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/*=========================================================================
Program: Insight Segmentation & Registration Toolkit
Module: itkCurvatureNDAnisotropicDiffusionFunction.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 __itkCurvatureNDAnisotropicDiffusionFunction_txx
#define __itkCurvatureNDAnisotropicDiffusionFunction_txx
namespace itk {
template<class TImage>
double CurvatureNDAnisotropicDiffusionFunction<TImage>
::m_MIN_NORM = 1.0e-10;
template<class TImage>
CurvatureNDAnisotropicDiffusionFunction<TImage>
::CurvatureNDAnisotropicDiffusionFunction()
{
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);
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 relevant, will be applied in a slice-based
// fashion.
dx_op.SetOrder(1);
dx_op.CreateDirectional();
}
template<class TImage>
typename CurvatureNDAnisotropicDiffusionFunction<TImage>::PixelType
CurvatureNDAnisotropicDiffusionFunction<TImage>
::ComputeUpdate(const NeighborhoodType &it, void *itkNotUsed(globalData),
const FloatOffsetType& itkNotUsed(offset))
{
unsigned int i, j;
double speed, dx_forward_Cn, dx_backward_Cn, propagation_gradient;
double grad_mag_sq, grad_mag_sq_d, grad_mag, grad_mag_d;
double Cx, Cxd;
double dx_forward[ImageDimension];
double dx_backward[ImageDimension];
double dx[ImageDimension];
double dx_aug;
double dx_dim;
// Calculate the partial derivatives for each dimension
for (i = 0; i < ImageDimension; i++)
{
// ``Half'' derivatives
dx_forward[i] = it.GetPixel(m_Center + m_Stride[i])
- it.GetPixel(m_Center);
dx_forward[i] *= this->m_ScaleCoefficients[i];
dx_backward[i] = it.GetPixel(m_Center)
- it.GetPixel(m_Center - m_Stride[i]);
dx_backward[i] *= this->m_ScaleCoefficients[i];
// Centralized differences
dx[i] = m_InnerProduct(x_slice[i], it, dx_op);
dx[i] *= this->m_ScaleCoefficients[i];
}
speed = 0.0;
for (i = 0; i < ImageDimension; i++)
{
// Gradient magnitude approximations
grad_mag_sq = dx_forward[i] * dx_forward[i];
grad_mag_sq_d = dx_backward[i] * dx_backward[i];
for (j = 0; j < ImageDimension; j++)
{
if (j != i)
{
dx_aug = m_InnerProduct(xa_slice[j][i], it, dx_op);
dx_aug *= this->m_ScaleCoefficients[j];
dx_dim = m_InnerProduct(xd_slice[j][i], it, dx_op);
dx_dim *= this->m_ScaleCoefficients[j];
grad_mag_sq += 0.25f * (dx[j]+dx_aug) * (dx[j]+dx_aug);
grad_mag_sq_d += 0.25f * (dx[j]+dx_dim) * (dx[j]+dx_dim);
}
}
grad_mag = vcl_sqrt(m_MIN_NORM + grad_mag_sq);
grad_mag_d = vcl_sqrt(m_MIN_NORM + grad_mag_sq_d);
// Conductance Terms
if (m_K == 0.0)
{
Cx = 0.0;
Cxd = 0.0;
}
else
{
Cx = vcl_exp( grad_mag_sq / m_K );
Cxd = vcl_exp( grad_mag_sq_d / m_K );
}
// First order normalized finite-difference conductance products
dx_forward_Cn = (dx_forward[i] / grad_mag) * Cx;
dx_backward_Cn = (dx_backward[i] / grad_mag_d) * Cxd;
// Second order conductance-modified curvature
speed += (dx_forward_Cn - dx_backward_Cn);
}
// ``Upwind'' gradient magnitude term
propagation_gradient = 0.0;
if (speed > 0)
{
for (i = 0; i < ImageDimension; i++)
{
propagation_gradient +=
vnl_math_sqr( vnl_math_min(dx_backward[i], 0.0) )
+ vnl_math_sqr( vnl_math_max(dx_forward[i], 0.0) );
}
}
else
{
for (i = 0; i < ImageDimension; i++)
{
propagation_gradient +=
vnl_math_sqr( vnl_math_max(dx_backward[i], 0.0) )
+ vnl_math_sqr( vnl_math_min(dx_forward[i], 0.0) );
}
}
return static_cast<PixelType>( vcl_sqrt(propagation_gradient) * speed );
}
} // end namespace itk
#endif
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