File: itkCoxDeBoorBSplineKernelFunction.h

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/*=========================================================================

  Program:   Insight Segmentation & Registration Toolkit
  Module:    $RCSfile: itkCoxDeBoorBSplineKernelFunction.h,v $
  Language:  C++
  Date:      $Date: 2008/10/24 12:52:08 $
  Version:   $Revision: 1.1 $

  Copyright (c) Insight Software Consortium. All rights reserved.
  See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
     PURPOSE.  See the above copyright notices for more information.

=========================================================================*/
#ifndef __itkCoxDeBoorBSplineKernelFunction_h
#define __itkCoxDeBoorBSplineKernelFunction_h

#include "itkKernelFunction.h"
#include "vnl/vnl_math.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 KernelFunction 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
 *
 * Contributed by Nicholas J. Tustison, James C. Gee
 * in the Insight Journal paper:
 * http://hdl.handle.net/1926/140
 *
 *
 * \sa KernelFunction
 *
 * \ingroup Functions
 */
template <unsigned int VSplineOrder = 3>
class ITK_EXPORT CoxDeBoorBSplineKernelFunction
: public KernelFunction
{
public:
  /** Standard class typedefs. */
  typedef CoxDeBoorBSplineKernelFunction        Self;
  typedef KernelFunction                        Superclass;
  typedef SmartPointer<Self>                    Pointer;
  typedef SmartPointer<const Self>              ConstPointer;

  /** Method for creation through the object factory. */
  itkNewMacro(Self);

  /** Run-time type information (and related methods). */
  itkTypeMacro( CoxDeBoorBSplineKernelFunction, KernelFunction );

  typedef double                                RealType;
  typedef vnl_vector<RealType>                  VectorType;
  typedef vnl_real_polynomial                   PolynomialType;
  typedef vnl_matrix<RealType>                  MatrixType;

  /** Get/Sets the Spline Order */
  void SetSplineOrder( unsigned int );
  itkGetMacro( SplineOrder, unsigned int );

  /** Evaluate the function. */
  inline RealType Evaluate( const RealType & u ) const
    {
    RealType absValue = vnl_math_abs( u );
    unsigned int which;
    if ( this->m_SplineOrder % 2 == 0 )
      {
      which = static_cast<unsigned int>( absValue+0.5 );
      }
    else
      {
      which = static_cast<unsigned int>( absValue );
      }
    if ( which < this->m_BSplineShapeFunctions.rows() )
      {
      return PolynomialType(
        this->m_BSplineShapeFunctions.get_row( which ) ).evaluate( absValue );
      }
    else
      {
      return NumericTraits<RealType>::Zero;
      }
    }

  /** Evaluate the derivative. */
  inline RealType EvaluateDerivative( const double & u ) const
    {
    RealType absValue = vnl_math_abs( u );
    unsigned int which;
    if ( this->m_SplineOrder % 2 == 0 )
      {
      which = static_cast<unsigned int>( absValue+0.5 );
      }
    else
      {
      which = static_cast<unsigned int>( absValue );
      }
    if( which < static_cast<unsigned int>( this->m_BSplineShapeFunctions.rows() ) )
      {
      RealType der = PolynomialType(
        this->m_BSplineShapeFunctions.get_row( which ) ).devaluate( absValue );
      if ( u < NumericTraits<RealType>::Zero )
        {
        return -der;
         }
      else
        {
         return der;
         }
      }
    else
      {
      return NumericTraits<RealType>::Zero;
      }
    }

  /**
   * For a specific order, return the (this->m_SplineOrder+1) pieces of
   * the single basis function centered at zero.
   */
  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();
  ~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( 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( unsigned short, VectorType, unsigned int, unsigned int );

  MatrixType    m_BSplineShapeFunctions;
  unsigned int  m_SplineOrder;

};

} // end namespace itk

#ifndef ITK_MANUAL_INSTANTIATION
#include "itkCoxDeBoorBSplineKernelFunction.txx"
#endif

#endif