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 | 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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| 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 | ConstPointer = SmartPointer< const Self > |
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| using | Pointer = SmartPointer< Self > |
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| using | Self = Object |
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| using | Superclass = LightObject |
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| using | ConstPointer = SmartPointer< const Self > |
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| using | Pointer = SmartPointer< Self > |
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| using | Self = LightObject |
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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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| 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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| NumberOfParametersType | GetNumberOfLocalParameters () const override |
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| TransformCategoryEnum | GetTransformCategory () const 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 (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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| virtual const std::string & | GetInputSpaceName () const |
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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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| virtual const std::string & | GetOutputSpaceName () const |
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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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| virtual void | SetInputSpaceName (std::string _arg) |
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| virtual void | SetOutputSpaceName (std::string _arg) |
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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 &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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| | itkLegacyMacro (virtual void ComputeJacobianWithRespectToPosition(const InputPointType &x, JacobianType &jacobian) const) |
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| | itkLegacyMacro (virtual void ComputeInverseJacobianWithRespectToPosition(const InputPointType &x, JacobianType &jacobian) const) |
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| std::enable_if_t< TImage::ImageDimension==VInputDimension &&TImage::ImageDimension==VOutputDimension, void > | ApplyToImageMetadata (TImage *image) const |
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| std::enable_if_t< TImage::ImageDimension==VInputDimension &&TImage::ImageDimension==VOutputDimension, void > | ApplyToImageMetadata (SmartPointer< TImage > image) const |
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| virtual void | SetParametersByValue (const ParametersType &p)=0 |
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| unsigned long | AddObserver (const EventObject &event, Command *) |
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| unsigned long | AddObserver (const EventObject &event, Command *) const |
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| unsigned long | AddObserver (const EventObject &event, std::function< void(const EventObject &)> function) const |
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| LightObject::Pointer | CreateAnother () const override |
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| virtual void | DebugOff () const |
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| virtual void | DebugOn () const |
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| Command * | GetCommand (unsigned long tag) |
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| bool | GetDebug () const |
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| MetaDataDictionary & | GetMetaDataDictionary () |
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| const MetaDataDictionary & | GetMetaDataDictionary () const |
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| virtual ModifiedTimeType | GetMTime () const |
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| virtual const TimeStamp & | GetTimeStamp () const |
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| bool | HasObserver (const EventObject &event) const |
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| void | InvokeEvent (const EventObject &) |
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| void | InvokeEvent (const EventObject &) const |
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| virtual void | Modified () const |
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| void | Register () const override |
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| void | RemoveAllObservers () |
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| void | RemoveObserver (unsigned long tag) |
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| void | SetDebug (bool debugFlag) const |
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| void | SetReferenceCount (int) override |
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| void | UnRegister () const noexcept override |
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| void | SetMetaDataDictionary (const MetaDataDictionary &rhs) |
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| void | SetMetaDataDictionary (MetaDataDictionary &&rrhs) |
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| virtual void | SetObjectName (std::string _arg) |
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| virtual const std::string & | GetObjectName () const |
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| Pointer | Clone () const |
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| virtual void | Delete () |
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| virtual int | GetReferenceCount () const |
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| void | Print (std::ostream &os, Indent indent=0) const |
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Inheritance diagram for itk::TimeVaryingBSplineVelocityFieldTransform< TParametersValueType, VDimension >:
1.8.16