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# Finite Difference Framework
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PDE-based image processing framework for level set methods, segmentation, and deformable models. This framework provides the foundation for implementing iterative algorithms that solve partial differential equations using finite difference methods, commonly used in image segmentation, denoising, and registration.
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## Capabilities
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### Base Finite Difference Classes
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Foundation classes for implementing PDE-based image processing algorithms.
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```python { .api }
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class FiniteDifferenceImageFilter[TInputImage, TOutputImage]:
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    """
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    Base class for finite difference image filters implementing PDE solvers.
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    Template Parameters:
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    - TInputImage: Input image type
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    - TOutputImage: Output image type
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    """
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    def SetNumberOfIterations(self, iterations: IdentifierType) -> None: ...
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    def GetNumberOfIterations(self) -> IdentifierType: ...
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    def SetTimeStep(self, time_step: TimeStepType) -> None: ...
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    def GetTimeStep(self) -> TimeStepType: ...
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    def SetElapsedIterations(self, iterations: IdentifierType) -> None: ...
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    def GetElapsedIterations(self) -> IdentifierType: ...
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    def SetUseImageSpacing(self, flag: bool) -> None: ...
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    def GetUseImageSpacing(self) -> bool: ...
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    def SetMaximumRMSError(self, error: double) -> None: ...
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    def GetMaximumRMSError(self) -> double: ...
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    def GetRMSChange(self) -> double: ...
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    def SetIsInitialized(self, flag: bool) -> None: ...
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    def GetIsInitialized(self) -> bool: ...
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    def SetManualReinitialization(self, flag: bool) -> None: ...
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    def GetManualReinitialization(self) -> bool: ...
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class DenseFiniteDifferenceImageFilter[TInputImage, TOutputImage]:
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    """Dense finite difference solver where all pixels are updated each iteration."""
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    def New() -> DenseFiniteDifferenceImageFilter[TInputImage, TOutputImage]: ...
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    def GetFiniteDifferenceFunction(self) -> FiniteDifferenceFunctionType: ...
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    def SetFiniteDifferenceFunction(self, function: FiniteDifferenceFunctionType) -> None: ...
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class SparseFiniteDifferenceImageFilter[TInputImage, TOutputImage, TSparseOutputImage]:
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    """Sparse finite difference solver that updates only active pixels."""
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    def New() -> SparseFiniteDifferenceImageFilter[TInputImage, TOutputImage, TSparseOutputImage]: ...
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    def SetNumberOfLayers(self, layers: ValueType) -> None: ...
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    def GetNumberOfLayers(self) -> ValueType: ...
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    def SetIsoSurfaceValue(self, value: ValueType) -> None: ...
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    def GetIsoSurfaceValue(self) -> ValueType: ...
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    def SetInterpolateSurfaceLocation(self, flag: bool) -> None: ...
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    def GetInterpolateSurfaceLocation(self) -> bool: ...
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```
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### Finite Difference Functions
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Functions that define the PDE update rules for different types of evolution equations.
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```python { .api }
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class FiniteDifferenceFunction[TImageType]:
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    """
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    Base class for finite difference functions that compute PDE updates.
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    Template Parameters:
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    - TImageType: Image type for the PDE evolution
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    """
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    def ComputeUpdate(self, neighborhood: NeighborhoodType, global_data: GlobalDataStruct, 
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                     gd: GlobalDataStruct) -> PixelType: ...
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    def GetRadius(self) -> RadiusType: ...
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    def GetScaleCoefficients(self) -> ScalarValueType: ...
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    def SetScaleCoefficients(self, coeffs: ScalarValueType) -> None: ...
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    def InitializeIteration(self) -> None: ...
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    def ComputeGlobalTimeStep(self, global_data: GlobalDataStruct) -> TimeStepType: ...
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class LevelSetFunction[TImageType]:
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    """Base class for level set evolution functions."""
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    def New() -> LevelSetFunction[TImageType]: ...
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    def SetAdvectionWeight(self, weight: ScalarValueType) -> None: ...
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    def GetAdvectionWeight(self) -> ScalarValueType: ...
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    def SetPropagationWeight(self, weight: ScalarValueType) -> None: ...
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    def GetPropagationWeight(self) -> ScalarValueType: ...
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    def SetCurvatureWeight(self, weight: ScalarValueType) -> None: ...
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    def GetCurvatureWeight(self) -> ScalarValueType: ...
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    def SetLaplacianSmoothingWeight(self, weight: ScalarValueType) -> None: ...
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    def GetLaplacianSmoothingWeight(self) -> ScalarValueType: ...
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    def SetEpsilonMagnitude(self, epsilon: ScalarValueType) -> None: ...
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    def GetEpsilonMagnitude(self) -> ScalarValueType: ...
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    def ComputeSpeedImage(self) -> None: ...
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    def ComputeAdvectionImage(self) -> None: ...
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    def Initialize(self, radius: RadiusType) -> None: ...
