Variational Level-Set Detection of Local Isosurfaces from Unstructured Point-based Volume Data

Abstract

A standard approach for visualizing scalar volume data is the extraction of isosurfaces. The most efficient methods for surface extraction operate on regular grids. When data is given on unstructured point-based samples, regularization can be applied but may introduce interpolation errors. We propose a method for smooth isosurface visualization that operates directly on unstructured point-based volume data avoiding any resampling. We derive a variational formulation for smooth local isosurface extraction using an implicit surface representation in form of a level-set approach, deploying Moving Least Squares (MLS) approximation, and operating on a kd-tree. The locality of our approach has two aspects: first, our algorithm extracts only those components of the isosurface, which intersect a subdomain of interest; second, the action of the main term in the governing equation is concentrated near the current isosurface position. Both aspects reduce the computation times per level-set iteration. As for most level-set methods a reinitialization
procedure is needed, but we also consider a modified algorithm where this step is eliminated. The final isosurface is extracted in form of a point cloud representation. We present a novel point completion
scheme that allows us to handle highly adaptive point sample distributions. Subsequently, splat-based or mere (shaded) point rendering is applied. We apply our method to several synthetic and real-world data sets to demonstrate its validity and efficiency.