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/*=========================================================================
Program: Insight Segmentation & Registration Toolkit
Module: itkVectorCurvatureNDAnisotropicDiffusionFunction.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 __itkVectorCurvatureNDAnisotropicDiffusionFunction_txx
#define __itkVectorCurvatureNDAnisotropicDiffusionFunction_txx
namespace itk {
template<class TImage>
double VectorCurvatureNDAnisotropicDiffusionFunction<TImage>
::m_MIN_NORM = 1.0e-10;
template<class TImage>
VectorCurvatureNDAnisotropicDiffusionFunction<TImage>
::VectorCurvatureNDAnisotropicDiffusionFunction()
{
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 VectorCurvatureNDAnisotropicDiffusionFunction<TImage>::PixelType
VectorCurvatureNDAnisotropicDiffusionFunction<TImage>
::ComputeUpdate(const NeighborhoodType &it, void *,
const FloatOffsetType&)
{
unsigned int i, j, k;
double speed;
double dx_forward_Cn[ImageDimension][VectorDimension];
double dx_backward_Cn[ImageDimension][VectorDimension];
double propagation_gradient;
double grad_mag_sq[VectorDimension];
double grad_mag_sq_d[VectorDimension];
double grad_mag[VectorDimension];
double grad_mag_d[VectorDimension];
double Cx[ImageDimension];
double Cxd[ImageDimension];
const ScalarValueType ScalarValueTypeZero = NumericTraits<ScalarValueType>::Zero;
PixelType dx_forward[ImageDimension];
PixelType dx_backward[ImageDimension];
PixelType dx[ImageDimension];
PixelType dx_aug;
PixelType dx_dim;
PixelType ans;
// 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] = dx_forward[i] * this->m_ScaleCoefficients[i];
dx_backward[i]= it.GetPixel(m_Center)
- it.GetPixel(m_Center - m_Stride[i]);
dx_backward[i] = dx_backward[i] * this->m_ScaleCoefficients[i];
// Centralized differences
dx[i] = m_InnerProduct(x_slice[i], it, dx_op);
dx[i] = dx[i] * this->m_ScaleCoefficients[i];
}
for (k = 0; k < VectorDimension; k++)
{
grad_mag_sq[k] = 0.0;
grad_mag_sq_d[k] = 0.0;
for (i = 0; i < ImageDimension; i++)
{
// Gradient magnitude approximations
grad_mag_sq[k] += dx_forward[i][k] * dx_forward[i][k];
grad_mag_sq_d[k] += dx_backward[i][k] * 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_aug = dx_aug * this->m_ScaleCoefficients[j];
dx_dim = m_InnerProduct(xd_slice[j][i],it, dx_op);
dx_dim = dx_dim * this->m_ScaleCoefficients[j];
grad_mag_sq[k] += 0.25f * (dx[j][k]+dx_aug[k]) * (dx[j][k]+dx_aug[k]);
grad_mag_sq_d[k] += 0.25f * (dx[j][k]+dx_dim[k]) * (dx[j][k]+dx_dim[k]);
}
}
}
grad_mag[k] = vcl_sqrt(m_MIN_NORM + grad_mag_sq[k]);
grad_mag_d[k] = vcl_sqrt(m_MIN_NORM + grad_mag_sq_d[k]);
// this grad mag should depend only on the current k
for (i = 0; i < ImageDimension; i++)
{
dx_forward_Cn[i][k] = dx_forward[i][k]/grad_mag[k];
dx_backward_Cn[i][k] = dx_backward[i][k]/grad_mag_d[k];
}
}
double grad_mag_sq_tmp = 0.0;
double grad_mag_sq_d_tmp = 0.0;
for (k = 0; k < VectorDimension; k++)
{
grad_mag_sq_tmp += grad_mag_sq[k];
grad_mag_sq_d_tmp += grad_mag_sq_d[k];
}
// this grad mag should depend on the sum over k's
// Conductance Terms
for (i = 0; i < ImageDimension; i++)
{
if (m_K == 0.0)
{
Cx[i] = 0.0;
Cxd[i] = 0.0;
}
else
{
Cx[i] = vcl_exp( grad_mag_sq_tmp / m_K );
Cxd[i] = vcl_exp( grad_mag_sq_d_tmp / m_K );
}
}
for (k = 0; k < VectorDimension; k++)
{
// First order normalized finite-difference conductance products
speed = 0.0;
for (i = 0; i < ImageDimension; i++)
{
dx_forward_Cn[i][k] *= Cx[i];
dx_backward_Cn[i][k] *= Cxd[i];
// Second order conductance-modified curvature
speed += (dx_forward_Cn[i][k] - dx_backward_Cn[i][k]);
}
// ``Upwind'' gradient magnitude term
propagation_gradient = 0.0;
if (speed > 0.0)
{
for (i = 0; i < ImageDimension; i++)
{
propagation_gradient +=
vnl_math_sqr( vnl_math_min(dx_backward[i][k], ScalarValueTypeZero) )
+ vnl_math_sqr( vnl_math_max(dx_forward[i][k], ScalarValueTypeZero) );
}
}
else
{
for (i = 0; i < ImageDimension; i++)
{
propagation_gradient +=
vnl_math_sqr( vnl_math_max(dx_backward[i][k], ScalarValueTypeZero) )
+ vnl_math_sqr( vnl_math_min(dx_forward[i][k], ScalarValueTypeZero) );
}
}
ans[k] = vcl_sqrt(propagation_gradient) * speed;
}
return ans;
}
} // end namespace itk
#endif
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