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    def CalculateAdvectionImage(self) -> None: ...
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    def CalculateSpeedImage(self) -> None: ...
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    def CalculateCurvatureImage(self) -> None: ...
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class SegmentationLevelSetFunction[TImageType, TFeatureImageType]:
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    """Level set function for image segmentation applications."""  
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    def New() -> SegmentationLevelSetFunction[TImageType, TFeatureImageType]: ...
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    def SetFeatureImage(self, image: TFeatureImageType) -> None: ...
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    def GetFeatureImage(self) -> TFeatureImageType: ...
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    def SetSpeedImage(self, image: ImageType) -> None: ...
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    def GetSpeedImage(self) -> ImageType: ...
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    def SetAdvectionImage(self, image: VectorImageType) -> None: ...
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    def GetAdvectionImage(self) -> VectorImageType: ...
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    def ReverseExpansionDirection(self) -> None: ...
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    def GetReverseExpansionDirection(self) -> bool: ...
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    def SetUseMinimalCurvature(self, flag: bool) -> None: ...
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    def GetUseMinimalCurvature(self) -> bool: ...
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```
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### Level Set Segmentation Functions
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Specialized level set functions for different segmentation approaches.
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```python { .api }
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class ShapeDetectionLevelSetFunction[TImageType, TFeatureImageType]:
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    """Shape detection level set for boundary-based segmentation."""
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    def New() -> ShapeDetectionLevelSetFunction[TImageType, TFeatureImageType]: ...
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    def CalculateSpeedImage(self) -> None: ...
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    def CalculateAdvectionImage(self) -> None: ...
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    def Initialize(self, radius: RadiusType) -> None: ...
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class GeodesicActiveContourLevelSetFunction[TImageType, TFeatureImageType]:
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    """Geodesic active contour level set function."""
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    def New() -> GeodesicActiveContourLevelSetFunction[TImageType, TFeatureImageType]: ...
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    def CalculateSpeedImage(self) -> None: ...
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    def CalculateAdvectionImage(self) -> None: ...
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    def Initialize(self, radius: RadiusType) -> None: ...
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class ThresholdSegmentationLevelSetFunction[TImageType, TFeatureImageType]:
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    """Threshold-based segmentation using level sets."""
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    def New() -> ThresholdSegmentationLevelSetFunction[TImageType, TFeatureImageType]: ...
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    def SetUpperThreshold(self, value: ScalarValueType) -> None: ...
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    def GetUpperThreshold(self) -> ScalarValueType: ...
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    def SetLowerThreshold(self, value: ScalarValueType) -> None: ...
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    def GetLowerThreshold(self) -> ScalarValueType: ...
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    def CalculateSpeedImage(self) -> None: ...
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    def SetEdgeWeight(self, weight: ScalarValueType) -> None: ...
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    def GetEdgeWeight(self) -> ScalarValueType: ...
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    def SetSmoothingIterations(self, iterations: int) -> None: ...
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    def GetSmoothingIterations(self) -> int: ...
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    def SetSmoothingTimeStep(self, time_step: ScalarValueType) -> None: ...
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    def GetSmoothingTimeStep(self) -> ScalarValueType: ...
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    def SetSmoothingConductance(self, conductance: ScalarValueType) -> None: ...
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    def GetSmoothingConductance(self) -> ScalarValueType: ...
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class CannySegmentationLevelSetFunction[TImageType, TFeatureImageType]:
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    """Canny edge-based level set segmentation."""
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    def New() -> CannySegmentationLevelSetFunction[TImageType, TFeatureImageType]: ...
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    def SetThreshold(self, threshold: ScalarValueType) -> None: ...
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    def GetThreshold(self) -> ScalarValueType: ...
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    def SetVariance(self, variance: double) -> None: ...
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    def GetVariance(self) -> double: ...
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    def CalculateSpeedImage(self) -> None: ...
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    def CalculateAdvectionImage(self) -> None: ...
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```
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### Boundary Conditions
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Classes that define how finite difference operations handle image boundaries.
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```python { .api }
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class ZeroFluxNeumannBoundaryCondition[TImageType]:
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    """Neumann boundary condition with zero flux (zero derivative)."""
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    def New() -> ZeroFluxNeumannBoundaryCondition[TImageType]: ...
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    def GetPixel(self, index: IndexType, image: TImageType) -> PixelType: ...
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    def GetInputRequestedRegion(self, input_requested_region: RegionType, 
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                               input_largest_region: RegionType) -> RegionType: ...
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    def RequiresCompleteNeighborhood(self) -> bool: ...
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class ConstantBoundaryCondition[TImageType]:
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    """Constant boundary condition that returns a fixed value outside the image."""
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    def New() -> ConstantBoundaryCondition[TImageType]: ...
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    def SetConstant(self, constant: PixelType) -> None: ...
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    def GetConstant(self) -> PixelType: ...
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    def GetPixel(self, index: IndexType, image: TImageType) -> PixelType: ...
