Deformable Surfaces for Feature Based Indirect Volume Rendering

In this paper we present an indirect volume visualization method, based on the deformable surface model, which is a three dimensional extension of the snake segmentation method. In contrast to classical indirect volume visualization methods, this model is not based on iso-values but on boundary information. Physically speaking it simulates a combination of a thin plate and a rubber skin, that is influenced by forces implied by feature information extracted from the given data set. The approach proves to be appropriate for data sets that represent a collection of objects separated by distinct boundaries. These kind of data sets often occur in medical and technical tomography, as we will demonstrate by a few examples. We propose a multilevel 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. This functional tends to produce very regular triangular meshes compared to results of the marching cubes algorithm. It makes this method attractive for meshing in numerical simulation or texture mapping. Red-green triangulation allows an adaptive refinement of the mesh. Special considerations have been made to prevent self inter-penetration of the surfaces.