1Numerical geometry of non-rigid shapes Introduction

Numerical geometry of non-rigid shapes

Introduction

Alexander Bronstein, Michael Bronstein, Ron Kimmel© 2007 All rights reserved. Web: tosca.technion.ac.il

2Numerical geometry of non-rigid shapes Introduction

Welcome to non-rigid world

Photo: M. Thyssen

3Numerical geometry of non-rigid shapes Introduction

Non-rigid shapes from micro to macro

4Numerical geometry of non-rigid shapes Introduction

Rock, scissors, paper

Rock Paper Scissors

5Numerical geometry of non-rigid shapes Introduction

Extrinsic vs intrinsic similarity

Extrinsic similarity Intrinsic similarity

Are the shapes congruent?

Invariant only to rigid

transformations

Classical solution: ICP

Do the shapes have the

same

metric structure?

Invariant to isometric

deformations

6Numerical geometry of non-rigid shapes Introduction

Invariants

Which properties describe the shape and which result from

deformation?

Invariants: geometric properties preserved by deformations

Deformation-invariant similarity

7Numerical geometry of non-rigid shapes Introduction

Similarity and correspondence

?

8Numerical geometry of non-rigid shapes Introduction

If it doesn’t fit, you must acquit

OJ Simpson measuring the glove that appeared as an evidence in the courtPhoto: AP

9Numerical geometry of non-rigid shapes Introduction

Analysis and synthesis

Elephant image: courtesy M. Kilian and H. Pottmann

Analysis(Computer vision)

Synthesis(Computer graphics)

10Numerical geometry of non-rigid shapes Introduction

8:30 – 8:45 Introduction

8:45 – 9:25 Basic geometry

9:25 – 9:35 Break

9:35 – 10:20 Numerical geometry

10:20 – 11:05Multidimensional scaling

11:05 – 11:15Break

11:15 – 11:50Non-rigid similarity

11:50 – 12:15Non-rigid correspondence

12:15 – 12:25Conclusion

12:25 – 12:30Q&A

Schedule

Alex

Michael

Alex

11Numerical geometry of non-rigid shapes Introduction

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Published by Springer Verlag

To appear in November 2007

Approximately 320 pages

Over 50 illustrations

Color figures