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Symmetry in Shapes – Theory and Practice

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Symmetry in Shapes – Theory and Practice

Niloy Mitra Maksim Ovsjanikov Mark Pauly Michael Wand Duygu Ceylan

(2)

Presenters

Mark Pauly EPFL Lausanne Switzerland

[email protected] [email protected]

Maksim Ovsjanikov École Polytechnique LIX, France

[email protected]

Michael Wand

Saarland University,

MPI Informatik, Germany [email protected]

[email protected] Niloy Mitra

University Colledge London, UK

(3)

Course Webpage

Course Webpage

•

Tutorial slides

•

Literature & references

Linked from:

•

http://www.mpi-inf.mpg.de/~mwand/

(4)

EG 2012 STAR Report

State-of-the-Art Report from EG 2012

• Symmetry in 3D Geometry: Extraction and Applications

Niloy J. Mitra, Mark Pauly, Michael Wand, Duygu Ceylan State-of-the-art Report EUROGRAPHICS 2012

• STAR Report webpage:

http://vecg.cs.ucl.ac.uk/Projects/SmartGeometry/

symmetry_survey/symmetrySurvey_12.html

• Journal version:

http://onlinelibrary.wiley.com/doi/10.1111/

cgf.12010/abstract

Provides many more details

(5)

What we cover

Topics

• Part I: What is symmetry?

• Part II: Extrinsic symmetry detection

• Part III: Intrinsic symmetries

• Part IV: Representations & applications

• Conclusions, wrap-up

(6)

Part I

What is Symmetry?

• Symmetry in nature

• Formalization:

Symmetry groups

• Symmetry is the

absence of information

Dyugu / Mark

(7)

Part II

Extrinsic Symmetry Detection

• Geometric matching

• Types of symmetry

• Stages:

Feature selection

Aggregation

Extraction

• Example algorithms

Niloy

(8)

Part III

Intrinsic Symmetry Detection

• Overview: intrinsic geometry

• Intrinsic symmetries, specific problems

• Overview of algorithms

• Spectral view

Maks

(9)

Part IV

Representations and Applications

• From pairwise matching to regularity

• Representations of symmetry

Pairwise equivalence

Permutation groups

Transformation groups

• Applications based on this classification

Michael

Referanser

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Symmetry in Shapes Theory and Practice

Niloy Mitra Maksim Ovsjanikov Mark Pauly Michael Wand Duygu