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class PeriodicBoundaryCondition[TImageType]:
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    """Periodic boundary condition that wraps around image boundaries."""
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    def New() -> PeriodicBoundaryCondition[TImageType]: ...
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    def GetPixel(self, index: IndexType, image: TImageType) -> PixelType: ...
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```
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### Neighborhood Iterators
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Iterators for accessing image neighborhoods used in finite difference operations.
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```python { .api }
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class NeighborhoodIterator[TImage, TBoundaryCondition]:
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    """Iterator for read-write access to image neighborhoods."""
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    def New() -> NeighborhoodIterator[TImage, TBoundaryCondition]: ...
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    def SetRadius(self, radius: RadiusType) -> None: ...
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    def GetRadius(self) -> RadiusType: ...
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    def GoToBegin(self) -> None: ...
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    def GoToEnd(self) -> None: ...
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    def IsAtBegin(self) -> bool: ...
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    def IsAtEnd(self) -> bool: ...
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    def GetCenterPixel(self) -> PixelType: ...
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    def SetCenterPixel(self, pixel: PixelType) -> None: ...
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    def GetPixel(self, offset: OffsetType) -> PixelType: ...
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    def SetPixel(self, offset: OffsetType, pixel: PixelType) -> None: ...
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    def GetIndex(self) -> IndexType: ...
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    def SetLocation(self, index: IndexType) -> None: ...
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    def InBounds(self) -> bool: ...
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class ConstNeighborhoodIterator[TImage, TBoundaryCondition]:
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    """Iterator for read-only access to image neighborhoods."""
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    def New() -> ConstNeighborhoodIterator[TImage, TBoundaryCondition]: ...
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    def SetRadius(self, radius: RadiusType) -> None: ...
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    def GetRadius(self) -> RadiusType: ...
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    def GoToBegin(self) -> None: ...
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    def GoToEnd(self) -> None: ...
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    def IsAtBegin(self) -> bool: ...
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    def IsAtEnd(self) -> bool: ...
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    def GetCenterPixel(self) -> PixelType: ...
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    def GetPixel(self, offset: OffsetType) -> PixelType: ...
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    def GetIndex(self) -> IndexType: ...
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    def SetLocation(self, index: IndexType) -> None: ...
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```
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### Anisotropic Diffusion
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Functions for anisotropic diffusion-based image smoothing and enhancement.
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```python { .api }
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class AnisotropicDiffusionFunction[TImage]:
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    """Base class for anisotropic diffusion functions."""
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    def ComputeUpdate(self, neighborhood: NeighborhoodType, global_data: GlobalDataStruct,
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                     gd: GlobalDataStruct) -> PixelType: ...
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    def SetTimeStep(self, time_step: TimeStepType) -> None: ...
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    def GetTimeStep(self) -> TimeStepType: ...
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    def SetConductanceParameter(self, conductance: double) -> None: ...
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    def GetConductanceParameter(self) -> double: ...
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    def InitializeIteration(self) -> None: ...
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class GradientAnisotropicDiffusionFunction[TImage]:
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    """Gradient-based anisotropic diffusion function."""
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    def New() -> GradientAnisotropicDiffusionFunction[TImage]: ...
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    def ComputeUpdate(self, neighborhood: NeighborhoodType, global_data: GlobalDataStruct,
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                     gd: GlobalDataStruct) -> PixelType: ...
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class CurvatureAnisotropicDiffusionFunction[TImage]:
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    """Curvature-based anisotropic diffusion function."""
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    def New() -> CurvatureAnisotropicDiffusionFunction[TImage]: ...
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    def ComputeUpdate(self, neighborhood: NeighborhoodType, global_data: GlobalDataStruct,
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                     gd: GlobalDataStruct) -> PixelType: ...
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```
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### Morphological Operations for Level Sets
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Mathematical morphology operations adapted for level set frameworks.
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```python { .api }
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class MorphologicalWatershedFromMarkersImageFilter[TInputImage, TLabelImage]:
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    """Watershed segmentation from marker points using morphological operations."""
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    def New() -> MorphologicalWatershedFromMarkersImageFilter[TInputImage, TLabelImage]: ...
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    def SetInput1(self, input: TInputImage) -> None: ...
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    def SetInput2(self, markers: TLabelImage) -> None: ...
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    def SetMarkWatershedLine(self, flag: bool) -> None: ...
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    def GetMarkWatershedLine(self) -> bool: ...
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    def SetFullyConnected(self, flag: bool) -> None: ...  
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    def GetFullyConnected(self) -> bool: ...
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```
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## Usage Examples
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### Basic Level Set Segmentation
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```python
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import itk
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import numpy as np
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# Create a test image with a circular object
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ImageType = itk.Image[itk.F, 2]
