Proposals:Statistics Framework Runtime Vector Size

Refactoring the Statistics Framework to have Runtime Length

Currently, the Statistics Framework requires the MeasurementVector to have a length defined at compile time.

Rationale for having compile time length

The statistics classes in ITK have MeasurementVectorSize (length of each measurement vector) as a static const value. This has until now been sufficient since typical statistics operations involve sampling an image where the number of measurement vectors is a variable, but the measurement vector size is usually fixed and depends on the dimension of the parametric space.

Rationale for having run time length

For algorithms such as Normalized cuts [1] and other Kernel PCA feature space projection techniques [2], it may be necessary to keep the dimensionality of the feature space as a variable. This requires removing MeasurementVectorSize as a static method and making it an iVar.

[1] PAMI - Vol26, No2, Spectral Grouping using the Nystrom method , Feb 2004

[2] Neural Computation - Nonlinear component analysis as a Kernel Eigenvalue problem, vol 10, 1998

Additions

1. VariableDimensionHistogram

Class to handle variable length histograms added in NAMIC sandbox NAMICSandBox/RefactoringITKStatisticsClasses/src/itkVariableDimensionHistogram.h, .txx NAMICSandBox/RefactoringITKStatisticsClasses/Tests/itkVariableDimensionHistogramTest.cxx

The class is similar to itk::Histogram with modifications to allow the dimension of the histogram (which is dependent on the size of each measurement vector) to be set at run-time.

2. VariableSizeMatrix NAMICSandBox/RefactoringITKStatisticsClasses/src/itkVariableSizeMatrix Similar to itk::Matrix with a similar API

3. MeasurementVectorTraits To have consistent API, we've created traits for measurement vectors. The traits are templated over the MeasurementVectorType (which was earlier constrained to be of type FixedArray or its subclasses.). For run-time size capability, we need to support itk::Array and possibly other containers like vnl_vector. To have a consistent way of dealing with GetSize(), SetSize calls etc, traits are used. This class is templated over the MeasurementVectorType. [From the doxygen headers for the class]

* For instance, the developer can create a measurement vector as
*
* typename SampleType:: MeasurementVectorType m_MeasurementVector 
* = MeasurementVectorTraits< typename 
*    SampleType::MeasurementVectorType >::SetSize( s ) );
*
* This will create a measurement vector of length s if it is a FixedArray or 
* a vnl_vector_fixed, itkVector etc.. If not it returns an array of length 0
* for the appropriate type. Other useful typedefs are defined to get the 
* length of the vector, for the MeanType, RealType for compuatations etc
*
* To get the length of a measurement vector, the user would
*
* MeasurementVectorTraits< MeasurementVectorType >::GetSize( &mv )
* 
* This calls the appropriate functions for the MeasurementVectorType to return
* the size of the measurement vector mv.
*
* MeasurementVectorTraits< MeasurementVectorType >::GetSize()
*
* This returns the length of MeasurementVectorType, which will be the true
* length of a FixedArray, Vector, vnl_vector_fixed, Point etc and 0 otherwise

NAMICSandBox/RefactoringITKStatisticsClasses/src/itkMeasurementVectorTraits.h

API changes / additions

1. itk::Sample

This class now supports a method to set/get the MeasurementVector length. This must be set explicitly in cases where measurement vectors are variable size containers (itk::Array etc) as below.

 typedef itk::Sample< Array < double > > SampleType;
 SampleType::Pointer sample = SampleType::New();
 sample->SetMeasurementVectorSize( length );
 SampleType::MeasurementVectorType m(length);
 m.Fill( 4.57 );
 sample->PushBack( m );

The earlier method will still be valid, along with all the macros. For instance the following would also work

 const unsigned int length = 3;
 typedef itk::Sample< FixedArray < double, length > > SampleType;
 SampleType::Pointer sample = SampleType::New();
 SampleType::MeasurementVectorType m;
 m.Fill( 4.57 );
 sample->PushBack( m );

The use of the MeasurementVectorSize macro to get the length of the measurement vector is deprecated. For instance,

 typedef itk::Sample< FixedArray < double, 3 > > SampleTypeA;
 std::cout << SampleTypeA::MeasurementVectorSize << std::endl;
 typedef itk::Sample< Array < double > > SampleTypeB;
 std::cout << SampleTypeB::MeasurementVectorSize << std::endl;

will produce 3 in the first case and 0 in the second. The appropriate/consistent way to do this is to get the size using the get macros sample->GetMeasurementVectorSize()which will yield 3 in both cases.

All classes that derive from sample or do filtering operations on sample (which is most classes) query the sample for the length of the measurement vector.

