Poset approach to 3D parallel thinning

Christophe Lohou; Gilles Bertrand

doi:10.1117/12.364107

23 September 1999 Poset approach to 3D parallel thinning

Christophe Lohou, Gilles Bertrand

Proceedings Volume 3811, Vision Geometry VIII; (1999) https://doi.org/10.1117/12.364107
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

One of the authors has proposed a study of homotopy and simplicity in partially ordered sets (or posets). The notion of unipolar point was introduced: a unipolar point can be seen as an 'inessential' element for the topology. Thus, the iterative deletion of unipolar points constitutes a first thinning algorithm. We show in this paper, that such an algorithm does not 'thin enough' certain images. This is the reason why we use the notion of (alpha) -simple point, introduced in the framework of posets, in Ref. 1. The definition of such a point is recursive. As we can locally decide whether a point is (alpha) -simple, we can use classical techniques (such as a binary decision diagram) to characterize them more quickly. Furthermore, it is possible to remove in parallel (alpha) -simple points in a poset, while preserving the topology of the image. Then, we discuss the characterization of end points in order to produce various skeletons. Particularly, we propose a new approach to characterize surface end points. This approach permits us to keep certain junctions of surfaces. Then, we propose very simple parallel algorithms based on the deletion of (alpha) - simple points, consisting in the repetition of two subiterations.

Citation Download Citation

Christophe Lohou and Gilles Bertrand "Poset approach to 3D parallel thinning", Proc. SPIE 3811, Vision Geometry VIII, (23 September 1999); https://doi.org/10.1117/12.364107

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