template<typename TParametersValueType, unsigned int VDimension>
class itk::TimeVaryingBSplineVelocityFieldTransform< TParametersValueType, VDimension >
Integrate a time-varying velocity field represented by a B-spline control point lattice.
Diffeomorphisms are topology-preserving mappings that are useful for describing biologically plausible deformations. Mathematically, a diffeomorphism, \( \phi \), is generated from a time-varying velocity field, v, as described by the integral equation:
\[ \phi(t_b) = \phi(t_a) + \int_{t_a}^{t_b} v(\phi(t),t) dt \]
In typical registration applications it is computationally more efficient to sample the B-spline transform to its corresponding displacement field. Therefore, the user needs to specify the domain parameters of that displacement field using the following functions:
SetDisplacementFieldSpacing()
SetDisplacementFieldOrigin()
SetDisplacementFieldSize()
SetDisplacementFieldDirection()
It's important that these parameters match up with the fixed parameters of this transform which are defined as the parameters of the (N+1)-D B-spline grid representing the continuous velocity field. This control point lattice is set using SetTimeVaryingVelocityFieldControlPointLattice()
or it can be created by setting the fixed parameters.
Note: For readability of the code, it is important to note that we store the control point lattice in the m_VelocityField variable since they are of the same type. It's only when we call IntegrateVelocityField() that a sampled velocity field is created from the control point lattice.
- Author
- Nick Tustison
-
Brian Avants
Definition at line 68 of file itkTimeVaryingBSplineVelocityFieldTransform.h.
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using | ConstPointer = SmartPointer< const Self > |
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using | DisplacementFieldDirectionType = typename DisplacementFieldType::DirectionType |
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using | DisplacementFieldPointType = typename DisplacementFieldType::PointType |
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using | DisplacementFieldSizeType = typename DisplacementFieldType::SizeType |
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using | DisplacementFieldSpacingType = typename DisplacementFieldType::SpacingType |
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using | DisplacementVectorType = typename DisplacementFieldType::PixelType |
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using | FixedParametersValueType = typename FixedParametersType::ValueType |
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using | ParametersValueType = typename ParametersType::ValueType |
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using | Pointer = SmartPointer< Self > |
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using | Self = TimeVaryingBSplineVelocityFieldTransform |
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using | Superclass = VelocityFieldTransform< TParametersValueType, VDimension > |
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using | TimeVaryingVelocityFieldControlPointLatticePointer = typename VelocityFieldType::Pointer |
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using | TimeVaryingVelocityFieldControlPointLatticeType = VelocityFieldType |
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using | VelocityFieldDirectionType = typename VelocityFieldType::DirectionType |
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using | VelocityFieldIntegratorType = typename Superclass::VelocityFieldInterpolatorType |
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using | VelocityFieldPointType = typename VelocityFieldType::PointType |
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using | VelocityFieldSizeType = typename VelocityFieldType::SizeType |
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using | VelocityFieldSpacingType = typename VelocityFieldType::SpacingType |
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using | ConstPointer = SmartPointer< const Self > |
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using | DirectionType = typename VelocityFieldType::DirectionType |
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using | DisplacementFieldPointer = typename DisplacementFieldType::Pointer |
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using | IndexType = typename VelocityFieldType::IndexType |
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using | OptimizerParametersHelperType = ImageVectorOptimizerParametersHelper< ScalarType, Dimension, VelocityFieldDimension > |
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using | PixelType = typename VelocityFieldType::PixelType |
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using | Pointer = SmartPointer< Self > |
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using | PointType = typename VelocityFieldType::PointType |
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using | RegionType = typename VelocityFieldType::RegionType |
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using | Self = VelocityFieldTransform |
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using | SizeType = typename VelocityFieldType::SizeType |
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using | SpacingType = typename VelocityFieldType::SpacingType |
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using | Superclass = DisplacementFieldTransform< TParametersValueType, VDimension > |
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using | VelocityFieldInterpolatorPointer = typename VelocityFieldInterpolatorType::Pointer |
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using | VelocityFieldInterpolatorType = VectorInterpolateImageFunction< VelocityFieldType, ScalarType > |
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using | VelocityFieldPointer = typename VelocityFieldType::Pointer |
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using | VelocityFieldType = Image< OutputVectorType, VelocityFieldDimension > |
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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 | FixedParametersType = OptimizerParameters< FixedParametersValueType > |
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using | FixedParametersValueType = double |
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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 | NumberOfParametersType = IdentifierType |
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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 | ParametersType = OptimizerParameters< ParametersValueType > |
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using | ParametersValueType = TParametersValueType |
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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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using | TransformCategoryEnum = TransformBaseTemplateEnums::TransformCategory |
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using | ConstPointer = SmartPointer< const Self > |
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using | FixedParametersType = OptimizerParameters< FixedParametersValueType > |
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using | FixedParametersValueType = double |
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using | NumberOfParametersType = IdentifierType |
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using | ParametersType = OptimizerParameters< ParametersValueType > |
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using | ParametersValueType = TParametersValueType |
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using | Pointer = SmartPointer< Self > |
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using | Self = TransformBaseTemplate |
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using | Superclass = Object |
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using | TransformCategoryEnum = TransformBaseTemplateEnums::TransformCategory |