2. DistanceMetrics

This class also contains methods to set/Get measurement vector length. As before this only needs to be set in cases here the measurement vector is of variable size. For instance the following code fragments are equivalent.

 typedef itk::Vector< float, 2 > MeasurementVectorType;
 typedef itk::Statistics::EuclideanDistance< MeasurementVectorType > DistanceMetricType;
 DistanceMetricType::Pointer distanceMetric = DistanceMetricType::New();
 DistanceMetricType::OriginType originPoint;
 MeasurementVectorType queryPointA;
 MeasurementVectorType queryPointB;
 originPoint[0] = 0;
 originPoint[1] = 0;
 queryPointA[0] = 2;
 queryPointA[1] = 2;
 queryPointB[0] = 3;
 queryPointB[1] = 3;
 distanceMetric->SetOrigin( originPoint );
 std::cout << "Euclidean distance between the two query points (A and B) = " 
           << distanceMetric->Evaluate( queryPointA, queryPointB ) << std::endl;

 typedef itk::Array< float > MeasurementVectorType;
 typedef itk::Statistics::EuclideanDistance< MeasurementVectorType > DistanceMetricType;
 DistanceMetricType::Pointer distanceMetric = DistanceMetricType::New();
 DistanceMetricType::OriginType originPoint( 2 );
 MeasurementVectorType queryPointA( 2 );
 MeasurementVectorType queryPointB( 2 );
 originPoint[0] = 0;
 originPoint[1] = 0;
 queryPointA[0] = 2;
 queryPointA[1] = 2;
 queryPointB[0] = 3;
 queryPointB[1] = 3;
 distanceMetric->SetOrigin( originPoint );
 std::cout << "Euclidean distance between the two query points (A and B) = " 
           << distanceMetric->Evaluate( queryPointA, queryPointB ) << std::endl;

3. DensityFunctions

The density functions also contain the MeasurementVector length as an ivar. Again, if you are not using a compile-time fixed length container as a measurement vector, you will need to add the following line

 densityfunction->SetMeasurementVectorSize( length );

4. SampleAlgorithms

Several statistics algorithms derive from SampleAlgorithmBase. They generally take an itk::Sample as an input and produce some statistically relevant information or another sample. These classes also contain the MeasurementVectorLength as an iVar and contain public: Set/Get macros to change the MeasurementVectorSize. At first thought, this might not seem necessary, since these methods should query the sample passed as input for the MeasurementVectorLength. This was done to introduce consistency checks when the measurement vector is a variable length container to ensure for instance that appropriate parameters are passed to the algorithm. For instance, consider the following two code-fragments.

 typedef itk::Sample< Array< float > > SampleType;
 typedef itk::Statistics::WeightedCovarianceCalculator< SampleType > CalculatorType;
 CalculatorType::MeanType mean( 3 );
 CalculatorType::Pointer calculator = CalculatorType::New();
 calculator->SetMean( mean );
 calculator->SetInputSample( sample );
 calculator->SetWeightFunction(weightFunction.GetPointer()) ;
 calculator->Update() ;
 std::cout << " variance: " << calculator->GetOutput()->GetVnlMatrix().get(0,0) << std::endl ;

Here it is the responsibility of the WeightedCovarianceCalculator to check that the length of the mean and the measurement vectors in sample have the same length and throw an exception on the line calculator->SetInputSample( sample ); if they are not.

5. itk::Histogram - thoughts

The current working setup has two histogram classes itk::VariableDimensionHistogram and the old itk::Histogram. This is murky. It necessitates having two sets of histogram user classes such as itk::ListSampleToHistogramGenerator and ListSampleToVariableDimensionHistogramGenerator etc. I would like to combine these classes into one class. This is possible via partial specialization.

For instance

 template < class TMeasurement = float, unsigned int VMeasurementVectorSize = 1,
            class TFrequencyContainer = DenseFrequencyContainer< float > > 
 class ITK_EXPORT Histogram 
   : public Sample < FixedArray< TMeasurement, VMeasurementVectorSize > >
   {
   //....
   //....
   }

 template < class TMeasurement, class TFrequencyContainer > 
 class ITK_EXPORT Histogram< TMeasurement, 0, TFrequencyContainer >
   : public Sample < Array< TMeasurement > >
   {
   //....
   //....
   }

This is also very convenient because the static const macros for MeasurementVectorSize return 0 when the size is dynamic.

For instance, the following definition takes care of selecting the appropriate histogram.

 template< class TListSample, 
           class THistogramMeasurement,  
           class TFrequencyContainer = DenseFrequencyContainer< float > >
 class ITK_EXPORT ListSampleToHistogramGenerator : public Object
 {
 public:
   /** the number of components in a measurement vector */
   itkStaticConstMacro(MeasurementVectorSize, unsigned int, MeasurementVectorTraits< 
     typename TListSample::MeasurementVectorType >::MeasurementVectorLength);
   typedef Histogram< THistogramMeasurement, 
                      itkGetStaticConstMacro(MeasurementVectorSize),
                      TFrequencyContainer > HistogramType;
 }

This is possible because traits have been set up to return 0 when the MV length is not known at compile time.

Why this has not been done yet? Although it can be confusing for new users of ITK to see two histogram classes, this hasn't been done because partial template specialization is not supported by VS6. We could get over that by two template specializations, one for DenseFrequencyContainer and the other for SparseFrequencyContainer and forcing the MeasurementType to be float. I am working on this now.