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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 itkComposeScaleSkewVersor3DTransform_hxx
#define itkComposeScaleSkewVersor3DTransform_hxx
#include "itkMath.h"
#include "vnl/vnl_inverse.h"
namespace itk
{
// Constructor with default arguments
template <typename TParametersValueType>
ComposeScaleSkewVersor3DTransform<TParametersValueType>::ComposeScaleSkewVersor3DTransform()
: Superclass(ParametersDimension)
{
m_Scale.Fill(NumericTraits<TParametersValueType>::OneValue());
m_Skew.Fill(TParametersValueType{});
}
// Constructor with arguments
template <typename TParametersValueType>
ComposeScaleSkewVersor3DTransform<TParametersValueType>::ComposeScaleSkewVersor3DTransform(
unsigned int parametersDimension)
: Superclass(parametersDimension)
{
m_Scale.Fill(1.0);
m_Skew.Fill(0.0);
}
// Constructor with arguments
template <typename TParametersValueType>
ComposeScaleSkewVersor3DTransform<TParametersValueType>::ComposeScaleSkewVersor3DTransform(
const MatrixType & matrix,
const OutputVectorType & offset)
: Superclass(matrix, offset)
{
this->ComputeMatrixParameters();
}
// Directly set the matrix
template <typename TParametersValueType>
void
ComposeScaleSkewVersor3DTransform<TParametersValueType>::SetMatrix(const MatrixType & matrix)
{
// Any matrix should work - bypass orthogonality testing
using Baseclass = MatrixOffsetTransformBase<TParametersValueType, 3, 3>;
this->Baseclass::SetMatrix(matrix);
}
template <typename TParametersValueType>
void
ComposeScaleSkewVersor3DTransform<TParametersValueType>::SetMatrix(const MatrixType & matrix,
const TParametersValueType itkNotUsed(tolerance))
{
// Any matrix should work - bypass orthogonality testing
using Baseclass = MatrixOffsetTransformBase<TParametersValueType, 3, 3>;
this->Baseclass::SetMatrix(matrix);
}
// Set Parameters
template <typename TParametersValueType>
void
ComposeScaleSkewVersor3DTransform<TParametersValueType>::SetParameters(const ParametersType & parameters)
{
itkDebugMacro("Setting parameters " << parameters);
// Save parameters. Needed for proper operation of TransformUpdateParameters.
if (¶meters != &(this->m_Parameters))
{
this->m_Parameters = parameters;
}
// Transfer the versor part
AxisType axis;
double norm = parameters[0] * parameters[0];
axis[0] = parameters[0];
norm += parameters[1] * parameters[1];
axis[1] = parameters[1];
norm += parameters[2] * parameters[2];
axis[2] = parameters[2];
if (norm > 0)
{
norm = std::sqrt(norm);
}
double epsilon = 1e-10;
if (norm >= 1.0 - epsilon)
{
axis = axis / (norm + epsilon * norm);
}
VersorType newVersor;
newVersor.Set(axis);
this->SetVarVersor(newVersor);
itkDebugMacro("Versor is now " << newVersor);
// Matrix must be defined before translation so that offset can be computed
// from translation
m_Scale[0] = parameters[6];
m_Scale[1] = parameters[7];
m_Scale[2] = parameters[8];
m_Skew[0] = parameters[9];
m_Skew[1] = parameters[10];
m_Skew[2] = parameters[11];
// Transfer the translation part
TranslationType newTranslation;
newTranslation[0] = parameters[3];
newTranslation[1] = parameters[4];
newTranslation[2] = parameters[5];
this->SetVarTranslation(newTranslation);
this->ComputeMatrix();
this->ComputeOffset();
// Modified is always called since we just have a pointer to the
// parameters and cannot know if the parameters have changed.
