template<typename TParametersValueType, unsigned int VDimension>
class itk::GaussianExponentialDiffeomorphicTransform< TParametersValueType, VDimension >
Exponential transform using a Gaussian smoothing kernel.
Exponential transform inspired by the work of J. Ashburner (see reference below). Assuming a constant velocity field, the transform takes as input the update field at time point t = 1, \(u\) and smooths it using Gaussian smoothing, \(S_{update}\) defined by GaussianSmoothingVarianceForTheUpdateField We add that the current estimate of the velocity field and then perform a second smoothing step such that the new velocity field is
\begin{eqnarray*} v_{new} = S_{velocity}( v_{old} + S_{update}( u ) ). \end{eqnarray*}
We then exponentiate \(v_{new}\) using the class ExponentialDisplacementImageFilter to yield both the forward and inverse displacement fields.
- J. Ashburner. A Fast Diffeomorphic Image Registration Algorithm. NeuroImage, 38(1):95-113, 2007.
- Author
- Nick Tustison
-
Brian Avants
Definition at line 56 of file itkGaussianExponentialDiffeomorphicTransform.h.
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| using | ConstPointer = SmartPointer< const Self > |
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| using | DerivativeValueType = typename DerivativeType::ValueType |
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| using | DisplacementFieldPointer = typename DisplacementFieldType::Pointer |
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| using | DisplacementFieldType = Image< OutputVectorType, Dimension > |
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| using | DisplacementVectorType = typename DisplacementFieldType::PixelType |
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| using | Pointer = SmartPointer< Self > |
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| using | Self = GaussianExponentialDiffeomorphicTransform |
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| using | Superclass = ConstantVelocityFieldTransform< TParametersValueType, VDimension > |
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| using | ConstantVelocityFieldInterpolatorPointer = typename ConstantVelocityFieldInterpolatorType::Pointer |
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| using | ConstantVelocityFieldInterpolatorType = VectorInterpolateImageFunction< ConstantVelocityFieldType, ScalarType > |
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| using | ConstantVelocityFieldPointer = typename ConstantVelocityFieldType::Pointer |
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| using | ConstantVelocityFieldType = Image< OutputVectorType, ConstantVelocityFieldDimension > |
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| using | ConstPointer = SmartPointer< const Self > |
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| using | DirectionType = typename ConstantVelocityFieldType::DirectionType |
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| using | DisplacementFieldPointer = typename DisplacementFieldType::Pointer |
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| using | DisplacementFieldType = Image< OutputVectorType, Dimension > |
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| using | IndexType = typename ConstantVelocityFieldType::IndexType |
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| using | OptimizerParametersHelperType = ImageVectorOptimizerParametersHelper< ScalarType, Dimension, ConstantVelocityFieldDimension > |
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| using | PixelType = typename ConstantVelocityFieldType::PixelType |
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| using | Pointer = SmartPointer< Self > |
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| using | PointType = typename ConstantVelocityFieldType::PointType |
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| using | RegionType = typename ConstantVelocityFieldType::RegionType |
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| using | Self = ConstantVelocityFieldTransform |
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| using | SizeType = typename ConstantVelocityFieldType::SizeType |
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| using | SpacingType = typename ConstantVelocityFieldType::SpacingType |
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| using | Superclass = DisplacementFieldTransform< TParametersValueType, VDimension > |
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| using | VelocityFieldType = ConstantVelocityFieldType |
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| using | ConstPointer = SmartPointer< const Self > |
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| using | DirectionType = typename DisplacementFieldType::DirectionType |
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| using | DisplacementFieldConstPointer = typename DisplacementFieldType::ConstPointer |
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| using | DisplacementFieldPointer = typename DisplacementFieldType::Pointer |
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| using | DisplacementFieldType = Image< OutputVectorType, Dimension > |
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| using | IndexType = typename DisplacementFieldType::IndexType |
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| using | InputTensorEigenVectorType = CovariantVector< ScalarType, InputDiffusionTensor3DType::Dimension > |
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| using | InterpolatorType = VectorInterpolateImageFunction< DisplacementFieldType, ScalarType > |
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| using | OptimizerParametersHelperType = ImageVectorOptimizerParametersHelper< ScalarType, OutputVectorType::Dimension, Dimension > |
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| using | OutputTensorEigenVectorType = CovariantVector< ScalarType, OutputDiffusionTensor3DType::Dimension > |
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| using | PixelType = typename DisplacementFieldType::PixelType |
