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

  Program:   Insight Segmentation & Registration Toolkit
  Module:    $RCSfile: itkKernelTransform.h,v $
  Language:  C++
  Date:      $Date: 2005/10/25 03:08:29 $
  Version:   $Revision: 1.39 $

  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 __itkKernelTransform_h
#define __itkKernelTransform_h

#include "itkTransform.h"
#include "itkPoint.h"
#include "itkVector.h"
#include "itkMatrix.h"
#include "itkPointSet.h"
#include <deque>
#include <math.h>
#include "vnl/vnl_matrix_fixed.h"
#include "vnl/vnl_matrix.h"
#include "vnl/vnl_vector.h"
#include "vnl/vnl_vector_fixed.h"
#include "vnl/algo/vnl_svd.h"
#include "vnl/vnl_sample.h"

namespace itk
{

/** \class KernelTransform
 * Intended to be a base class for elastic body spline and thin plate spline.
 * This is implemented in as straightforward a manner as possible from the
 * IEEE TMI paper by Davis, Khotanzad, Flamig, and Harms, Vol. 16,
 * No. 3 June 1997. Notation closely follows their paper, so if you have it
 * in front of you, this code will make a lot more sense.
 *
 * KernelTransform:
 *  Provides support for defining source and target landmarks
 *  Defines a number of data types used in the computations
 *  Defines the mathematical framework used to compute all splines,
 *    so that subclasses need only provide a kernel specific to
 *    that spline
 *
 * This formulation allows the stiffness of the spline to
 * be adjusted, allowing the spline to vary from interpolating the
 * landmarks to approximating the landmarks.  This part of the
 * formulation is based on the short paper by R. Sprengel, K. Rohr,
 * H. Stiehl. "Thin-Plate Spline Approximation for Image
 * Registration". In 18th International Conference of the IEEE
 * Engineering in Medicine and Biology Society. 1996.
 *
 * \ingroup Transforms
 *
 */
template <class TScalarType, // probably only float and double make sense here
          unsigned int NDimensions>   // Number of dimensions
class ITK_EXPORT KernelTransform : 
                    public Transform<TScalarType, NDimensions,NDimensions>
{
public:
  /** Standard class typedefs. */
  typedef KernelTransform Self;
  typedef Transform<TScalarType, NDimensions, NDimensions >   Superclass;
  typedef SmartPointer<Self>        Pointer;
  typedef SmartPointer<const Self>  ConstPointer;
  
  /** Run-time type information (and related methods). */
  itkTypeMacro( KernelTransform, Transform );

  /** New macro for creation of through a Smart Pointer */
  itkNewMacro( Self );

  /** Dimension of the domain space. */
  itkStaticConstMacro(SpaceDimension, unsigned int, NDimensions);

  /** Scalar type. */
  typedef typename Superclass::ScalarType  ScalarType;

  /** Parameters type. */
  typedef typename Superclass::ParametersType  ParametersType;

  /** Jacobian type. */
  typedef typename Superclass::JacobianType  JacobianType;

  /** Standard coordinate point type for this class. */
  typedef typename Superclass::InputPointType   InputPointType;
  typedef typename Superclass::OutputPointType  OutputPointType;
  
  /** Standard vector type for this class. */
  typedef typename Superclass::InputVectorType   InputVectorType;
  typedef typename Superclass::OutputVectorType  OutputVectorType;
  
  /** PointList typedef. This type is used for maintaining lists of points,
   * specifically, the source and target landmark lists. */
  typedef DefaultStaticMeshTraits<TScalarType,
                                  NDimensions,
                                  NDimensions,
                                  TScalarType,
                                  TScalarType> PointSetTraitsType;
  typedef PointSet<InputPointType, NDimensions, PointSetTraitsType> PointSetType;
  typedef typename PointSetType::Pointer                        PointSetPointer;
  typedef typename PointSetType::PointsContainer                PointsContainer;
  typedef typename PointSetType::PointsContainerIterator        PointsIterator;
  typedef typename PointSetType::PointsContainerConstIterator   PointsConstIterator;
    