this->Modified();
itkDebugMacro("After setting parameters ");
}
//
// Get Parameters
//
// Parameters are ordered as:
//
// p[0:2] = right part of the versor (axis times std::sin(t/2))
// p[3:5] = translation components
// p[6:8] = Scale
// p[9:11] = Skew {x, y, z}
//
template <typename TParametersValueType>
auto
ComposeScaleSkewVersor3DTransform<TParametersValueType>::GetParameters() const -> const ParametersType &
{
itkDebugMacro("Getting parameters ");
this->m_Parameters[0] = this->GetVersor().GetX();
this->m_Parameters[1] = this->GetVersor().GetY();
this->m_Parameters[2] = this->GetVersor().GetZ();
this->m_Parameters[3] = this->GetTranslation()[0];
this->m_Parameters[4] = this->GetTranslation()[1];
this->m_Parameters[5] = this->GetTranslation()[2];
this->m_Parameters[6] = this->GetScale()[0];
this->m_Parameters[7] = this->GetScale()[1];
this->m_Parameters[8] = this->GetScale()[2];
this->m_Parameters[9] = this->GetSkew()[0];
this->m_Parameters[10] = this->GetSkew()[1];
this->m_Parameters[11] = this->GetSkew()[2];
itkDebugMacro("After getting parameters " << this->m_Parameters);
return this->m_Parameters;
}
template <typename TParametersValueType>
void
ComposeScaleSkewVersor3DTransform<TParametersValueType>::SetIdentity()
{
m_Scale.Fill(NumericTraits<ScaleVectorValueType>::OneValue());
m_Skew.Fill(SkewVectorValueType{});
Superclass::SetIdentity();
}
template <typename TParametersValueType>
void
ComposeScaleSkewVersor3DTransform<TParametersValueType>::SetScale(const ScaleVectorType & scale)
{
m_Scale = scale;
this->ComputeMatrix();
this->ComputeOffset();
}
template <typename TParametersValueType>
void
ComposeScaleSkewVersor3DTransform<TParametersValueType>::SetSkew(const SkewVectorType & skew)
{
m_Skew = skew;
this->ComputeMatrix();
this->ComputeOffset();
}
// Compute the matrix
template <typename TParametersValueType>
void
ComposeScaleSkewVersor3DTransform<TParametersValueType>::ComputeMatrix()
{
this->Superclass::ComputeMatrix();
MatrixType newMatrix = this->GetMatrix();
MatrixType scaleM;
scaleM.SetIdentity();
scaleM[0][0] = m_Scale[0];
scaleM[1][1] = m_Scale[1];
scaleM[2][2] = m_Scale[2];
MatrixType skewM;
skewM(0, 0) = 1;
skewM(0, 1) = m_Skew[0];
skewM(0, 2) = m_Skew[1];
skewM(1, 0) = 0;
skewM(1, 1) = 1;
skewM(1, 2) = m_Skew[2];
skewM(2, 0) = 0;
skewM(2, 1) = 0;
skewM(2, 2) = 1;
MatrixType Q = scaleM * skewM;
MatrixType res = newMatrix * Q;
this->SetVarMatrix(res);
}
template <typename TParametersValueType>
void
ComposeScaleSkewVersor3DTransform<TParametersValueType>::ComputeMatrixParameters()
{
MatrixType M = this->GetMatrix();
OutputVectorType scaleV;
scaleV[0] = M(0, 0);
scaleV[1] = M(1, 0);
scaleV[2] = M(2, 0);
m_Scale[0] = scaleV.GetVnlVector().magnitude();
M(0, 0) /= m_Scale[0];
M(1, 0) /= m_Scale[0];
M(2, 0) /= m_Scale[0];
double ortho = M(0, 0) * M(0, 1) + M(1, 0) * M(1, 1) + M(2, 0) * M(2, 1);
M(0, 1) -= ortho * M(0, 0);
