/usr/include/ITK-4.5/itkCoxDeBoorBSplineKernelFunction.h is in libinsighttoolkit4-dev 4.5.0-3.
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*
* Copyright Insight Software Consortium
*
* 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
*
* http://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 __itkCoxDeBoorBSplineKernelFunction_h
#define __itkCoxDeBoorBSplineKernelFunction_h
#include "itkKernelFunctionBase.h"
#include "vnl/vnl_real_polynomial.h"
#include "vnl/vnl_matrix.h"
namespace itk
{
/** \class CoxDeBoorBSplineKernelFunction
* \brief BSpline kernel used for density estimation and nonparameteric
* regression.
*
* This class enscapsulates BSpline kernel for
* density estimation or nonparameteric regression.
* See documentation for KernelFunctionBase for more details.
*
* This class is templated over the spline order to cohere with
* the previous incarnation of this class. One can change the
* order during an instantiation's existence. Note that
* other authors have defined the B-spline order as being the
* degree of spline + 1. In the ITK context (e.g. in this
* class), the spline order is equivalent to the degree of
* the spline.
*
* \author Nicholas J. Tustison
*
* This code was contributed in the Insight Journal paper:
* "N-D C^k B-Spline Scattered Data Approximation"
* by Nicholas J. Tustison, James C. Gee
* http://hdl.handle.net/1926/140
* http://www.insight-journal.org/browse/publication/57
*
*
* \sa KernelFunctionBase
*
* \ingroup ITKImageGrid
*/
template<unsigned int VSplineOrder = 3, typename TRealValueType = double>
class CoxDeBoorBSplineKernelFunction:
public KernelFunctionBase<TRealValueType>
{
public:
/** Standard class typedefs. */
typedef CoxDeBoorBSplineKernelFunction Self;
typedef KernelFunctionBase<TRealValueType> Superclass;
typedef SmartPointer<Self> Pointer;
typedef SmartPointer<const Self> ConstPointer;
typedef typename Superclass::RealType RealType;
/** Method for creation through the object factory. */
itkNewMacro( Self );
/** Run-time type information (and related methods). */
itkTypeMacro( CoxDeBoorBSplineKernelFunction, KernelFunctionBase );
typedef vnl_vector<TRealValueType> VectorType;
typedef vnl_real_polynomial PolynomialType;
typedef vnl_matrix<TRealValueType> MatrixType;
/** Set the spline order. */
void SetSplineOrder( const unsigned int );
/** Get the spline order. */
itkGetConstMacro( SplineOrder, unsigned int );
/** Evaluate the function. */
TRealValueType Evaluate( const TRealValueType & ) const;
/** Evaluate the first derivative. */
TRealValueType EvaluateDerivative( const TRealValueType & ) const;
/** Evaluate the Nth derivative. */
TRealValueType EvaluateNthDerivative( const TRealValueType &, const unsigned int ) const;
/**
* For a specific order, return the ceil( 0.5*(m_SplineOrder+1) )
* pieces of the single basis function centered at zero for positive
* parametric values.
*/
MatrixType GetShapeFunctions();
/**
* For a specific order, generate and return the (this->m_SplineOrder+1)
* pieces of the different basis functions in the [0, 1] interval.
*/
MatrixType GetShapeFunctionsInZeroToOneInterval();
protected:
CoxDeBoorBSplineKernelFunction();
virtual ~CoxDeBoorBSplineKernelFunction();
void PrintSelf( std::ostream & os, Indent indent ) const;
private:
CoxDeBoorBSplineKernelFunction( const Self & ); //purposely not implemented
void operator=( const Self & ); //purposely not implemented
/**
* For a specific order, generate the (this->m_SplineOrder+1) pieces of
* the single basis function centered at zero.
*/
void GenerateBSplineShapeFunctions( const unsigned int );
/**
* Use the CoxDeBoor recursion relation to generate the piecewise
* polynomials which compose the basis function.
* See, for example, L. Piegl, L. Tiller, "The NURBS Book,"
* Springer 1997, p. 50.
*/
PolynomialType CoxDeBoor( const unsigned short, const VectorType,
const unsigned int, const unsigned int );
MatrixType m_BSplineShapeFunctions;
unsigned int m_SplineOrder;
};
} // end namespace itk
#ifndef ITK_MANUAL_INSTANTIATION
#include "itkCoxDeBoorBSplineKernelFunction.hxx"
#endif
#endif
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