understanding the topology of point-cloud surfaces via Morse theory.
Example decomposition into Morse cells of a vest and an algebraic surface.
In this project, we develop a reconstruction algorithm based on a direct topological study of a sampled surface that allows us to obtain a cellular decomposition of it via a Morse function. The results are a piecewise decomposition of the surface as a union of Morse cells (i.e. topological disks) 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. For an outline of our method see (Alberich-Carramiñana et al., 2022) and (Coltraro et al., 2023). For full details, see the pre-print bellow.
Graphical abstract of the reconstruction algorithm.
@inproceedings{MorseCEIG,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 Amor\'os, Jaume and Alberich-Carrami\~{n}ana, Maria and Torras, Carme},year={2023},publisher={The Eurographics Association},isbn={978-3-03868-230-1},doi={10.2312/ceig.20231146},}
2022
Morse cell decomposition and parametrization of surfaces from point-clouds
Maria Alberich-Carramiñana , Jaume Amorós , Franco Coltraro, and 2 more authors
Proceedings of XVII EACA 2022 (Encuentro Álgebra Computacional y Aplicaciones), 2022
@article{MorseEACA,title={Morse cell decomposition and parametrization of surfaces from point-clouds},author={Alberich-Carrami\~{n}ana, Maria and Amor\'os, Jaume and Coltraro, Franco and Torras, Carme and Verdaguer, Miquel},journal={Proceedings of XVII EACA 2022 (Encuentro \'Algebra Computacional y Aplicaciones)},pages={35--38},year={2022},url={http://dx.doi.org/10.6035/INFiTEC.51},}