M(1, 1) -= ortho * M(1, 0);
M(2, 1) -= ortho * M(2, 0);
scaleV[0] = M(0, 1);
scaleV[1] = M(1, 1);
scaleV[2] = M(2, 1);
m_Scale[1] = scaleV.GetVnlVector().magnitude();
M(0, 1) /= m_Scale[1];
M(1, 1) /= m_Scale[1];
M(2, 1) /= m_Scale[1];
m_Skew[0] = ortho / m_Scale[0];
double ortho0 = M(0, 0) * M(0, 2) + M(1, 0) * M(1, 2) + M(2, 0) * M(2, 2);
double ortho1 = M(0, 1) * M(0, 2) + M(1, 1) * M(1, 2) + M(2, 1) * M(2, 2);
M(0, 2) -= (ortho0 * M(0, 0) + ortho1 * M(0, 1));
M(1, 2) -= (ortho0 * M(1, 0) + ortho1 * M(1, 1));
M(2, 2) -= (ortho0 * M(2, 0) + ortho1 * M(2, 1));
scaleV[0] = M(0, 2);
scaleV[1] = M(1, 2);
scaleV[2] = M(2, 2);
m_Scale[2] = scaleV.GetVnlVector().magnitude();
M(0, 2) /= m_Scale[2];
M(1, 2) /= m_Scale[2];
M(2, 2) /= m_Scale[2];
m_Skew[1] = ortho0 / m_Scale[0];
m_Skew[2] = ortho1 / m_Scale[1];
if (vnl_determinant(M.GetVnlMatrix()) < 0)
{
m_Scale[0] *= -1;
M(0, 0) *= -1;
M(1, 0) *= -1;
M(2, 0) *= -1;
}
VersorType v;
v.Set(M);
this->SetVarVersor(v);
}
// Print self
template <typename TParametersValueType>
void
ComposeScaleSkewVersor3DTransform<TParametersValueType>::PrintSelf(std::ostream & os, Indent indent) const
{
Superclass::PrintSelf(os, indent);
os << indent << "Scale: " << m_Scale << std::endl;
os << indent << "Skew: " << m_Skew << std::endl;
}
template <typename TParametersValueType>
void
ComposeScaleSkewVersor3DTransform<TParametersValueType>::ComputeJacobianWithRespectToParameters(
const InputPointType & p,
JacobianType & jacobian) const
{
// Jacobian computed via
// pip install sympy
//
// from sympy import Derivative, simplify
// from sympy import symbols
// from sympy.matrices import Matrix
// x0, x1, x2, v0, v1, v2, w, o0, o1, o2, s0, s1, s2, k0, k1, k2 =
// symbols('x0 x1 x2 v0 v1 v2 w o0 o1 o2 s0 s1 s2 k0 k1 k2')
// M = Matrix([[1-2*(v1*v1+v2*v2), 2*(v0*v1-v2*w), 2*(v0*v2+v1*w), o0],
// [2*(v0*v1+v2*w), 1-2*(v0*v0+v2*v2), 2*(v1*v2-v0*w), o1],
// [2*(v0*v2-v1*w), 2*(v1*v2+v0*w), 1-2*(v0*v0+v1*v1), o2],
// [0, 0, 0, 1]])
// # Quaternion to Matrix from:
// # https://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToMatrix/index.htm
// S = Matrix([[s0, 0, 0, 0], [0, s1, 0, 0], [0, 0, s2, 0], [0, 0, 0, 1]])
// K = Matrix([[1, k0, k1, 0], [0, 1, k2, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
// x = Matrix(4,1,[x0,x1,x2,1])
// f = M*S*K*x
// fx = Derivative(f,v1) # substitute v0, v2, s0 etc for v1 to list all equs.
// simplify(fx)
//
using ValueType = typename VersorType::ValueType;
// compute derivatives with respect to rotation
const ValueType v0 = this->GetVersor().GetX();
const ValueType v1 = this->GetVersor().GetY();
const ValueType v2 = this->GetVersor().GetZ();
const ValueType w = this->GetVersor().GetW();
const ValueType s0 = this->GetScale()[0];
const ValueType s1 = this->GetScale()[1];
const ValueType s2 = this->GetScale()[2];
const ValueType k0 = this->GetSkew()[0];
const ValueType k1 = this->GetSkew()[1];
