Separatrix Persistence: Extraction of Salient Edges on Surfaces Using Topological Methods

Authors: Weinkauf, T.; Günther, D.

Source: Computer Graphics Forum, Volume 28, Number 5, July 2009 , pp. 1519-1528(10)

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Abstract:

Salient edges are perceptually prominent features of a surface. Most previous extraction schemes utilize the notion of ridges and valleys for their detection, thereby requiring curvature derivatives which are rather sensitive to noise. We introduce a novel method for salient edge extraction which does not depend on curvature derivatives. It is based on a topological analysis of the principal curvatures and salient edges of the surface are identified as parts of separatrices of the topological skeleton. Previous topological approaches obtain results including non-salient edges due to inherent properties of the underlying algorithms. We extend the profound theory by introducing the novel concept of separatrix persistence, which is a smooth measure along a separatrix and allows to keep its most salient parts only. We compare our results with other methods for salient edge extraction.

Keywords: G.2.3 [Mathematics of Computing]: Discrete Mathema; Applications I.3.0 [Computer Graphics]: General

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-8659.2009.01528.x

Affiliations: 1: Zuse Institute Berlin, Germany

Publication date: 2009-07-01