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| using | Pointer = SmartPointer< Self > |
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| using | PointType = typename DisplacementFieldType::PointType |
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| using | RegionType = typename DisplacementFieldType::RegionType |
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| using | Self = DisplacementFieldTransform |
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| using | SizeType = typename DisplacementFieldType::SizeType |
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| using | SpacingType = typename DisplacementFieldType::SpacingType |
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| using | Superclass = Transform< TParametersValueType, VDimension, VDimension > |
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| using | VectorImageDisplacementFieldType = VectorImage< TParametersValueType, Dimension > |
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| using | ConstPointer = SmartPointer< const Self > |
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| using | DerivativeType = Array< ParametersValueType > |
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| using | DirectionChangeMatrix = Matrix< double, Self::OutputSpaceDimension, Self::InputSpaceDimension > |
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| using | InputCovariantVectorType = CovariantVector< TParametersValueType, VInputDimension > |
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| using | InputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType > |
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| using | InputDirectionMatrix = Matrix< double, Self::InputSpaceDimension, Self::InputSpaceDimension > |
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| using | InputPointType = Point< TParametersValueType, VInputDimension > |
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| using | InputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, VInputDimension > |
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| using | InputVectorPixelType = VariableLengthVector< TParametersValueType > |
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| using | InputVectorType = Vector< TParametersValueType, VInputDimension > |
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| using | InputVnlVectorType = vnl_vector_fixed< TParametersValueType, VInputDimension > |
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| using | InverseJacobianPositionType = vnl_matrix_fixed< ParametersValueType, VInputDimension, VOutputDimension > |
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| using | InverseTransformBasePointer = typename InverseTransformBaseType::Pointer |
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| using | InverseTransformBaseType = Transform< TParametersValueType, VOutputDimension, VInputDimension > |
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| using | JacobianPositionType = vnl_matrix_fixed< ParametersValueType, VOutputDimension, VInputDimension > |
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| using | JacobianType = Array2D< ParametersValueType > |
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| using | MatrixType = Matrix< TParametersValueType, Self::OutputSpaceDimension, Self::InputSpaceDimension > |
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| using | OutputCovariantVectorType = CovariantVector< TParametersValueType, VOutputDimension > |
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| using | OutputDiffusionTensor3DType = DiffusionTensor3D< TParametersValueType > |
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| using | OutputDirectionMatrix = Matrix< double, Self::OutputSpaceDimension, Self::OutputSpaceDimension > |
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| using | OutputPointType = Point< TParametersValueType, VOutputDimension > |
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| using | OutputSymmetricSecondRankTensorType = SymmetricSecondRankTensor< TParametersValueType, VOutputDimension > |
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| using | OutputVectorPixelType = VariableLengthVector< TParametersValueType > |
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| using | OutputVectorType = Vector< TParametersValueType, VOutputDimension > |
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| using | OutputVnlVectorType = vnl_vector_fixed< TParametersValueType, VOutputDimension > |
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| using | Pointer = SmartPointer< Self > |
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| using | ScalarType = ParametersValueType |
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| using | Self = Transform |
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| using | Superclass = TransformBaseTemplate< TParametersValueType > |
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| virtual ConstantVelocityFieldPointer | GaussianSmoothConstantVelocityField (ConstantVelocityFieldType *, ScalarType) |
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| const char * | GetNameOfClass () const override |
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| void | UpdateTransformParameters (const DerivativeType &update, ScalarType factor=1.0) override |
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| virtual void | SetGaussianSmoothingVarianceForTheConstantVelocityField (ScalarType _arg) |
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| virtual ScalarType | GetGaussianSmoothingVarianceForTheConstantVelocityField () const |
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| virtual void | SetGaussianSmoothingVarianceForTheUpdateField (ScalarType _arg) |
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| virtual ScalarType | GetGaussianSmoothingVarianceForTheUpdateField () const |
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| virtual void | CalculateNumberOfIntegrationStepsAutomaticallyOn () |
