@article{SKRODZKI2020101875,
title = "Variational shape approximation of point set surfaces",
journal = "Computer Aided Geometric Design",
volume = "80",
pages = "101875",
year = "2020",
issn = "0167-8396",
doi = "https://doi.org/10.1016/j.cagd.2020.101875",
url = "http://www.sciencedirect.com/science/article/pii/S0167839620300625",
author = "Martin Skrodzki and Eric Zimmermann and Konrad Polthier",
keywords = "Variational shape approximation, Point set segmentation, Simplification",
abstract = "In this work, we present a translation of the complete pipeline for variational shape approximation (VSA) to the setting of point sets. First, we describe an explicit example for the theoretically known non-convergence of the currently available VSA approaches. The example motivates us to introduce an alternate version of VSA based on a switch operation for which we prove convergence. Second, we discuss how two operations—split and merge—can be included in a fully automatic pipeline that is in turn independent of the placement and number of initial seeds. Third and finally, we present two approaches how to obtain a simplified mesh from the output of the VSA procedure. This simplification is either based on simple plane intersection or based on a variational optimization problem. Several qualitative and quantitative results prove the relevance of our approach."
}