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/*=========================================================================
*
* Copyright NumFOCUS
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* https://www.apache.org/licenses/LICENSE-2.0.txt
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*=========================================================================*/
#ifndef itkCurvatureFlowFunction_hxx
#define itkCurvatureFlowFunction_hxx
#include "itkMath.h"
namespace itk
{
template <typename 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;
}
template <typename TImage>
auto
CurvatureFlowFunction<TImage>::ComputeGlobalTimeStep(void * itkNotUsed(gd)) const -> TimeStepType
{
return this->GetTimeStep();
}
template <typename TImage>
auto
CurvatureFlowFunction<TImage>::ComputeUpdate(const NeighborhoodType & it,
void * itkNotUsed(gd),
const FloatOffsetType & itkNotUsed(offset)) -> PixelType
{
PixelRealType firstderiv[ImageDimension];
PixelRealType secderiv[ImageDimension];
PixelRealType crossderiv[ImageDimension][ImageDimension] = {};
IdentifierType center;
IdentifierType 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((IdentifierType)i);
}
PixelRealType 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])) *
itk::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];
}
// accumulate the gradient magnitude squared
magnitudeSqr += itk::Math::sqr(static_cast<double>(firstderiv[i]));
}
if (magnitudeSqr < 1e-9)
{
return PixelType{};
}
// compute the update value = mean curvature * magnitude
PixelRealType update = 0.0;
PixelRealType 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 * itk::Math::sqr(static_cast<double>(firstderiv[i]));
}
// accumulate -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;
return static_cast<PixelType>(update);
}
} // end namespace itk
#endif
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