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Feature-sensitive 3D Shape Matching Andrei Sharf Tel-Aviv University Ariel Shamir IDC Hertzliya Introduction Shape matching measures similarity distance between shapes Common distance metrics: Geometric Volumetric User defined No unique measure defines shape similarity Motivation

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feature sensitive 3d shape matching

Feature-sensitive 3D Shape Matching

Andrei Sharf

Tel-Aviv University

Ariel Shamir

IDC Hertzliya

introduction
Introduction
  • Shape matching measures similarity distance between shapes
  • Common distance metrics:
    • Geometric
    • Volumetric
    • User defined
  • No unique measure defines shape similarity
motivation
Motivation

Goal: enhanced similarity measures

Motivation:

  • Discrimination of complex shapes:
    • Complex topology models
    • CAD models
    • Molecules
  • Topology is hard (geometric matching can be assisted by user)
previous work
Previous Work
  • General Shape Matching:

[Prokop et. al 92] [Loncaric 98] [Paquet et. al 00] [Bardinet et. al 00] [Novotni et. al 01][Veltkamp 01] [Funkhouser et. al 03]

  • CAD:

[Keim 99] [Cicirello et al. 01]

  • Molecular Biology:

[Rackovsky et. al 88] [Vriend et. al 91] [Fischer 92] [Taylor 92] [Yee et. al 93] [Holm et. al 93]

  • Topological Matching:

Topology matching for fully automatic similarity estimation of 3D shapes [Hilaga et. al 01]

overview
Overview
  • Topology and features are extracted from shape representation
    • Shape is represented with Union of Spheres and dual skeleton zero-alpha-complex
  • Feature sensitive multi-resolution hierarchy
    • Decimation operations preserve topology and features structure
  • Metric accounts features distance
    • Weighted distance
shape features
Holes

Rings

Tunnels

Shape Features
  • Topological features:
    • 0 - connected components
    • 1 - holes
    • 2 - voids
  • Sharp features
  • User defined
union of spheres and zero alpha complex
Union of Spheres and Zero-Alpha-Complex

Union of Spheres are topological equivalent to zero-alpha-complex

Topological features are easy to compute on zero-alpha-complex

Union of Spheres are extracted using distance transform

slide8
Feature-sensitive Multi-resolution
  • Topology constrain:
    • clustering of shortest alpha-edge
  • Feature separation:
    • clustering inside a feature
    • propagate features properties to enclosing ball
feature sensitive adaptive cut
Feature-sensitive adaptive cut
  • Shape matching performs from coarse to fine
  • Match result is most influenced by coarse levels match
  • Feature approximation: shape approximation should correspond to distance metric
matching algorithm
Matching Algorithm
  • Initial best match
  • Descend hierarchy
  • Inherit match
  • Refine match among descendant spheres
  • Refine alignment based on new match
weighted distance metric
Weighted distance metric
  • π(pi, qj): geometric distance
  • |Vi-Vj|: volume difference
  • Dt(si, sj): topology/feature distance
matching inside a molecular family
Matching inside a molecular family

features similarity

geometric similarity

slide16
Matching inside a molecular family

features similarity

geometric similarity

matching of dissimilar molecules
Matching of dissimilar molecules

features similarity

geometric similarity

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