  /** VectorSet typedef. */
  typedef itk::VectorContainer<unsigned long,InputVectorType> VectorSetType;
  typedef typename VectorSetType::Pointer        VectorSetPointer;
  
  /** Get the source landmarks list, which we will denote \f$ p \f$. */
  itkGetObjectMacro( SourceLandmarks, PointSetType);
  
  /** Set the source landmarks list. */
  virtual void SetSourceLandmarks(PointSetType *);
  
  /** Get the target landmarks list, which we will denote  \f$ q \f$. */
  itkGetObjectMacro( TargetLandmarks, PointSetType);
  
  /** Set the target landmarks list. */
  virtual void SetTargetLandmarks(PointSetType *);
  
  /** Get the displacements list, which we will denote \f$ d \f$,
   * where \f$ d_i = q_i - p_i \f$. */
  itkGetObjectMacro( Displacements, VectorSetType );
  
  /** Compute W matrix. */
  void ComputeWMatrix(void);
  
  /** Compute the position of point in the new space */
  virtual OutputPointType TransformPoint(const InputPointType& thisPoint) const;
  
  /** 'I' (identity) matrix typedef. */
  typedef vnl_matrix_fixed<TScalarType, NDimensions, NDimensions> IMatrixType;


  /** Compute the Jacobian Matrix of the transformation at one point */
  virtual const JacobianType & GetJacobian(const InputPointType  &point ) const;

  /** Set the Transformation Parameters and update the internal transformation. 
   * The parameters represent the source landmarks. Each landmark point is represented
   * by NDimensions doubles. All the landmarks are concatenated to form one flat
   * Array<double>. */
  virtual void SetParameters(const ParametersType &);
  
  /** Set Transform Fixed Parameters:
   *     To support the transform file writer this function was 
   *     added to set the target landmarks similar to the
   *     SetParameters function setting the source landmarks
   */
  virtual void SetFixedParameters(const ParametersType &);

  /** Update the Parameters array from the landmarks corrdinates. */
  virtual void UpdateParameters(void) const;

  /** Get the Transformation Parameters - Gets the Source Landmarks */
  virtual const ParametersType& GetParameters(void) const;
  
  /** Get Transform Fixed Parameters - Gets the Target Landmarks */
  virtual const ParametersType& GetFixedParameters(void) const;

  /** Stiffness of the spline.  A stiffness of zero results in the
   * standard interpolating spline.  A non-zero stiffness allows the
   * spline to approximate rather than interpolate the landmarks.
   * Stiffness values are usually rather small, typically in the range
   * of 0.001 to 0.1. The approximating spline formulation is based on
   * the short paper by R. Sprengel, K. Rohr, H. Stiehl. "Thin-Plate
   * Spline Approximation for Image Registration". In 18th
   * International Conference of the IEEE Engineering in Medicine and
   * Biology Society. 1996.
   */
  itkSetClampMacro(Stiffness, double, 0.0, NumericTraits<double>::max());
  itkGetMacro(Stiffness, double);


protected:
  KernelTransform();
  virtual ~KernelTransform();
  void PrintSelf(std::ostream& os, Indent indent) const;

public:  
  /** 'G' matrix typedef. */
  typedef vnl_matrix_fixed<TScalarType, NDimensions, NDimensions> GMatrixType;
  
  /** 'L' matrix typedef. */
  typedef vnl_matrix<TScalarType> LMatrixType;
  
  /** 'K' matrix typedef. */
  typedef vnl_matrix<TScalarType> KMatrixType;
  
  /** 'P' matrix typedef. */
  typedef vnl_matrix<TScalarType> PMatrixType;
  
  /** 'Y' matrix typedef. */
  typedef vnl_matrix<TScalarType> YMatrixType;

  /** 'W' matrix typedef. */
  typedef vnl_matrix<TScalarType> WMatrixType;
  
