMacro (Self)
	itkTypeMacro (PSMProcrustesFunction, Object)
void	RunGeneralizedProcrustes (SimilarityTransformListType &transform, ShapeListType &shapes)
RealType	ComputeSumOfSquares (ShapeListType &shapes)
ShapeType	TransformShape (ShapeType shape, SimilarityTransform3D &transform)

Detailed Description

template<unsigned int VDimension>
class itk::PSMProcrustesFunction< VDimension >

Generalized Procrustes Analysis is the rigid registration between different input shapes represented by point correspondences to produce an optimal mean shape. One transformation per shape is computed using the PSMProcrustesFunction. The point sets are registered by translation, rotation and uniform scaling. Scaling can be turned off if required.

Definition at line 43 of file itkPSMProcrustesFunction.h.

Member Typedef Documentation

template<unsigned int VDimension>

typedef PSMProcrustesFunction itk::PSMProcrustesFunction< VDimension >::Self

Standard class typedefs.

Definition at line 65 of file itkPSMProcrustesFunction.h.

Member Function Documentation

template<unsigned int VDimension>

PSMProcrustesFunction< VDimension >::RealType itk::PSMProcrustesFunction< VDimension >::ComputeSumOfSquares

(

ShapeListType &

shapes

)

Calculate the sum of squares of the discrepancies between the registered input shapes and the reference shape points. This yields the maximum likelihood estimate.

Definition at line 368 of file itkPSMProcrustesFunction.cxx.

{
  ShapeListIteratorType shapeIt1, shapeIt2;
  ShapeIteratorType pointIt1, pointIt2;
  
  RealType sum = 0.0;
  
  for(shapeIt1 = shapes.begin(); shapeIt1 != shapes.end(); shapeIt1++)
    {
    for(shapeIt2 = shapes.begin(); shapeIt2 != shapes.end(); shapeIt2++)
      {
      ShapeType & shape1 = (*shapeIt1);
      ShapeType & shape2 = (*shapeIt2);
      
      pointIt1 = shape1.begin();
      pointIt2 = shape2.begin();
      while(pointIt1 != shape1.end() && pointIt2 != shape2.end())
        {
        sum += ((*pointIt1) - (*pointIt2)).squared_magnitude();
        pointIt1++;
        pointIt2++;
        }
      }
    }
  return sum / static_cast<RealType>(shapes.size() * shapes[0].size());
}

template<unsigned int VDimension>

itk::PSMProcrustesFunction< VDimension >::itkNewMacro

(

Self

)

Method for creation through the object factory.

template<unsigned int VDimension>

itk::PSMProcrustesFunction< VDimension >::itkTypeMacro	(	PSMProcrustesFunction< VDimension >	,
		Object
	)

Run-time type information (and related methods).

template<unsigned int VDimension>

template void itk::PSMProcrustesFunction< VDimension >::RunGeneralizedProcrustes	(	SimilarityTransformListType &	transform,
		ShapeListType &	shapes
	)

Align a list of shapes using Generalized Procrustes Analysis

Definition at line 28 of file itkPSMProcrustesFunction.cxx.

{
  ShapeListIteratorType leaveOutIt;
  SimilarityTransformListIteratorType transformIt;
  ShapeIteratorType shapeIt, meanIt;
  ShapeType shape, mean;
  SimilarityTransform3D transform;
  PointType ssqShape, ssqMean;

  const RealType SOS_EPSILON = 0.1; //1.0e-8;

  int numOfShapes = shapes.size();
  std::string errstring = "";
  // Initialize transform structure
  transform.rotation.set_identity();
  transform.scale = 1.0;
  transform.translation.fill(0.0);
  
  // Initialize transforms vector
  transforms.clear();
  transforms.reserve(shapes.size());
  for(int i = 0; i<numOfShapes; i++)
    {
    transforms.push_back(transform);
    }
  