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image = ImageType.New()
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size = itk.Size[2]([100, 100])
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region = itk.ImageRegion[2]()
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region.SetSize(size)
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image.SetRegions(region)
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image.SetSpacing([1.0, 1.0])
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image.Allocate()
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# Create a circular object
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center_x, center_y = 50, 50
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radius = 20
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for x in range(100):
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    for y in range(100):
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        idx = itk.Index[2]([x, y])
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        dist = np.sqrt((x - center_x)**2 + (y - center_y)**2)
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        if dist < radius:
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            image.SetPixel(idx, 200.0)  # Inside object
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        else:
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            image.SetPixel(idx, 50.0)   # Background
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# Create initial level set (signed distance function)
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initial_level_set = ImageType.New()
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initial_level_set.SetRegions(region)
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initial_level_set.SetSpacing([1.0, 1.0])
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initial_level_set.Allocate()
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# Initialize level set as signed distance to a smaller circle
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init_radius = 15
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for x in range(100):
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    for y in range(100):
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        idx = itk.Index[2]([x, y])
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        dist = np.sqrt((x - center_x)**2 + (y - center_y)**2)
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        signed_dist = dist - init_radius
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        initial_level_set.SetPixel(idx, signed_dist)
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# Create threshold segmentation level set function
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LevelSetFunctionType = itk.ThresholdSegmentationLevelSetFunction[ImageType, ImageType]
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level_set_function = LevelSetFunctionType.New()
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level_set_function.SetFeatureImage(image)
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level_set_function.SetPropagationWeight(1.0)
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level_set_function.SetAdvectionWeight(0.0)
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level_set_function.SetCurvatureWeight(0.1)
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level_set_function.SetUpperThreshold(150.0)
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level_set_function.SetLowerThreshold(100.0)
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# Create segmentation filter
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SegmentationFilterType = itk.SegmentationLevelSetImageFilter[ImageType, ImageType, itk.F]
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segmentation_filter = SegmentationFilterType.New()
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segmentation_filter.SetInput(initial_level_set)
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segmentation_filter.SetFeatureImage(image)
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segmentation_filter.SetSegmentationFunction(level_set_function)
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segmentation_filter.SetMaximumRMSError(0.02)
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segmentation_filter.SetNumberOfIterations(100)
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# Run segmentation
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try:
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    segmentation_filter.Update()
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    result = segmentation_filter.GetOutput()
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    print(f"Segmentation completed in {segmentation_filter.GetElapsedIterations()} iterations")
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    print(f"Final RMS error: {segmentation_filter.GetRMSChange():.6f}")
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except Exception as e:
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    print(f"Segmentation failed: {e}")
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```
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### Anisotropic Diffusion
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```python
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import itk
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import numpy as np
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# Create noisy test image
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ImageType = itk.Image[itk.F, 2] 
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image = ImageType.New()
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size = itk.Size[2]([100, 100])
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region = itk.ImageRegion[2]()
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region.SetSize(size)
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image.SetRegions(region)
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image.Allocate()
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# Create image with edges and noise
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np.random.seed(42)
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for x in range(100):
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    for y in range(100):
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        idx = itk.Index[2]([x, y])
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        # Create step edges
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        base_value = 100.0 if x > 50 else 50.0
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        if y > 50:
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            base_value += 75.0
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        # Add noise
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        noise = np.random.normal(0, 10)
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        value = base_value + noise
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        image.SetPixel(idx, value)
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# Create anisotropic diffusion filter
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DiffusionFilterType = itk.GradientAnisotropicDiffusionImageFilter[ImageType, ImageType]
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diffusion_filter = DiffusionFilterType.New()
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diffusion_filter.SetInput(image)
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diffusion_filter.SetNumberOfIterations(20)
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diffusion_filter.SetTimeStep(0.0625)  # Should be <= 0.25 for stability in 2D
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diffusion_filter.SetConductanceParameter(3.0)
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# Run diffusion
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diffusion_filter.Update()
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smoothed_image = diffusion_filter.GetOutput()
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print(f"Anisotropic diffusion completed")