const ValueType k2 = this->GetSkew()[2];
const double x0 = p[0] - this->GetCenter()[0];
const double x1 = p[1] - this->GetCenter()[1];
const double x2 = p[2] - this->GetCenter()[2];
jacobian.SetSize(3, this->GetNumberOfLocalParameters());
jacobian.Fill(0.0);
double v0v0 = v0 * v0;
double v0v1 = v0 * v1;
double v0v2 = v0 * v2;
double v0w = v0 * w;
double v1v1 = v1 * v1;
double v1v2 = v1 * v2;
double v1w = v1 * w;
double v2v2 = v2 * v2;
double v2w = v2 * w;
// compute Jacobian with respect to quaternion parameters
jacobian[0][0] = 2 * s1 * v1 * x1 + x2 * (2 * k2 * s1 * v1 + 2 * s2 * v2);
jacobian[1][0] =
2 * s0 * v1 * x0 + x1 * (2 * k0 * s0 * v1 - 4 * s1 * v0) - x2 * (-2 * k1 * s0 * v1 + 4 * k2 * s1 * v0 + 2 * s2 * w);
jacobian[2][0] =
2 * s0 * v2 * x0 + 2 * x1 * (k0 * s0 * v2 + s1 * w) + x2 * (2 * k1 * s0 * v2 + 2 * k2 * s1 * w - 4 * s2 * v0);
jacobian[0][1] = -4 * s0 * v1 * x0 - x1 * (4 * k0 * s0 * v1 - 2 * s1 * v0) +
x2 * (-4 * k1 * s0 * v1 + 2 * k2 * s1 * v0 + 2 * s2 * w);
jacobian[1][1] = 2 * k0 * s0 * v0 * x1 + 2 * s0 * v0 * x0 - x2 * (-2 * k1 * s0 * v0 - 2 * s2 * v2);
jacobian[2][1] =
-2 * s0 * w * x0 + 2 * x1 * (-k0 * s0 * w + s1 * v2) + x2 * (-2 * k1 * s0 * w + 2 * k2 * s1 * v2 - 4 * s2 * v1);
jacobian[0][2] =
-4 * s0 * v2 * x0 - x1 * (4 * k0 * s0 * v2 + 2 * s1 * w) + x2 * (-4 * k1 * s0 * v2 - 2 * k2 * s1 * w + 2 * s2 * v0);
jacobian[1][2] =
2 * s0 * w * x0 + x1 * (2 * k0 * s0 * w - 4 * s1 * v2) - x2 * (-2 * k1 * s0 * w + 4 * k2 * s1 * v2 - 2 * s2 * v1);
jacobian[2][2] = 2 * s0 * v0 * x0 + 2 * x1 * (k0 * s0 * v0 + s1 * v1) + x2 * (2 * k1 * s0 * v0 + 2 * k2 * s1 * v1);
jacobian[0][3] = 1.0;
jacobian[1][4] = 1.0;
jacobian[2][5] = 1.0;
jacobian[0][6] =
-k0 * x1 * (2 * v1v1 + 2 * v2v2 - 1) - k1 * x2 * (2 * v1v1 + 2 * v2v2 - 1) - x0 * (2 * v1v1 + 2 * v2v2 - 1);
jacobian[1][6] = 2 * k0 * x1 * (v0v1 + v2w) + 2 * k1 * x2 * (v0v1 + v2w) + 2 * x0 * (v0v1 + v2w);
jacobian[2][6] = 2 * k0 * x1 * (v0v2 - v1w) + 2 * k1 * x2 * (v0v2 - v1w) + 2 * x0 * (v0v2 - v1w);
jacobian[0][7] = 2 * k2 * x2 * (v0v1 - v2w) - x1 * (-2 * v0v1 + 2 * v2w);
jacobian[1][7] = -k2 * x2 * (2 * v0v0 + 2 * v2v2 - 1) + x1 * (-2 * v0v0 - 2 * v2v2 + 1);
jacobian[2][7] = 2 * k2 * x2 * (v0w + v1v2) + 2 * x1 * (v0w + v1v2);
jacobian[0][8] = x2 * (2 * v0v2 + 2 * v1w);
jacobian[1][8] = -x2 * (2 * v0w - 2 * v1v2);
jacobian[2][8] = x2 * (-2 * v0v0 - 2 * v1v1 + 1);
jacobian[0][9] = -s0 * x1 * (2 * v1v1 + 2 * v2v2 - 1);
jacobian[1][9] = 2 * s0 * x1 * (v0v1 + v2w);
jacobian[2][9] = 2 * s0 * x1 * (v0v2 - v1w);
jacobian[0][10] = -s0 * x2 * (2 * v1v1 + 2 * v2v2 - 1);
jacobian[1][10] = 2 * s0 * x2 * (v0v1 + v2w);
jacobian[2][10] = 2 * s0 * x2 * (v0v2 - v1w);
jacobian[0][11] = 2 * s1 * x2 * (v0v1 - v2w);
jacobian[1][11] = -s1 * x2 * (2 * v0v0 + 2 * v2v2 - 1);
jacobian[2][11] = 2 * s1 * x2 * (v0w + v1v2);
}
} // namespace itk
#endif
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