  RealType sumOfSquares = ComputeSumOfSquares(shapes);
  RealType newSumOfSquares, diff = 1e5; // 1e10;
  
  int counter = 0;
  try
  {
    while(diff > SOS_EPSILON)
    {
      // Initialize ssqShape vector
      ssqShape.fill(0.0);
      // Initialize ssqMean vector
      ssqMean.fill(0.0);
      transformIt = transforms.begin();
      //int count = 0;
      for(leaveOutIt = shapes.begin(); leaveOutIt != shapes.end(); leaveOutIt++)
      {
        // Calculate mean of all shapes but one
        LeaveOneOutMean(mean, shapes, leaveOutIt);
        (*leaveOutIt) = RunProcrustes((*transformIt), mean, leaveOutIt);
        transformIt++;
      } // End shape list iteration
      
      // Fix scalings so geometric average = 1
      RealType scaleAve = 0.0;
      for(transformIt = transforms.begin(); transformIt != transforms.end(); transformIt++)
        scaleAve += log((*transformIt).scale);
      
      scaleAve = exp(scaleAve / static_cast<RealType>(transforms.size()));
      
      SimilarityTransform3D scaleSim;
      scaleSim.rotation.set_identity();
      scaleSim.translation.fill(0.0);
      scaleSim.scale = 1.0 / scaleAve;
      
      ShapeListIteratorType shapeListIt = shapes.begin();
      transformIt = transforms.begin();
      while(shapeListIt != shapes.end())
      {
        TransformShape((*shapeListIt), scaleSim);
        (*transformIt).scale /= scaleAve;
        
        shapeListIt++;
        transformIt++;
      }
      // Calculate the sum of squares of discrepancies between
      // the shapes
      newSumOfSquares = ComputeSumOfSquares(shapes);
      diff = sumOfSquares - newSumOfSquares;
      
      sumOfSquares = newSumOfSquares;
      counter++;
      std::cout << "DIFF VALUE : " << diff << std::endl;
      std::cout << "******PROCRUSTES FUNCTION COUNTER******: " << counter << std::endl;
      if(counter >= 1000)
      {
        errstring = "Number of iterations on shapes is too high.";
        ExceptionObject e( __FILE__, __LINE__ );
        e.SetDescription( errstring.c_str() );
        throw e;
      }
    } // End while loop
  } // End try
  catch(itk::ExceptionObject &e)
  {
    errstring = "ITK exception with description: " + std::string(e.GetDescription())
    + std::string("\n at location:") + std::string(e.GetLocation())
    + std::string("\n in file:") + std::string(e.GetFile());
  }
  catch(...)
  {
    errstring = "Unknown exception thrown";
  }
}

template<unsigned int VDimension>

PSMProcrustesFunction< VDimension >::ShapeType itk::PSMProcrustesFunction< VDimension >::TransformShape	(	ShapeType	shape,
		SimilarityTransform3D &	transform
	)

Helper function to transform a shape by a similarity transform

Definition at line 321 of file itkPSMProcrustesFunction.cxx.

{
  int numPoints = shape.size();
  ShapeIteratorType shapeIt;
  shapeIt = shape.begin();
  
  // Multiply by scale
  while(shapeIt != shape.end())
    {
    PointType & point = *shapeIt;
    (*shapeIt) = transform.scale * point;
    shapeIt++;
    }
  
  ShapeType transformedShape;
  vnl_vector_fixed<RealType, VDimension> vec;
  vec.fill(0.0);
  for(int i = 0; i < numPoints; i++)
    transformedShape.push_back(vec);
  
  // Multiply by rotation
  for(int i = 0; i<numPoints; i++)
    {
    for(int j = 0; j<VDimension; j++)
      {
      for(int k = 0; k<VDimension; k++)
        {
        transformedShape[i][j] += shape[i][k] * transform.rotation[k][j];
        }
      }
    }
  
  shapeIt = transformedShape.begin();
  
  // Add translation
  while(shapeIt != transformedShape.end())
    {
    PointType & point = (*shapeIt);
    point += transform.translation;
    shapeIt++;
    }
  return transformedShape;
}

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The documentation for this class was generated from the following files:

• C:/Users/Brig/Documents/ShapeWorksStudio/src/ParticleShapeworks/include/itkPSMProcrustesFunction.h
• C:/Users/Brig/Documents/ShapeWorksStudio/src/ParticleShapeworks/src/itkPSMProcrustesFunction.cxx