Deformable Solid Modeling using Sampled Medial Surfaces: A Multiscale Approach Technical Report TR00-005

We introduce a multiscale approach to modeling and rendering deformable solid objects, replacing polygonal or spline-based B-reps with a medial representation (M-rep) based on hierarchically linked, discretely sampled medial figures. Each medial figure is a widthproportionally sampled medial surface which implies object boundaries within a width-proportional tolerance; boundary variations within this tolerance are specified separately by surface displacements or texture-maps. M-reps share advantages of other skeletal techniques for modeling deformable and articulated figures, but by decoupling object-shape from fine surface detail, they (a) eliminate skeletal instabilities due to small-scale boundary-perturbation, and (b) induce a natural hierarchy and level-of-detail for object-based deformations. This work discusses the theoretical foundation of M-reps, their data structures and implementation, their current use in medical-image analysis and volume rendering, and how model building and rendering are done via M-reps, using texture maps and subdivision surfaces for fine detail. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representation; Object hierarchies; Boundary representation; I.3.6 [Computer Graphics]: Methodology and Techniques—Graphics data structures and data types; I.4.8 [Image Processing and Computer Vision]: Scene Analysis—Shape; Surface fitting