Reconstruction of sampled surfaces with boundary via Morse theory

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Date
2023
Authors
Coltraro, Franco
Amorós, Jaume
Alberich-Carramiñana, Maria
Torras, Carme
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
We study the perception problem for garments (e.g. a pair of pants) using tools from computational topology: the identification of their geometry and position from point-cloud samples, as obtained e.g. with 3D scanners. We present a reconstruction algorithm based on Morse theory that proceeds directly from the point-cloud to obtain a cellular decomposition of the surface derived via a Morse function. No intermediate triangulation or local implicit equations are used, avoiding reconstruction-induced artifices. The results are a piecewise parametrization of the surface as a union of Morse cells, suitable for tasks such as noise-filtering or mesh-independent reparametrization, and a cell complex of small rank determining the surface topology. This algorithm can be applied to smooth surfaces with or without boundary, embedded in an ambient space of any dimension.
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@inproceedings{
10.2312:ceig.20231146
,
booktitle = {
Spanish Computer Graphics Conference (CEIG)
},
editor = {
Gimeno Sancho, Jesús
 and 
Comino Trinidad, Marc
},
title = {{
Reconstruction of sampled surfaces with boundary via Morse theory
}},
author = {
Coltraro, Franco
 and 
Amorós, Jaume
 and 
Alberich-Carramiñana, Maria
 and 
Torras, Carme
},
year = {
2023
},
publisher = {
The Eurographics Association
},
ISBN = {
978-3-03868-230-1
},
DOI = {
10.2312/ceig.20231146
}
}
Citation
URI
https://doi.org/10.2312/ceig.20231146
 https://diglib.eg.org:443/handle/10.2312/ceig20231146
Collections
CEIG2023