ENH: Add vtkScatteredBSplineTransform

[lassoan]

Adds vtkScatteredBSplineTransform, a cubic B-spline transform fitted to displacement vectors given at the points of any vtkPointSet (surface mesh, volumetric mesh, or point cloud). Once fitted, the transform can be evaluated and inverted anywhere in space, not only at the input points.

This is needed to show a displacement field that is only known at the points of a mesh, for example in Slicer slice views. vtkProbeFilter can only interpolate inside the cells of a volumetric mesh, so it returns nothing for a surface mesh or a point cloud.

Method

• Fitting: coefficients are computed with the multilevel B-spline approximation (MBA) of Lee, Wolberg and Shin (IEEE TVCG 1997). A coarse control point lattice is fitted first, then the lattice is repeatedly refined (halving the spacing) and fitted to the remaining residual. Refinement stops when the largest residual at the input points is below Tolerance, or when MaximumNumberOfLevels or MinimumControlPointSpacing is reached.
• Basis: the implementation follows the algorithm in the ScatteredTransform extension, specialized to 3D. It writes the coefficients directly into the vtkImageData that vtkBSplineTransform uses, with no reindexing, because VTK and MBA use the same cubic B-spline basis functions in the same order.
• Base class: it derives from vtkOrientedBSplineTransform, so the result can be stored in a vtkMRMLBSplineTransformNode and written to an ITK transform file.

Options

• DisplacementArrayName: the point data array to fit. If it is not set, the active vectors are used.
• ControlPointSpacing: the spacing of the coarsest lattice. The default is 1/10 of the fitting domain.
• MinimumControlPointSpacing, MaximumNumberOfLevels, Tolerance: these limit refinement.
• UseLinearApproximation: seeds the coarsest level with a least-squares linear fit, so the transform extrapolates the overall trend outside the sampled region instead of flattening out.
• GridBounds / AutomaticGridBounds: the fitting domain. By default it is the bounds of the input points.
• GetResidual() and GetNumberOfLevels(): report the accuracy and depth of the last fit.

The transform refits automatically when the input point set is modified. Invalid input is reported, and the transform is then left as identity.

Testing

vtkScatteredBSplineTransformTest1 uses a smooth analytic warp as ground truth on a surface mesh and on a hexahedral volumetric mesh. It checks:

• the fit at the mesh points, and that the reported residual matches the actual error;
• the approximation between the mesh points;
• the inverse transform;
• fallback to the active vectors;
• linear approximation;
• explicit and minimum control point spacing;
• explicit fitting bounds;
• refitting when the mesh is modified;
• DeepCopy / MakeTransform;
• handling of invalid input.

The test passes in a Slicer Release build on Windows (MSVC 2022, VTK 9.6.2).

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