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print(f"Iterations: {diffusion_filter.GetElapsedIterations()}")
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print(f"Final RMS change: {diffusion_filter.GetRMSChange():.6f}")
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# Compare original and smoothed values at a few points
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test_points = [
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    itk.Index[2]([25, 25]),  # Uniform region
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    itk.Index[2]([50, 25]),  # Vertical edge
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    itk.Index[2]([25, 50]),  # Horizontal edge
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    itk.Index[2]([50, 50])   # Corner
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]
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for idx in test_points:
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    original = image.GetPixel(idx)
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    smoothed = smoothed_image.GetPixel(idx)
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    print(f"Point {idx}: Original={original:.1f}, Smoothed={smoothed:.1f}")
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```
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### Shape Detection Level Set
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```python
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import itk
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import numpy as np
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# Create feature image with edge information
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ImageType = itk.Image[itk.F, 2]
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feature_image = ImageType.New()
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size = itk.Size[2]([80, 80])
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region = itk.ImageRegion[2]()
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region.SetSize(size)
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feature_image.SetRegions(region)
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feature_image.SetSpacing([1.0, 1.0])
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feature_image.Allocate()
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# Create edge map (lower values at edges)
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center_x, center_y = 40, 40
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radius = 25
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for x in range(80):
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    for y in range(80):
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        idx = itk.Index[2]([x, y])
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        dist = np.sqrt((x - center_x)**2 + (y - center_y)**2)
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        # Create edge feature: low values at circle boundary
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        edge_strength = abs(dist - radius)
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        edge_feature = 1.0 / (1.0 + edge_strength)  # High at edges
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        speed = 1.0 - edge_feature  # Low speed at edges (for stopping)
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        feature_image.SetPixel(idx, speed)
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# Create initial level set (smaller circle inside)
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initial_level_set = ImageType.New()
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initial_level_set.SetRegions(region)
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initial_level_set.SetSpacing([1.0, 1.0])
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initial_level_set.Allocate()
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init_radius = 15
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for x in range(80):
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    for y in range(80):
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        idx = itk.Index[2]([x, y])
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        dist = np.sqrt((x - center_x)**2 + (y - center_y)**2)
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        signed_dist = init_radius - dist  # Negative outside, positive inside
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        initial_level_set.SetPixel(idx, signed_dist)
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# Create shape detection level set function
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ShapeDetectionType = itk.ShapeDetectionLevelSetFunction[ImageType, ImageType]
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shape_function = ShapeDetectionType.New()
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shape_function.SetFeatureImage(feature_image)
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shape_function.SetPropagationWeight(1.0)
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shape_function.SetAdvectionWeight(0.0)
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shape_function.SetCurvatureWeight(0.05)
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# Create shape detection filter
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FilterType = itk.ShapeDetectionLevelSetImageFilter[ImageType, ImageType]
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shape_filter = FilterType.New()
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shape_filter.SetInput(initial_level_set)
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shape_filter.SetFeatureImage(feature_image)
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shape_filter.SetSegmentationFunction(shape_function)
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shape_filter.SetMaximumRMSError(0.01)
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shape_filter.SetNumberOfIterations(100)
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# Run shape detection
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shape_filter.Update()
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result = shape_filter.GetOutput()
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print(f"Shape detection completed in {shape_filter.GetElapsedIterations()} iterations")
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print(f"Final RMS error: {shape_filter.GetRMSChange():.6f}")
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# Extract zero level set (the detected shape boundary)
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ThresholdFilterType = itk.BinaryThresholdImageFilter[ImageType, itk.Image[itk.UC, 2]]
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threshold_filter = ThresholdFilterType.New()
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threshold_filter.SetInput(result)
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threshold_filter.SetLowerThreshold(-1000.0)
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threshold_filter.SetUpperThreshold(0.0)
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threshold_filter.SetInsideValue(255)
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threshold_filter.SetOutsideValue(0)
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threshold_filter.Update()
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binary_result = threshold_filter.GetOutput()
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print("Binary segmentation created")
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```
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### Custom Finite Difference Function
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```python
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import itk
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# This example shows the structure for creating custom finite difference functions
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# Note: In practice, you would typically use existing ITK functions
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class CustomDiffusionFunction(itk.FiniteDifferenceFunction[itk.Image[itk.F, 2]]):
491
    """Custom diffusion function example (simplified)."""
492
    
