Practical considerations on Marching Cubes 33 topological correctness

Abstract

Chernyaev's Marching Cubes 33 is one of the first algorithms intended to preserve the topology of the trilinear interpolant. In this work, we address three issues with the Marching Cubes 33 algorithm, two of which are related to its original description and one that is related to its variant. In particular, we solve a problem with the core disambiguation procedure of Marching Cubes 33 that prevents the extraction of topologically correct isosurfaces for the ambiguous configuration 13.5. This work closes an existing gap in the topological correctness of Marching Cubes 33. Furthermore, we make our results reproducible, meaning that examples provided in this work can be easily explored and studied. Finally, as part of the philosophy of reproducibility, we provide a corrected version of the Marching Cubes 33 open-source implementation and access to datasets that can be used to verify the correctness of any available topologically correct isosurface extraction implementation that preserves the topology of the trilinear interpolant.

Construction of Topologically Correct and Manifold Isosurfaces

“…Manifoldness: Etiene et al [ENS*12] and Custodio et al [CEPS13] showed that manifoldness might be lost, if the topological correct triangulation of a cell introduces non‐manifold edges at cell boundary. Nelson [Nie03] presented a set of lookup tables with triangulation schemes including interior vertices generating topologically correct and consistent surfaces.…”

“…Whereas manifoldness can be solved by a carefully triangulation of the cell satisfying the conditions imposed by the asymptotic decider [NH91], guaranteeing topological correctness is a much more difficult problem. After the Chernyaev's MC33 appeared much effort has been spent in the development of new lookup tables and deciders to tackle topological correctness, [CGMS00, Nie03, CEPS13, LB03].…”

A “loop” shape descriptor and its application to automated segmentation of airways from CT scans

“…This step limits the image analysis within the lung regions and meanwhile improves the efficiency in memory and time. Second, the marching cubes algorithm (MCA) [36][37][38] is used to model the 3D lung anatomical structures as a triangle mesh surface, where airways, vessels, and other diseased or noisy regions (e.g., emphysema) are modeled [Figs. 2(c) and 2(d)].…”

A Evolução do Algoritmo Marching Cubes

“…Na Figura (1) apresentamos malhas extraídas do dado Bonsai, referentes aos isovalores 130, 70 e 30, utilizando a versão de Custodio et al [2] do algortimo Marching Cubes.…”