Surface reconstruction of sampled textiles via Morse theory
<|reference_start|>Surface reconstruction of sampled textiles via Morse theory: In this work, we study the perception problem for garments using tools from computational topology: the identification of their geometry and position in space from point-cloud samples, as obtained e.g. with 3D scanners. We present a reconstruction algorithm based on a direct topological study of the sampled textile surface that allows us to obtain a cellular decomposition of it via a Morse function. No intermediate triangulation or local implicit equations are used, avoiding reconstruction-induced artifices. No a priori knowledge of the surface topology, density or regularity of the point-sample is required to run the algorithm. The results are a piecewise decomposition of the surface as a union of Morse cells (i.e. topological disks), 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.<|reference_end|>
@article{coltraro2024topological,
    title={Topological reconstruction of sampled surfaces via Morse theory},
    author={Franco Coltraro, Jaume Amor'os, Maria Alberich-Carrami~nana, Carme
  Torras},
    journal={arXiv preprint arXiv:2405.17257},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.17257},
    primaryClass={cs.CG cs.CV math.AT}
}