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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 itkCumulativeGaussianCostFunction_h
#define itkCumulativeGaussianCostFunction_h
#include "itkMultipleValuedCostFunction.h"
#include "ITKOptimizersExport.h"
namespace itk
{
/** \class CumulativeGaussianCostFunction
* \brief Cost function for the Cumulative Gaussian Optimizer.
*
* The Cumulative Gaussian is defined as the integral of
* a normalized Gaussian over the domain \f$ [-\infty, \infty] \f$.
*
* \par Let G(x) be the normalized Gaussian defined as
* \f$ G(x) = \frac{1}{{\sigma \sqrt {2\pi } }}e^{ - \frac{{\left( {x -
* \mu } \right)^2 }}{{2\sigma ^2 }}} \f$.
* The Cumulative Gaussian, is acquired by integrating G(x) then scaling and
* offsetting it by the lower asymptotes \f$ I_1 \f$ and upper \f$ I_2 \f$:
* \f$ C\left( x \right) = I_1 + \frac{{I_2 - I_1 }}{2}\left( {1 +
* erf\left( {\frac{{x - \mu }}{{\sigma \sqrt 2 }}} \right)} \right) \f$, where
* \f$ C\left( { - \infty } \right) = I_1 \f$ and
* \f$ C\left( \infty \right) = I_2 \f$.
*
* \par C(x) can only be tabulated since it's a variation of the
* error function. It is included in this class
* as the function EvaluateCumulativeGaussian, where the argument
* of the function is \f$ {\frac{{x - \mu }}{{\sigma \sqrt 2 }}} \f$.
*
* \ingroup Numerics Cost Functions
* \ingroup ITKOptimizers
*/
class ITKOptimizers_EXPORT CumulativeGaussianCostFunction : public MultipleValuedCostFunction
{
public:
/** Standard type alias. */
using Self = CumulativeGaussianCostFunction;
using Superclass = MultipleValuedCostFunction;
using Pointer = SmartPointer<Self>;
using ConstPointer = SmartPointer<const Self>;
/** \see LightObject::GetNameOfClass() */
itkOverrideGetNameOfClassMacro(CumulativeGaussianCostFunction);
/** Method for creation through the object factory. */
itkNewMacro(Self);
/** Array Typedefs. */
using ParametersType = Superclass::ParametersType;
using MeasureType = Superclass::MeasureType;
using DerivativeType = Superclass::DerivativeType;
/** The dimensions of parameter space; mean, standard deviation, lower and
upper asymptotes. */
enum
{
SpaceDimension = 4
};
/** Not necessary for this optimizer. */
void
GetDerivative(const ParametersType & itkNotUsed(parameters), DerivativeType & itkNotUsed(derivative)) const override
{}
/** Return the values evaluated for the given parameters. */
MeasureType
GetValue(const ParametersType & parameters) const override;
/** Return a pointer of values evaluated for the given parameters. */
MeasureType *
GetValuePointer(ParametersType & parameters);
/** Calculate a fit error between the data and the fit curve. */
double
CalculateFitError(MeasureType * setTestArray);
/** Given the argument of a Cumulative Gaussian, return its value. */
double
EvaluateCumulativeGaussian(double argument) const;
/** Get the SpaceDimension. */
unsigned int
GetNumberOfParameters() const override;
/** Get the number Range Dimension. */
unsigned int
GetNumberOfValues() const override;
/** Initialize the arrays. */
void
Initialize(unsigned int rangeDimension);
/** Set the original data array. */
void
SetOriginalDataArray(MeasureType * setOriginalDataArray);
protected:
CumulativeGaussianCostFunction();
~CumulativeGaussianCostFunction() override;
void
PrintSelf(std::ostream & os, Indent indent) const override;
private:
/** The original data array. */
MeasureType m_OriginalDataArray{};
/** Number of data samples. */
unsigned int m_RangeDimension{ 0 };
/** Different arrays. */
mutable MeasureType m_Measure{};
mutable MeasureType m_MeasurePointer{};
mutable ParametersType m_Parameters{};
};
} // end namespace itk
#endif
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