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A topological approach for surface reconstruction from sample points

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Abstract

Most algorithms for surface reconstruction from sample points rely on computationally demanding operations to derive the reconstruction. In this paper we introduce an innovative approach for generating 3D piecewise linear approximations from sample points that relies strongly on topological information, thus reducing the computational cost and numerical instabilities typically associated with geometric computations. Discrete Morse theory provides the basis for a topological framework that supports a robust reconstruction algorithm capable of handling multiple components and has low computational cost. We describe the proposed approach and introduce the reconstruction algorithm, called TSR – topological surface reconstructor. Some reconstruction results are presented and the performance of TSR is compared with that of other reconstruction approaches for some standard point sets.

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Authors and Affiliations

  1. Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Bettio, 1000, São Paulo, SP, 03828-000, Brazil

    Helton Hideraldo Bíscaro

  2. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Av. Trabalhador São-carlense, 400, Centro Caixa Postal: 668, São Carlos, SP, 13560-970, Brazil

    Antonio Castelo Filho, Luis Gustavo Nonato & Maria Cristina Ferreira de Olivira

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  1. Helton Hideraldo Bíscaro
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  2. Antonio Castelo Filho
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  3. Luis Gustavo Nonato
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  4. Maria Cristina Ferreira de Olivira
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Correspondence to Helton Hideraldo Bíscaro.

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Bíscaro, H., Filho, A., Nonato, L. et al. A topological approach for surface reconstruction from sample points. Visual Comput 23, 793–801 (2007). https://doi.org/10.1007/s00371-007-0134-7

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