493
    def __init__(self):
494
        super().__init__()
495
        self.time_step = 0.1
496
        self.conductance = 1.0
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498
    def ComputeUpdate(self, neighborhood, global_data, gd):
499
        """Compute the update for a single pixel."""
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        # Get center pixel
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        center_pixel = neighborhood.GetCenterPixel()
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503
        # Compute gradients using neighborhood
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        dx_forward = neighborhood.GetNext(0, 1) - center_pixel  # Right neighbor
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        dx_backward = center_pixel - neighborhood.GetPrevious(0, 1)  # Left neighbor
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        dy_forward = neighborhood.GetNext(1, 1) - center_pixel  # Bottom neighbor  
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        dy_backward = center_pixel - neighborhood.GetPrevious(1, 1)  # Top neighbor
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509
        # Simple diffusion update (this is a simplified example)
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        laplacian = dx_forward + dx_backward + dy_forward + dy_backward - 4 * center_pixel
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        update = self.time_step * laplacian
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        return update
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515
    def GetRadius(self):
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        """Return the neighborhood radius."""
517
        return itk.Size[2]([1, 1])  # 3x3 neighborhood
518
    
519
    def ComputeGlobalTimeStep(self, global_data):
520
        """Return the time step for this iteration."""
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        return self.time_step
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# Example usage would involve registering this custom function
524
# with a finite difference image filter (implementation details omitted)
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print("Custom finite difference function structure defined")
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```
527

