Featuresensitive 3D Shape Matching

1
Feature-sensitive 3D Shape Matching

• Andrei Sharf
• Tel-Aviv University

Ariel Shamir IDC Hertzliya
2
Introduction

• Shape matching measures similarity distance
  between shapes
• Common distance metrics
• Geometric
• Volumetric
• User defined
• No unique measure defines shape similarity

3
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)

4
Previous Work

• General Shape Matching
• Prokop et. al 92 Loncaric 98 Paquet et. al
  00 Bardinet et. al 00 Novotni et. al
  01Veltkamp 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

5
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

6
Shape Features

• Topological features
• ?0 - connected components
• ?1 - holes
• ?2 - voids
• Sharp features
• User defined

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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

8
Feature-sensitive Multi-resolution

• Topology constrain
• clustering of shortest alpha-edge
• Feature separation
• clustering inside a feature
• propagate features properties to enclosing ball

9
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

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Matching Algorithm

• Initial best match
• Descend hierarchy
• Inherit match
• Refine match among descendant spheres
• Refine alignment based on new match

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Weighted distance metric

• p(pi, qj) geometric distance
• Vi-Vj volume difference
• Dt(si, sj) topology/feature distance

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Feature Enhanced Database
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Topology Shape Queries
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Feature Shape Queries
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Matching inside a molecular family
features similarity geometric similarity
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Matching inside a molecular family
features similarity geometric similarity
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Matching of dissimilar molecules
features similarity geometric similarity
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• The End