Topological features constitute the highest abstraction in object representation. Euler characteristic is one of the most widely used topological invariants. The computation of the Euler characteristic is mainly based on three well-known mathematical formulae, which calculate either on the boundary of object or on the whole object. However, as digital objects are often non-manifolds, none of the known formulae can correctly compute the genus of digital surfaces. In this paper, we show that a new topological surface invariant of 3D digital objects, called BIUP/sup 3/, can be obtained through a special homeomorphic transform: front propagation at a constant speed. BIUP/sup 3/ overcomes the theoretic weakness of the Euler characteristic and it applies to both manifolds and non-manifolds. The computation of BIUP/sup 3/ can be done efficiently through a virtual front propagation, leaving the images unaffected.
X. F. Liu, "BIUP3: Boundary Topological Invariant of 3D Objects Through Front Propagation at a Constant Speed," Proceedings of the Geometric Modeling and Processing, 2004, Institute of Electrical and Electronics Engineers (IEEE), Jan 2004.
The definitive version is available at https://doi.org/10.1109/GMAP.2004.1290062
Geometric Modeling and Processing, 2004
Keywords and Phrases
3D Digital Objects; 3D Objects; BIUP/Sup 3/; Euler Characteristic; Boundary Topological Invariant; Computational Geometry; Computer Graphics; Constant Speed; Digital Surfaces; Digital Topology; Homeomorphic Transform; Mathematical Formulae; Object Boundary; Object Representation; Topological Features; Topological Surface Invariant; Topology; Virtual Front Propagation
Article - Conference proceedings
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