  /** 'D' matrix typedef. Deformation component */
  typedef vnl_matrix<TScalarType> DMatrixType;
  
  /** 'A' matrix typedef. Rotational part of the Affine component */
  typedef vnl_matrix_fixed<TScalarType,NDimensions,NDimensions> AMatrixType;
  
  /** 'B' matrix typedef. Translational part of the Affine component */
  typedef vnl_vector_fixed<TScalarType,NDimensions> BMatrixType;
  
  /** Row matrix typedef. */
  typedef vnl_matrix_fixed<TScalarType, 1, NDimensions> RowMatrixType;
  
  /** Column matrix typedef. */
  typedef vnl_matrix_fixed<TScalarType, NDimensions, 1> ColumnMatrixType;

  /** The list of source landmarks, denoted 'p'. */
  PointSetPointer m_SourceLandmarks;
  
  /** The list of target landmarks, denoted 'q'. */
  PointSetPointer m_TargetLandmarks;
  
protected:
  /** Compute G(x)
   * This is essentially the kernel of the transform.
   * By overriding this method, we can obtain (among others):
   *    Elastic body spline
   *    Thin plate spline
   *    Volume spline */
  virtual const GMatrixType & ComputeG(const InputVectorType & landmarkVector) const;

  /** Compute a G(x) for a point to itself (i.e. for the block
   * diagonal elements of the matrix K. Parameter indicates for which
   * landmark the reflexive G is to be computed. The default
   * implementation for the reflexive contribution is a diagonal
   * matrix where the diagonal elements are the stiffness of the
   * spline. */
  virtual const GMatrixType & ComputeReflexiveG(PointsIterator) const;

  
  /** Compute the contribution of the landmarks weighted by the kernel funcion
      to the global deformation of the space  */
  virtual void ComputeDeformationContribution( const InputPointType & inputPoint,
                                                     OutputPointType & result ) const;

  /** Compute K matrix. */
  void ComputeK();
  
  /** Compute L matrix. */
  void ComputeL();
  
  /** Compute P matrix. */
  void ComputeP();
  
  /** Compute Y matrix. */
  void ComputeY();
  
  /** Compute displacements \f$ q_i - p_i \f$. */
  void ComputeD();

  /** Reorganize the components of W into 
    D (deformable), A (rotation part of affine) 
    and B (translational part of affine ) components.
    \warning This method release the memory of the W Matrix  */
  void ReorganizeW(void);

  /** Stiffness parameter */
  double m_Stiffness;

  /** The list of displacements.
   * d[i] = q[i] - p[i]; */
  VectorSetPointer m_Displacements;

  /** The L matrix. */
  LMatrixType m_LMatrix;

  /** The K matrix. */
  KMatrixType m_KMatrix;

  /** The P matrix. */
  PMatrixType m_PMatrix;

  /** The Y matrix. */
  YMatrixType m_YMatrix;
  
  /** The W matrix. */
  WMatrixType m_WMatrix;

  /** The Deformation matrix.
      This is an auxiliary matrix that will hold the
      Deformation (non-affine) part of the transform.
      Those are the coefficients that will multiply the
      Kernel function */
  DMatrixType m_DMatrix;

  /** Rotatinoal/Shearing part of the Affine component of the Transformation */
  AMatrixType m_AMatrix;

  /** Translational part of the Affine component of the Transformation */
  BMatrixType m_BVector;

  /** The G matrix. 
    It is made mutable because m_GMatrix was made an ivar
    only to avoid copying the matrix at return time */
  mutable GMatrixType m_GMatrix;

  /** Has the W matrix been computed? */
  bool m_WMatrixComputed;

  /** Identity matrix. */
  IMatrixType m_I;

 private:
  KernelTransform(const Self&); //purposely not implemented
  void operator=(const Self&); //purposely not implemented

};

} // end namespace itk

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

#endif // __itkKernelTransform_h
