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

  Program:   Insight Segmentation & Registration Toolkit
  Module:    $RCSfile: itkVectorGradientNDAnisotropicDiffusionFunction.txx,v $
  Language:  C++
  Date:      $Date: 2003/09/10 14:28:59 $
  Version:   $Revision: 1.11 $

  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 __itkVectorGradientNDAnisotropicDiffusionFunction_txx_
#define __itkVectorGradientNDAnisotropicDiffusionFunction_txx_

namespace itk {

template<class TImage>
double VectorGradientNDAnisotropicDiffusionFunction<TImage>
::m_MIN_NORM = 1.0e-10;
  
template<class TImage>
VectorGradientNDAnisotropicDiffusionFunction<TImage>
::VectorGradientNDAnisotropicDiffusionFunction()
{
  unsigned int i, j;
  RadiusType r;

  for (i = 0; i < ImageDimension; ++i)
    {
    r[i] = 1;
    }
  this->SetRadius(r);

  // Dummy neighborhood used to set up the slices.
  Neighborhood<PixelType, ImageDimension> it;
  it.SetRadius(r);
  
  // Slice the neighborhood
  m_Center =  it.Size() / 2;

  for (i = 0; i< ImageDimension; ++i)
    { m_Stride[i] = it.GetStride(i); }

  for (i = 0; i< ImageDimension; ++i)
    { x_slice[i]  = std::slice( m_Center - m_Stride[i], 3, m_Stride[i]); }
  
  for (i = 0; i< ImageDimension; ++i)
    {
    for (j = 0; j < ImageDimension; ++j)
      {
      // For taking derivatives in the i direction that are offset one
      // pixel in the j direction.
      xa_slice[i][j]
        = std::slice((m_Center + m_Stride[j])-m_Stride[i], 3, m_Stride[i]); 
      xd_slice[i][j]
        = std::slice((m_Center - m_Stride[j])-m_Stride[i], 3, m_Stride[i]);
      }
    }
  
  // Allocate the derivative operator.
  dx_op.SetDirection(0); // Not relelevant, we'll apply in a slice-based
                         // fashion 
  dx_op.SetOrder(1);
  dx_op.CreateDirectional();
}

template<class TImage>
typename VectorGradientNDAnisotropicDiffusionFunction<TImage>::PixelType
VectorGradientNDAnisotropicDiffusionFunction<TImage>
::ComputeUpdate(const NeighborhoodType &it, void *,
                const FloatOffsetType&)
{
  unsigned int i, j, k;
  PixelType delta;

  double GradMag;
  double GradMag_d;
  double Cx[ImageDimension];
  double Cxd[ImageDimension];

  // Remember: PixelType is a Vector of length VectorDimension.
  PixelType dx_forward[ImageDimension];
  PixelType dx_backward[ImageDimension];
  PixelType dx[ImageDimension];
  PixelType dx_aug;
  PixelType dx_dim;

  // Calculate the directional and centralized derivatives.
  for (i = 0; i < ImageDimension; i++)
    {
    dx_forward[i] = it.GetPixel(m_Center + m_Stride[i])
      - it.GetPixel(m_Center);
    dx_backward[i]=  it.GetPixel(m_Center)
      - it.GetPixel(m_Center - m_Stride[i]);
    dx[i]      = m_InnerProduct(x_slice[i], it, dx_op);
    }

  // Calculate the conductance term for each dimension.
  for (i = 0; i < ImageDimension; i++)
    {
    // Calculate gradient magnitude approximation in this
    // dimension linked (summed) across the vector components.
    GradMag   = 0.0;
    GradMag_d = 0.0;
    for (k =0; k < VectorDimension; k++)
      {
      GradMag   +=  vnl_math_sqr( dx_forward[i][k] );
      GradMag_d +=  vnl_math_sqr( dx_backward[i][k] );

      for (j = 0; j < ImageDimension; j++)
        {
        if ( j != i)
          {
          dx_aug  = m_InnerProduct(xa_slice[j][i], it, dx_op);
          dx_dim  = m_InnerProduct(xd_slice[j][i], it, dx_op);
          GradMag   += 0.25f * vnl_math_sqr( dx[j][k]+dx_aug[k] );
          GradMag_d += 0.25f * vnl_math_sqr( dx[j][k]+dx_dim[k] );
          }
        }
      }
      
    if (m_K == 0.0)
      {       
      Cx[i] = 0.0;
      Cxd[i] = 0.0;
      }
    else
      {
      Cx[i]  = ::exp( GradMag   / m_K );
      Cxd[i] = ::exp( GradMag_d / m_K ); 
      }
    }

  // Compute update value  
  for (k = 0; k < VectorDimension; k++)
    {
    delta[k] = NumericTraits<ScalarValueType>::Zero;
      
    for (i = 0; i < ImageDimension; ++i)
      {
      dx_forward[i][k]  *= Cx[i];
      dx_backward[i][k] *= Cxd[i];
      delta[k] += dx_forward[i][k] - dx_backward[i][k];
      }
    }
      
  return delta;
}

} // end namespace itk

#endif
