Wavelet SDF-Reps: Solid Modeling With Volumetric Scans

This paper describes a new formulation of solid modeling that addresses the issue of including parts whose geometry is determined from volumetric scans (CT, MRI, PET, etc.) along with parts whose geometry is designed by traditional computer-aided design (CAD) operations. Such issues arise frequently in the design of medical devices or prostheses where fit and/or interference between man-made artifacts and existing anatomy are essential considerations, but the modeling formulation presented is not limited to medical applications and can be applied to any parts whose volume can be actually or virtually scanned. Scanner data typically comprises a grid of intensity values and segmentation must be performed to determine the extent of the part. In current practice, the segmented scanner data is run through a polygonizer to obtain an approximate tessellation of the object’s surface. Even in the best case scenario where the triangles obtained form a closed surface that accurately approximates the surface of the scanned object, such triangulated models can be problematic due to excessive size. We present an alternative approach based on recent advances in segmentation with level set methods. The output of the level set computation is a grid of approximate values for the signed distance from each grid point to the nearest point on the surface of the scanned object. We propose interpolating the grid of signed distance values to obtain an implicit or function-based representation (f-rep) for the object, and we introduce appropriate wavelets to effectively perform the interpolation while also providing a number of other useful properties including data compression, inherently multi-scale modeling, and capabilities for skeletal-based modeling operations.