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### Working with Boundary Conditions
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```python
531
import itk
532
import numpy as np
533

534
# Create test image
535
ImageType = itk.Image[itk.F, 2]
536
image = ImageType.New()
537

538
size = itk.Size[2]([50, 50])
539
region = itk.ImageRegion[2]()
540
region.SetSize(size)
541
image.SetRegions(region)
542
image.Allocate()
543

544
# Fill with gradient
545
for x in range(50):
546
    for y in range(50):
547
        idx = itk.Index[2]([x, y])
548
        value = float(x + y)
549
        image.SetPixel(idx, value)
550

551
# Create different boundary condition objects
552
ZeroFluxType = itk.ZeroFluxNeumannBoundaryCondition[ImageType]
553
ConstantType = itk.ConstantBoundaryCondition[ImageType]
554

555
zero_flux_bc = ZeroFluxType.New()
556
constant_bc = ConstantType.New()
557
constant_bc.SetConstant(999.0)
558

559
# Create neighborhood iterators with different boundary conditions
560
NeighborhoodIteratorType = itk.NeighborhoodIterator[ImageType, ZeroFluxType]
561
radius = itk.Size[2]([1, 1])  # 3x3 neighborhood
562

563
# Iterator with zero flux boundary condition
564
zero_flux_iterator = NeighborhoodIteratorType.New()
565
zero_flux_iterator.SetRadius(radius)
566
zero_flux_iterator.SetImage(image)
567
zero_flux_iterator.SetBoundaryCondition(zero_flux_bc)
568

569
# Test boundary handling at image edge
570
edge_index = itk.Index[2]([0, 0])  # Top-left corner
571
zero_flux_iterator.SetLocation(edge_index)
572

573
print("Testing boundary conditions at corner (0,0):")
574
print(f"Center pixel: {zero_flux_iterator.GetCenterPixel()}")
575

576
# Access pixels that would be outside the image
577
# With zero flux, these should return edge values
578
for offset_x in [-1, 0, 1]:
579
    for offset_y in [-1, 0, 1]:
580
        offset = itk.Offset[2]([offset_x, offset_y])
581
        pixel_value = zero_flux_iterator.GetPixel(offset)
582
        print(f"Offset ({offset_x}, {offset_y}): {pixel_value}")
583

584
print("\nBoundary condition testing completed")
585
```
586

587
### Neighborhood Iterator Usage
588

589
```python
590
import itk
591

592
# Create test image
593
ImageType = itk.Image[itk.F, 2]
594
image = ImageType.New()
595

596
size = itk.Size[2]([20, 20])
597
region = itk.ImageRegion[2]()
598
region.SetSize(size)
599
image.SetRegions(region)
600
image.Allocate()
601

602
# Fill with simple pattern
603
for x in range(20):
604
    for y in range(20):
605
        idx = itk.Index[2]([x, y])
606
        value = float(x * y)
607
        image.SetPixel(idx, value)
608

609
# Create neighborhood iterator
610
BoundaryConditionType = itk.ZeroFluxNeumannBoundaryCondition[ImageType]
611
IteratorType = itk.NeighborhoodIterator[ImageType, BoundaryConditionType]
612

613
boundary_condition = BoundaryConditionType.New()
614
iterator = IteratorType.New()
615
iterator.SetRadius(itk.Size[2]([1, 1]))  # 3x3 neighborhood
616
iterator.SetImage(image)
617
iterator.SetBoundaryCondition(boundary_condition)
618

619
# Perform a simple averaging filter
620
output_image = ImageType.New()
621
output_image.SetRegions(region)
622
output_image.Allocate()
623

624
# Iterate through all pixels
625
for iterator.GoToBegin(); not iterator.IsAtEnd(); iterator.__iadd__(1):
626
    # Compute local average
627
    total = 0.0
628
    count = 0
629
    
630
    # Sum all pixels in neighborhood
631
    for i in range(iterator.Size()):
632
        total += iterator.GetPixel(i)
633
        count += 1
634
    
635
    average = total / count
636
    
637
    # Set output pixel
638
    output_image.SetPixel(iterator.GetIndex(), average)
639

640
print("Neighborhood averaging completed")
641

642
# Compare a few values
643
test_indices = [
644
    itk.Index[2]([5, 5]),
645
    itk.Index[2]([10, 10]),
646
    itk.Index[2]([15, 15])
647
]
648

649
for idx in test_indices:
650
    original = image.GetPixel(idx)
651
    smoothed = output_image.GetPixel(idx)
652
    print(f"Index {idx}: Original={original}, Smoothed={smoothed:.1f}")
653
```