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| virtual bool | GetCalculateNumberOfIntegrationStepsAutomatically () const |
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| virtual const ModifiedTimeType & | GetConstantVelocityFieldSetTime () const |
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| bool | GetInverse (Self *inverse) const |
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| InverseTransformBasePointer | GetInverseTransform () const override |
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| virtual ScalarType | GetLowerTimeBound () const |
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| const char * | GetNameOfClass () const override |
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| virtual unsigned int | GetNumberOfIntegrationSteps () const |
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| virtual ScalarType | GetUpperTimeBound () const |
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| virtual void | IntegrateVelocityField () |
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| virtual void | SetCalculateNumberOfIntegrationStepsAutomatically (bool _arg) |
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| void | SetFixedParameters (const FixedParametersType &) override |
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| virtual void | SetLowerTimeBound (ScalarType _arg) |
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| virtual void | SetNumberOfIntegrationSteps (unsigned int _arg) |
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| virtual void | SetUpperTimeBound (ScalarType _arg) |
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| virtual void | SetConstantVelocityField (ConstantVelocityFieldType *) |
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| virtual ConstantVelocityFieldType * | GetModifiableConstantVelocityField () |
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| virtual void | SetConstantVelocityFieldInterpolator (ConstantVelocityFieldInterpolatorType *) |
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| virtual ConstantVelocityFieldInterpolatorType * | GetModifiableConstantVelocityFieldInterpolator () |
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| void | ComputeInverseJacobianWithRespectToPosition (const InputPointType &point, InverseJacobianPositionType &jacobian) const override |
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| virtual void | ComputeJacobianWithRespectToParameters (const IndexType &, JacobianType &j) const |
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| virtual void | ComputeJacobianWithRespectToPosition (const IndexType &index, JacobianPositionType &jacobian) const |
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| void | ComputeJacobianWithRespectToPosition (const InputPointType &point, JacobianPositionType &jacobian) const override |
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| virtual const ModifiedTimeType & | GetDisplacementFieldSetTime () const |
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| bool | GetInverse (Self *inverse) const |
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| virtual void | GetInverseJacobianOfForwardFieldWithRespectToPosition (const IndexType &index, JacobianPositionType &jacobian, bool useSVD=false) const |
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| virtual void | GetInverseJacobianOfForwardFieldWithRespectToPosition (const InputPointType &point, JacobianPositionType &jacobian, bool useSVD=false) const |
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| InverseTransformBasePointer | GetInverseTransform () const override |
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| const char * | GetNameOfClass () const override |
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| NumberOfParametersType | GetNumberOfLocalParameters () const override |
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| TransformCategoryEnum | GetTransformCategory () const override |
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| void | SetFixedParameters (const FixedParametersType &) override |
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| virtual void | SetIdentity () |
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| OutputVectorPixelType | TransformCovariantVector (const InputVectorPixelType &) const override |
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| OutputVectorPixelType | TransformDiffusionTensor (const InputVectorPixelType &) const |
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| OutputPointType | TransformPoint (const InputPointType &inputPoint) const override |
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| OutputVectorPixelType | TransformVector (const InputVectorPixelType &) const override |
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| OutputVnlVectorType | TransformVector (const InputVnlVectorType &) const override |
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| virtual void | SetDisplacementField (DisplacementFieldType *field) |
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| virtual void | SetDisplacementField (VectorImageDisplacementFieldType *field) |
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| void | SetDisplacementField (std::nullptr_t)=delete |
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| virtual DisplacementFieldType * | GetModifiableDisplacementField () |
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| virtual void | SetInverseDisplacementField (DisplacementFieldType *inverseField) |
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| virtual DisplacementFieldType * | GetModifiableInverseDisplacementField () |
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| virtual void | SetInterpolator (InterpolatorType *interpolator) |
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| virtual InterpolatorType * | GetModifiableInterpolator () |
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| virtual void | SetInverseInterpolator (InterpolatorType *interpolator) |
