Reconstruction of sampled surfaces with boundary via Morse theory

Conference Article


Congreso Español de Informática Gráfica (CEIG)





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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.


computer vision, object recognition.

Author keywords

computational topology; Morse functions; surface reconstruction; point-clouds

Scientific reference

F. Coltraro, J. Amorós, M. Alberich-Carramiñana and C. Torras. Reconstruction of sampled surfaces with boundary via Morse theory, 2023 Congreso Español de Informática Gráfica, 2023, Mallorca, pp. 21-24.