α-Decomposition of polygons

Abstract

Decomposing a shape into visually meaningful parts comes naturally to humans, but recreating this fundamental operation in computers has been shown to be difficult. Similar challenges have puzzled researchers in shape reconstruction for decades. In this paper, we recognize the strong connection between shape reconstruction and shape decomposition at a fundamental level and propose a method called α-decomposition. The α-decomposition generates a space of decompositions parameterized by α, the diameter of a circle convolved with the input polygon. As we vary the value of α, some structural features appear and disappear quickly while others persist. Therefore, by analyzing the persistence of the features, we can determine better decompositions that are more robust to both geometrical and topological noises. © 2012 Elsevier Ltd. All rights reserved.

Document Type

Conference Proceeding

DOI

https://doi.org/10.1016/j.cag.2012.03.018

Keywords

Concavity measurement, Convolution, Geometrical and topological noises, Persistence analysis, Shape decomposition

Publication Date

1-1-2012

Journal Title

Computers and Graphics (Pergamon)

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