SmoothIsoPoints: Making PDE-based Surface Extraction from Point-based Volume Data Fast Paul Rosenthal 1 , Vladimir Molchanov 2 and Lars Linsen 2,3 1 University of Rostock, Rostock, Germany 2 Jacobs University, Bremen, Germany 3 Westf¨ alische Wilhelms-Universit¨ at M¨ unster, M¨ unster, Germany Keywords: Surface Extraction, Isosurfaces, Level Sets, Unstructured Point-based Volume Data. Abstract: 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. 1 INTRODUCTION Many modern simulation methods generate unstruc- tured point-based volume data, i. e., scalar fields where the data points may have an arbitrary distribu- tion in a 3D space and do not exhibit any connectivity. A major group of such data stems from Lagrangian numerical simulations of natural phenomena such as fluid dynamics. They allow for the reproduction of complex natural phenomena by not only simulating the evolution of data at the sample points but also sim- ulating the flow of the sample points under respective forces. Hence, data points move over time, change their neighborhoods, and are distributed with a highly varying density. Such simulations are typically car- ried out with millions of particles. Level-set methods have a large variety of applica- tions. In scientific visualization, they are used to ex- tract boundary surfaces of features from volume data. Typically, the algorithms operate on rectilinear cells and a given initial level-set function is modified to ex- plicitly or implicitly minimize a given energy func- tional. An approach generalizing the basic idea of level sets to work directly on unstructured point-based vol- ume data was presented in (Rosenthal and Linsen, 2008b). They do not resample the data over a struc- tured grid using scattered data interpolation, which inevitably introduces resampling errors, which can grow enormously for data sets with highly varying point density, unless the sampling points are chosen very densely which lets the data size explode. un- structured points avoids this source of error. The level-set approach models the evolution of a surface by applying forces in normal direction. To allow for easy change of the topology of the sur- face, it is implicitly represented as the zero-level set of a level-set function. The evolution is carried out by transforming the level-set function using an itera- tive numerical integration scheme, which implicitly transforms the surface. The approach typically in- duces complex calculations and the evaluation of par- tial differential equations at each sample location and each iteration step. When dealing with large data sets and small time-integration steps, this can lead to enormous computation times until convergence of the level-set process. The calculations for unstructured point-based data are even more complex than those in the gridded case which was the major drawback of the method by Rosenthal and Linsen. Later, the approach was modified to utilize a narrow-band technique and significantly speed up the computations (Rosenthal Rosenthal, P., Molchanov, V. and Linsen, L. SmoothIsoPoints: Making PDE-based Surface Extraction from Point-based Volume Data Fast. DOI: 10.5220/0006537200170028 In Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2018) - Volume 3: IVAPP, pages 17-28 ISBN: 978-989-758-289-9 Copyright © 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved 17