Feature sensitive 3d shape matching
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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 l.jpg

Feature-sensitive 3D Shape Matching

Andrei Sharf

Tel-Aviv University

Ariel Shamir

IDC Hertzliya


Introduction l.jpg
Introduction

  • Shape matching measures similarity distance between shapes

  • Common distance metrics:

    • Geometric

    • Volumetric

    • User defined

  • No unique measure defines shape similarity


Motivation l.jpg
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 l.jpg
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 l.jpg
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 l.jpg

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 l.jpg
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 l.jpg

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 l.jpg
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 l.jpg
Matching Algorithm

  • Initial best match

  • Descend hierarchy

  • Inherit match

  • Refine match among descendant spheres

  • Refine alignment based on new match


Weighted distance metric l.jpg
Weighted distance metric

  • π(pi, qj): geometric distance

  • |Vi-Vj|: volume difference

  • Dt(si, sj): topology/feature distance



Topology shape queries l.jpg

topology weight

geometry weight

Topology Shape Queries


Feature shape queries l.jpg

sharpness weight

geometry weight

Feature Shape Queries


Matching inside a molecular family l.jpg
Matching inside a molecular family

features similarity

geometric similarity


Slide16 l.jpg

Matching inside a molecular family

features similarity

geometric similarity


Matching of dissimilar molecules l.jpg
Matching of dissimilar molecules

features similarity

geometric similarity



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