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using | TransformCategoryType = TransformCategoryEnum |
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const char * | GetNameOfClass () const override |
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VelocityFieldType * | GetTimeVaryingVelocityFieldControlPointLattice () |
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void | IntegrateVelocityField () override |
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virtual void | SetTimeVaryingVelocityFieldControlPointLattice (VelocityFieldType *fieldLattice) |
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void | UpdateTransformParameters (const DerivativeType &update, ScalarType factor=1.0) override |
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virtual void | SetVelocityFieldOrigin (VelocityFieldPointType _arg) |
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virtual VelocityFieldPointType | GetVelocityFieldOrigin () const |
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virtual void | SetVelocityFieldSpacing (VelocityFieldSpacingType _arg) |
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virtual VelocityFieldSpacingType | GetVelocityFieldSpacing () const |
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virtual void | SetVelocityFieldSize (VelocityFieldSizeType _arg) |
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virtual VelocityFieldSizeType | GetVelocityFieldSize () const |
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virtual void | SetVelocityFieldDirection (VelocityFieldDirectionType _arg) |
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virtual VelocityFieldDirectionType | GetVelocityFieldDirection () const |
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virtual void | SetSplineOrder (unsigned int _arg) |
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virtual unsigned int | GetSplineOrder () 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 const unsigned long & | GetVelocityFieldSetTime () const |
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virtual void | IntegrateVelocityField () |
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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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void | UpdateTransformParameters (const DerivativeType &update, ScalarType factor=1.0) override |
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virtual void | SetVelocityField (VelocityFieldType *) |
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virtual VelocityFieldType * | GetModifiableVelocityField () |
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virtual void | SetVelocityFieldInterpolator (VelocityFieldInterpolatorType *) |
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virtual VelocityFieldInterpolatorType * | GetModifiableVelocityFieldInterpolator () |
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void | SetDisplacementField (DisplacementFieldType *displacementField) override |
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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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void | UpdateTransformParameters (const DerivativeType &update, ScalarType factor=1.0) override |
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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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virtual InverseTransformBasePointer | GetInverseTransform () const |
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const char * | GetNameOfClass () const override |
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virtual NumberOfParametersType | GetNumberOfFixedParameters () const |
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virtual NumberOfParametersType | GetNumberOfLocalParameters () 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 | SetFixedParameters (const FixedParametersType &) override=0 |
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void | SetParameters (const ParametersType &) override=0 |
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void | SetParametersByValue (const ParametersType &p) override |
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virtual OutputCovariantVectorType | TransformCovariantVector (const InputCovariantVectorType &) const |
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virtual OutputCovariantVectorType | TransformCovariantVector (const InputCovariantVectorType &vector, const InputPointType &point) const |
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virtual OutputVectorPixelType | TransformCovariantVector (const InputVectorPixelType &) 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 OutputPointType | TransformPoint (const InputPointType &) const=0 |
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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 &) const |
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virtual OutputVectorPixelType | TransformVector (const InputVectorPixelType &vector, const InputPointType &point) const |
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virtual OutputVectorType | TransformVector (const InputVectorType &) const |
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virtual OutputVectorType | TransformVector (const InputVectorType &vector, const InputPointType &point) const |
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virtual OutputVnlVectorType | TransformVector (const InputVnlVectorType &) const |
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virtual OutputVnlVectorType | TransformVector (const InputVnlVectorType &vector, const InputPointType &point) const |
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virtual void | UpdateTransformParameters (const DerivativeType &update, ParametersValueType factor=1.0) |
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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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virtual void | CopyInFixedParameters (const FixedParametersValueType *const begin, const FixedParametersValueType *const end)=0 |
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virtual void | CopyInParameters (const ParametersValueType *const begin, const ParametersValueType *const end)=0 |
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virtual const FixedParametersType & | GetFixedParameters () const =0 |
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virtual unsigned int | GetInputSpaceDimension () const =0 |
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virtual NumberOfParametersType | GetNumberOfParameters () const =0 |
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virtual unsigned int | GetOutputSpaceDimension () const =0 |
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virtual const ParametersType & | GetParameters () const =0 |
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virtual TransformCategoryEnum | GetTransformCategory () const =0 |
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virtual std::string | GetTransformTypeAsString () const =0 |
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| ITK_DISALLOW_COPY_AND_MOVE (TransformBaseTemplate) |
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| itkGetConstReferenceMacro (InputSpaceName, std::string) |
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| itkGetConstReferenceMacro (OutputSpaceName, std::string) |
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| itkOverrideGetNameOfClassMacro (TransformBaseTemplate) |
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| itkSetMacro (InputSpaceName, std::string) |
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| itkSetMacro (OutputSpaceName, std::string) |
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virtual void | SetFixedParameters (const FixedParametersType &)=0 |
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virtual void | SetParameters (const ParametersType &)=0 |
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virtual void | SetParametersByValue (const ParametersType &p)=0 |
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