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Bayesian closed surface fitting through tensor products

Publication ,  Journal Article
Binette, O; Pati, D; Dunson, DB
Published in: Journal of Machine Learning Research
July 1, 2020

Closed surfaces provide a useful model for 3-d shapes, with the data typically consisting of a cloud of points in R3. The existing literature on closed surface modeling focuses on frequentist point estimation methods that join surface patches along the edges, with surface patches created via Bezier surfaces or tensor products of B-splines. However, the resulting surfaces are not smooth along the edges and the geometric constraints required to join the surface patches lead to computational drawbacks. In this article, we develop a Bayesian model for closed surfaces based on tensor products of a cyclic basis resulting in infinitely smooth surface realizations. We impose sparsity on the control points through a doubleshrinkage prior. Theoretical properties of the support of our proposed prior are studied and it is shown that the posterior achieves the optimal rate of convergence under reasonable assumptions on the prior. The proposed approach is illustrated with some examples.

Duke Scholars

Published In

Journal of Machine Learning Research

EISSN

1533-7928

ISSN

1532-4435

Publication Date

July 1, 2020

Volume

21

Start / End Page

1 / 26

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4905 Statistics
  • 4611 Machine learning
  • 17 Psychology and Cognitive Sciences
  • 08 Information and Computing Sciences
 

Citation

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MLA
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Binette, O., Pati, D., & Dunson, D. B. (2020). Bayesian closed surface fitting through tensor products. Journal of Machine Learning Research, 21, 1–26.
Binette, O., D. Pati, and D. B. Dunson. “Bayesian closed surface fitting through tensor products.” Journal of Machine Learning Research 21 (July 1, 2020): 1–26.
Binette O, Pati D, Dunson DB. Bayesian closed surface fitting through tensor products. Journal of Machine Learning Research. 2020 Jul 1;21:1–26.
Binette, O., et al. “Bayesian closed surface fitting through tensor products.” Journal of Machine Learning Research, vol. 21, July 2020, pp. 1–26.
Binette O, Pati D, Dunson DB. Bayesian closed surface fitting through tensor products. Journal of Machine Learning Research. 2020 Jul 1;21:1–26.

Published In

Journal of Machine Learning Research

EISSN

1533-7928

ISSN

1532-4435

Publication Date

July 1, 2020

Volume

21

Start / End Page

1 / 26

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4905 Statistics
  • 4611 Machine learning
  • 17 Psychology and Cognitive Sciences
  • 08 Information and Computing Sciences