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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 itkDiffusionTensor3D_hxx
#define itkDiffusionTensor3D_hxx
#include "itkNumericTraits.h"
namespace itk
{
template <typename T>
DiffusionTensor3D<T>::DiffusionTensor3D(const Superclass & r)
: SymmetricSecondRankTensor<T, 3>(r)
{}
template <typename T>
DiffusionTensor3D<T>::DiffusionTensor3D(const ComponentType & r)
: SymmetricSecondRankTensor<T, 3>(r)
{}
template <typename T>
DiffusionTensor3D<T>::DiffusionTensor3D(const ComponentArrayType r)
: SymmetricSecondRankTensor<T, 3>(r)
{}
template <typename T>
DiffusionTensor3D<T> &
DiffusionTensor3D<T>::operator=(const ComponentType & r)
{
Superclass::operator=(r);
return *this;
}
template <typename T>
DiffusionTensor3D<T> &
DiffusionTensor3D<T>::operator=(const ComponentArrayType r)
{
Superclass::operator=(r);
return *this;
}
template <typename T>
DiffusionTensor3D<T> &
DiffusionTensor3D<T>::operator=(const Superclass & r)
{
Superclass::operator=(r);
return *this;
}
template <typename T>
auto
DiffusionTensor3D<T>::GetTrace() const -> AccumulateValueType
{
AccumulateValueType trace = (*this)[0];
trace += (*this)[3];
trace += (*this)[5];
return trace;
}
template <typename T>
auto
DiffusionTensor3D<T>::GetFractionalAnisotropy() const -> RealValueType
{
// Computed as
// FA = std::sqrt(1.5*sum(sum(N.*N))/sum((sum(D.*D))))
// where N = D - ((1/3)*trace(D)*eye(3,3))
// equation (28) in
// http://lmi.bwh.harvard.edu/papers/pdfs/2002/westinMEDIA02.pdf
const RealValueType isp = this->GetInnerScalarProduct();
if (isp > 0.0)
{
const RealValueType trace = this->GetTrace();
const RealValueType anisotropy = 3.0 * isp - trace * trace;
// sometimes anisotropy has been reported to be a small negative
// number, and then std::sqrt returns NaN. If it is a small
// negative number, the obvious thing is to round to zero. If
// it is a larger negative number, I'm not sure what the proper
// result would be. In either case, returning zero makes as much
// sense in those cases as any other number.
if (anisotropy > 0.0)
{
const auto fractionalAnisotropy = static_cast<RealValueType>(std::sqrt(anisotropy / (2.0 * isp)));
return fractionalAnisotropy;
}
}
return 0.0;
}
template <typename T>
auto
DiffusionTensor3D<T>::GetRelativeAnisotropy() const -> RealValueType
{
const RealValueType trace = this->GetTrace();
const RealValueType isp = this->GetInnerScalarProduct();
// Avoid negative trace and traces small enough to look like a division by
// zero.
if (trace < NumericTraits<RealValueType>::min())
{
return RealValueType{};
}
const RealValueType anisotropy = 3.0 * isp - trace * trace;
if (anisotropy < RealValueType{})
{
return RealValueType{};
}
const auto relativeAnisotropySquared = static_cast<RealValueType>(anisotropy / (std::sqrt(3.0) * trace));
const auto relativeAnisotropy = static_cast<RealValueType>(std::sqrt(relativeAnisotropySquared));
return relativeAnisotropy;
}
template <typename T>
auto
DiffusionTensor3D<T>::GetInnerScalarProduct() const -> RealValueType
{
const RealValueType xx = (*this)[0];
const RealValueType xy = (*this)[1];
const RealValueType xz = (*this)[2];
const RealValueType yy = (*this)[3];
const RealValueType yz = (*this)[4];
const RealValueType zz = (*this)[5];
return (xx * xx + yy * yy + zz * zz + 2.0 * (xy * xy + xz * xz + yz * yz));
}
} // end namespace itk
#endif
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