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itkCurvatureFlowFunction.txx
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itkCurvatureFlowFunction.txx
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/*=========================================================================
Program: Insight Segmentation & Registration Toolkit
Module: itkCurvatureFlowFunction.txx
Language: C++
Date: $Date$
Version: $Revision$
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 __itkCurvatureFlowFunction_txx
#define __itkCurvatureFlowFunction_txx
#include "itkCurvatureFlowFunction.h"
#include "vnl/vnl_math.h"
namespace itk {
/**
* Constructor
*/
template<class TImage>
CurvatureFlowFunction<TImage>
::CurvatureFlowFunction()
{
RadiusType r;
unsigned int j;
for( j = 0; j < ImageDimension; j++ )
{
r[j] = 1;
}
this->SetRadius(r);
m_TimeStep = 0.05f;
}
/**
* Compute the global time step
*/
template<class TImage>
typename CurvatureFlowFunction<TImage>::TimeStepType
CurvatureFlowFunction<TImage>
::ComputeGlobalTimeStep( void *itkNotUsed(gd) ) const
{
return this->GetTimeStep();
// \todo compute timestep based on CFL condition
#if 0
GlobalDataStruct *globalData = (GlobalDataStruct *)gd;
TimeStepType dt;
if ( globalData->m_MaxChange > 0.0 )
{
dt = 1.0 / globalData->m_MaxChange;
}
else
{
dt = 0.0;
}
return dt;
#endif
}
/**
* Update the solution at pixels which lies on the data boundary.
*/
template<class TImage>
typename CurvatureFlowFunction<TImage>::PixelType
CurvatureFlowFunction<TImage>
::ComputeUpdate(const NeighborhoodType &it, void * itkNotUsed(gd),
const FloatOffsetType& itkNotUsed(offset))
{
PixelType firstderiv[ImageDimension];
PixelType secderiv[ImageDimension];
PixelType crossderiv[ImageDimension][ImageDimension];
unsigned long center;
unsigned long stride[ImageDimension];
unsigned int i,j;
const NeighborhoodScalesType neighborhoodScales = this->ComputeNeighborhoodScales();
// get the center pixel position
center = it.Size() / 2;
// cache the stride for each dimension
for( i = 0; i < ImageDimension; i++ )
{
stride[i] = it.GetStride( (unsigned long) i );
}
PixelType magnitudeSqr = 0.0;
for( i = 0; i < ImageDimension; i++ )
{
// compute first order derivatives
firstderiv[i] = 0.5 * ( it.GetPixel(center + stride[i]) -
it.GetPixel(center - stride[i]) ) * neighborhoodScales[i];
// compute second order derivatives
secderiv[i] = ( it.GetPixel(center + stride[i]) -
2 * it.GetPixel(center) + it.GetPixel( center - stride[i] ) ) * vnl_math_sqr( neighborhoodScales[i] );
// compute cross derivatives
for( j = i + 1; j < ImageDimension; j++ )
{
crossderiv[i][j] = 0.25 * (
it.GetPixel( center - stride[i] - stride[j] )
- it.GetPixel( center - stride[i] + stride[j] )
- it.GetPixel( center + stride[i] - stride[j] )
+ it.GetPixel( center + stride[i] + stride[j] ) )
* neighborhoodScales[i] * neighborhoodScales[j];
}
// accumlate the gradient magnitude squared
magnitudeSqr += vnl_math_sqr( (double)firstderiv[i] );
}
if ( magnitudeSqr < 1e-9 )
{
return NumericTraits<PixelType>::Zero;
}
// compute the update value = mean curvature * magnitude
PixelType update = 0.0;
PixelType temp;
// accumulate dx^2 * (dyy + dzz) terms
for( i = 0; i < ImageDimension; i++ )
{
temp = 0.0;
for( j = 0; j < ImageDimension; j++ )
{
if( j == i ) continue;
temp += secderiv[j];
}
update += temp * vnl_math_sqr( (double)firstderiv[i] );
}
// accumlate -2 * dx * dy * dxy terms
for( i = 0; i < ImageDimension; i++ )
{
for( j = i + 1; j < ImageDimension; j++ )
{
update -= 2 * firstderiv[i] * firstderiv[j] *
crossderiv[i][j];
}
}
update /= magnitudeSqr;
// \todo compute timestep based on CFL condition
#if 0
GlobalDataStruct *globalData = (GlobalDataStruct *)gd;
globalData->m_MaxChange =
vnl_math_max( globalData->m_MaxChange, vnl_math_abs(update) );
#endif
return update;
}
} // end namespace itk
#endif