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The Shock Scaffold for Representing 3D Shape

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Visual Form 2001 (IWVF 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2059))

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Abstract

The usefulness of the 3D Medial Axis (MA)is dependent on both the availability of accurate and stable methods for computing individual MA points and on schemes for deriving the local structure and connectivity among these points. VVc propose a framework which achieves both by combining the advantages of exact bisector computations used in computational geometry: on the one hand, and the local nature of propagation-based algorithms, on the other, but without the computational complexity, connectivity, added dimensionality, and post processing issues commonly found in these approaches. Specifically, the notion of flow of shocks along the MA manifold is used to identify flow along special points and curves which define a shock scaffold. This 1D scaffold is of lower dimensional complexity than the typical geometric locus of medial points which are represented as 2D sheets. The scaffold not only organizes shape information in a hierarchical manner, but is a tool for the efficient recovery of the scaffold itself and can lead to exact reconstruction. VVe present examples of this approach for synthetic data, as well as for sherd data from the domain of digital archaeology.

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Author information

Authors and Affiliations

  1. Division of Engineering, Brown University, Providence, RI, USA

    Frederic F. Leymarie & Benjamin B. Kimia

Authors
  1. Frederic F. Leymarie
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  2. Benjamin B. Kimia
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Editor information

Editors and Affiliations

  1. Istituto di Cibernetica, Via Toiano 6, 80072, Arco Felice (Naples), Italy

    Carlo Arcelli  & Gabriella Sanniti di Baja  & 

  2. Dipartimento di Informatica e Sitemistica, Universitá di Napoli “Frederico II”, Via Claudio 21, 80125, Naples, Italy

    Luigi P. Cordella

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© 2001 Springer-Verlag Berlin Heidelberg

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Leymarie, F.F., Kimia, B.B. (2001). The Shock Scaffold for Representing 3D Shape. In: Arcelli, C., Cordella, L.P., di Baja, G.S. (eds) Visual Form 2001. IWVF 2001. Lecture Notes in Computer Science, vol 2059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45129-3_19

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  • DOI: https://doi.org/10.1007/3-540-45129-3_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42120-7

  • Online ISBN: 978-3-540-45129-7

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