Hierarchical solutions for the deformable surface problem in visualization

In this paper we present a hierarchical approach for the deformable surface technique. This technique is a three dimensional extension of the snake segmentation method. We use it in the context of visualizing three dimensional scalar data sets. In contrast to classical indirect volume visualization methos, this reconstruction is not based on iso-values but on boundary information derived from discontinuities in the data. We propose a mulitlevel adaptive finite difference solver, which generates a target surface minimizing an energy functional based on an internal energy of the surface and an outer energy induced by the gradient of the volume. The method is attractive for preprocessing in numerical simulation or texture mapping. Red-green triangulation allows adaptive refinement of the mesh. Special considerations help to prevent self interpenetration of the surfaces. We will also show some techniques that introduce the hierarchical aspect into the inhomogeneity of the partial differential equation. The approach proves to be appropriate for data sets that contain a collection of objects separated by distinct boundaries. Thes kind of data sets often occur in medical and technical tomography, as we will demonstrate in a few examples.