Featuresensitive 3D Shape Matching

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Featuresensitive 3D Shape Matching

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Shape matching measures similarity distance between shapes. Common distance ... 88] [Vriend et. al 91] [Fischer 92] [Taylor 92] [Yee et. al 93] [Holm et. al 93] ... – PowerPoint PPT presentation

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Title: 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

7
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

10
Matching Algorithm

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

11
Weighted distance metric

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

12
Feature Enhanced Database
13
Topology Shape Queries
14
Feature Shape Queries
15
Matching inside a molecular family
features similarity geometric similarity
16
Matching inside a molecular family
features similarity geometric similarity
17
Matching of dissimilar molecules
features similarity geometric similarity
18