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| virtual InterpolatorType * | GetModifiableInverseInterpolator () |
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| OutputVectorType | TransformVector (const InputVectorType &) const override |
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| OutputDiffusionTensor3DType | TransformDiffusionTensor (const InputDiffusionTensor3DType &) const |
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| OutputCovariantVectorType | TransformCovariantVector (const InputCovariantVectorType &) const override |
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| void | SetParameters (const ParametersType ¶ms) override |
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| void | ComputeJacobianWithRespectToParameters (const InputPointType &, JacobianType &j) const override |
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| virtual void | SetCoordinateTolerance (double _arg) |
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| virtual double | GetCoordinateTolerance () const |
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| virtual void | SetDirectionTolerance (double _arg) |
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| virtual double | GetDirectionTolerance () const |
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| virtual void | ComputeJacobianWithRespectToParametersCachedTemporaries (const InputPointType &p, JacobianType &jacobian, JacobianType &) const |
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| void | CopyInFixedParameters (const FixedParametersValueType *const begin, const FixedParametersValueType *const end) override |
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| void | CopyInParameters (const ParametersValueType *const begin, const ParametersValueType *const end) override |
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| const FixedParametersType & | GetFixedParameters () const override |
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| unsigned int | GetInputSpaceDimension () const override |
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| bool | GetInverse (Self *) const |
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| const char * | GetNameOfClass () const override |
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| virtual NumberOfParametersType | GetNumberOfFixedParameters () const |
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| NumberOfParametersType | GetNumberOfParameters () const override |
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| unsigned int | GetOutputSpaceDimension () const override |
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| const ParametersType & | GetParameters () const override |
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| TransformCategoryEnum | GetTransformCategory () const override |
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| std::string | GetTransformTypeAsString () const override |
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| virtual bool | IsLinear () const |
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| | itkCloneMacro (Self) |
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| void | SetParametersByValue (const ParametersType &p) override |
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| virtual OutputCovariantVectorType | TransformCovariantVector (const InputCovariantVectorType &vector, const InputPointType &point) const |
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| virtual OutputVectorPixelType | TransformCovariantVector (const InputVectorPixelType &vector, const InputPointType &point) const |
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| virtual OutputDiffusionTensor3DType | TransformDiffusionTensor3D (const InputDiffusionTensor3DType &) const |
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| virtual OutputDiffusionTensor3DType | TransformDiffusionTensor3D (const InputDiffusionTensor3DType &inputTensor, const InputPointType &point) const |
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| virtual OutputVectorPixelType | TransformDiffusionTensor3D (const InputVectorPixelType &) const |
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| virtual OutputVectorPixelType | TransformDiffusionTensor3D (const InputVectorPixelType &inputTensor, const InputPointType &point) const |
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| virtual OutputSymmetricSecondRankTensorType | TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &) const |
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| virtual OutputSymmetricSecondRankTensorType | TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &inputTensor, const InputPointType &point) const |
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| virtual OutputVectorPixelType | TransformSymmetricSecondRankTensor (const InputVectorPixelType &) const |
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| virtual OutputVectorPixelType | TransformSymmetricSecondRankTensor (const InputVectorPixelType &inputTensor, const InputPointType &point) const |
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| virtual OutputVectorPixelType | TransformVector (const InputVectorPixelType &vector, const InputPointType &point) const |
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| virtual OutputVectorType | TransformVector (const InputVectorType &vector, const InputPointType &point) const |
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| virtual OutputVnlVectorType | TransformVector (const InputVnlVectorType &vector, const InputPointType &point) const |
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| template< typename TImage > std std::enable_if_t< TImage::ImageDimension==VInputDimension &&TImage::ImageDimension==VOutputDimension, void > | ApplyToImageMetadata (SmartPointer< TImage > image) const |
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Inheritance diagram for itk::GaussianExponentialDiffeomorphicTransform< TParametersValueType, VDimension >:
1.8.16