SmoothIsoPoints: Making PDE-based Surface Extraction from Point-based Volume Data Fast

PDE-based methods like level-set methods are a valuable and well-established approach in visualization to extract surfaces from volume data. We propose a novel method for the efficient computation of a signed-distance function to a surface in point-cloud representation and embed this method into a framework for PDE-based surface extraction from point-based volume data. This enables us to develop a fast level-set approach for extracting smooth isosurfaces from data with highly varying point density. The level-set method operates just locally in a narrow band around the zero-level set. It relies on the explicit representation of the zero-level set and the fast generation of a signed-distance function to it. A level-set step is executed in the narrow band utilizing the properties and derivatives of the signed-distance function. The zero-level set is extracted after each level-set step using direct isosurface extraction from point-based volume data. In contrast to existing methods for unstructured data which operate on implicit representations, our approach can use any starting surface for the level-set approach. Since for most applications a rough estimate of the desired surface can be obtained quickly, the overall level-set process can be shortened significantly. Additionally, we avoid the computational overhead and numerical difficulties of PDE-based reinitialization. Still, our approach achieves equivalent quality, flexibility, and robustness as existing methods for point-based volume data.