Last update: May 2004

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3D Shape Representation based on Shocks

Frederic F. Leymarie and Benjamin B. Kimia

NB: All our datasets are made of 3D points ([x,y,z] floating pt. coordinates) for which we do NOT know (or do not assume to know) a priori the connectivity; i.e., these are unorganized 3D clouds of samples.

  • Box
  • Bunny
  • David's face
  • Dendritic Spine
  • Knot
  • Man
  • Pottery sherd
  • Toutatis asteroid
  • Venus' face
  • V-gutter
  • 3D Transitions

    • Aorta data :

    Dataset ( CT scan of a human aorta) a courtesy of Dr. Verroust and Dr. Lazarus from the INRIA, France.

    Box data :

    Bunny data :

    Dataset a courtesy of the Stanford Graphics group, USA.

    David data :

    Dataset a courtesy of the Stanford Graphics group, USA.

    Dendritic Spine data :

    Dataset a courtesy of the Department of Neuroscience @ Brown.

    Man data :

    Dataset a courtesy of Cyberware, Inc., USA.

    Knot data :

    Sherd data :

    Toutatis asteroid data :

    Dataset a courtesy of Scott Hudson, Washington State University.

    Venus data :

    V-gutter data :

    3D Transitions :

    Arnold et al., Bogaevski, and more recently Giblin & Kimia, showed that only a small family of seven transitions of the 3D MA are possible under perturbations - we study these.

    1. A_1 A_3 - I Transition : protrusion-like event
    2. A_1 A_3 - II : pulling apart-like event
    3. A_1^5 Transition : Squashed Prism
    4. A_1^4 Transition : Squeezed tube
    5. A_5 : tube with ridges
    6. A_1^2 A_3 - I : protrusion near axis
    7. A_1^2 A_3 - II : protrusion thru axis

    April 2002 -> May 2004

    F.F.Leymarie

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