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Robust Poisson Surface Reconstruction

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Scale Space and Variational Methods in Computer Vision (SSVM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9087))

Abstract

We propose a method to reconstruct surfaces from oriented point clouds with non-uniform sampling and noise by formulating the problem as a convex minimization that reconstructs the indicator function of the surface’s interior. Compared to previous models, our reconstruction is robust to noise and outliers because it substitutes the least-squares fidelity term by a robust Huber penalty; this allows to recover sharp corners and avoids the shrinking bias of least squares. We choose an implicit parametrization to reconstruct surfaces of unknown topology and close large gaps in the point cloud. For an efficient representation, we approximate the implicit function by a hierarchy of locally supported basis elements adapted to the geometry of the surface. Unlike ad-hoc bases over an octree, our hierarchical B-splines from isogeometric analysis locally adapt the mesh and degree of the splines during reconstruction. The hierarchical structure of the basis speeds-up the minimization and efficiently represents clustered data. We also advocate for convex optimization, instead isogeometric finite-element techniques, to efficiently solve the minimization and allow for non-differentiable functionals. Experiments show state-of-the-art performance within a more flexible framework.

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Author information

Authors and Affiliations

  1. Univeristy of California, Los Angeles, USA

    Virginia Estellers & Stefano Soatto

  2. Brigham Young University, Provo, USA

    Michael Scott & Kevin Tew

Authors
  1. Virginia Estellers
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  2. Michael Scott
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  3. Kevin Tew
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  4. Stefano Soatto
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Corresponding author

Correspondence to Virginia Estellers .

Editor information

Editors and Affiliations

  1. University of Bordeaux, Talence, France

    Jean-François Aujol

  2. ENS Cachan, Cachan, France

    Mila Nikolova

  3. University of Bordeaux, Talence, France

    Nicolas Papadakis

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© 2015 Springer International Publishing Switzerland

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Estellers, V., Scott, M., Tew, K., Soatto, S. (2015). Robust Poisson Surface Reconstruction. In: Aujol, JF., Nikolova, M., Papadakis, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2015. Lecture Notes in Computer Science(), vol 9087. Springer, Cham. https://doi.org/10.1007/978-3-319-18461-6_42

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  • DOI: https://doi.org/10.1007/978-3-319-18461-6_42

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-18461-6

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