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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.
*
*=========================================================================*/
#ifndef itkGaussianMembershipFunction_h
#define itkGaussianMembershipFunction_h
#include "itkMatrix.h"
#include "itkMembershipFunctionBase.h"
namespace itk
{
namespace Statistics
{
/**
* \class GaussianMembershipFunction
* \brief GaussianMembershipFunction models class membership through a
* multivariate Gaussian function.
*
* GaussianMembershipFunction is a subclass of MembershipFunctionBase
* that models class membership (or likelihood) using a multivariate
* Gaussian function. The mean and covariance structure of the
* Gaussian are established using the methods SetMean() and
* SetCovariance(). The mean is a vector-type that is the same
* vector-type as the measurement vector but guaranteed to have a real
* element type. For instance, if the measurement type is an
* Vector<int,3>, then the mean is Vector<double,3>. If the
* measurement type is a VariableLengthVector<float>, then the mean is
* VariableLengthVector<double>. In contrast to this behavior, the
* covariance is always a VariableSizeMatrix<double>.
*
* If the covariance is singular or nearly singular, the membership function
* behaves somewhat like an impulse located at the mean. In this case,
* we specify the covariance to be a diagonal matrix with large values
* along the diagonal. This membership function, therefore,
* will return small but differentiable values everywhere and increase
* sharply near the mean.
*
* \ingroup ITKStatistics
*/
template <typename TMeasurementVector>
class ITK_TEMPLATE_EXPORT GaussianMembershipFunction : public MembershipFunctionBase<TMeasurementVector>
{
public:
ITK_DISALLOW_COPY_AND_MOVE(GaussianMembershipFunction);
/** Standard class type aliases */
using Self = GaussianMembershipFunction;
using Superclass = MembershipFunctionBase<TMeasurementVector>;
using Pointer = SmartPointer<Self>;
using ConstPointer = SmartPointer<const Self>;
/** \see LightObject::GetNameOfClass() */
itkOverrideGetNameOfClassMacro(GaussianMembershipFunction);
itkNewMacro(Self);
/** SmartPointer class for superclass */
using MembershipFunctionPointer = typename Superclass::Pointer;
/** Typedef alias for the measurement vectors */
using MeasurementVectorType = TMeasurementVector;
/** Length of each measurement vector */
using typename Superclass::MeasurementVectorSizeType;
/** Type of the mean vector. RealType on a vector-type is the same
* vector-type but with a real element type. */
using MeasurementVectorRealType = typename itk::NumericTraits<MeasurementVectorType>::RealType;
using MeanVectorType = MeasurementVectorRealType;
/** Type of the covariance matrix */
using CovarianceMatrixType = VariableSizeMatrix<double>;
/** Set the mean of the Gaussian distribution. Mean is a vector type
* similar to the measurement type but with a real element type. */
void
SetMean(const MeanVectorType & mean);
/** Get the mean of the Gaussian distribution. Mean is a vector type
* similar to the measurement type but with a real element type. */
itkGetConstReferenceMacro(Mean, MeanVectorType);
/** Set the covariance matrix. Covariance matrix is a
* VariableSizeMatrix of doubles. The inverse of the covariance
* matrix and the normalization term for the multivariate Gaussian
* are calculated whenever the covariance matrix is changed. */
void
SetCovariance(const CovarianceMatrixType & cov);
/* Get the covariance matrix. Covariance matrix is a
VariableSizeMatrix of doubles. */
itkGetConstReferenceMacro(Covariance, CovarianceMatrixType);
/* Get the inverse covariance matrix. Covariance matrix is a
VariableSizeMatrix of doubles. */
itkGetConstReferenceMacro(InverseCovariance, CovarianceMatrixType);
/** Evaluate the probability density of a measurement vector. */
double
Evaluate(const MeasurementVectorType & measurement) const override;
/** Method to clone a membership function, i.e. create a new instance of
* the same type of membership function and configure its ivars to
* match. */
typename LightObject::Pointer
InternalClone() const override;
protected:
GaussianMembershipFunction();
~GaussianMembershipFunction() override = default;
void
PrintSelf(std::ostream & os, Indent indent) const override;
private:
MeanVectorType m_Mean{}; // mean
CovarianceMatrixType m_Covariance{}; // covariance matrix
// inverse covariance matrix. automatically calculated
// when covariance matrix is set.
CovarianceMatrixType m_InverseCovariance{};
// pre_factor (normalization term). automatically calculated
// when covariance matrix is set.
double m_PreFactor{};
/** Boolean to cache whether the covariance is singular or nearly singular */
bool m_CovarianceNonsingular{};
};
} // end of namespace Statistics
} // end namespace itk
#ifndef ITK_MANUAL_INSTANTIATION
# include "itkGaussianMembershipFunction.hxx"
#endif
#endif
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