1. 1 Numerical 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

2. 2 Numerical geometry of non-rigid shapes Introduction Welcome to non-rigid world Photo: M. Thyssen

3. 3 Numerical geometry of non-rigid shapes Introduction Non-rigid shapes from micro to macro

4. 4 Numerical geometry of non-rigid shapes Introduction Rock, scissors, paper RockPaperScissors

5. 5 Numerical geometry of non-rigid shapes Introduction Extrinsic vs intrinsic similarity Extrinsic similarityIntrinsic 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

6. 6 Numerical 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

7. 7 Numerical geometry of non-rigid shapes Introduction Similarity and correspondence ?

8. 8 Numerical 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 court Photo: AP

9. 9 Numerical geometry of non-rigid shapes Introduction Analysis and synthesis Elephant image: courtesy M. Kilian and H. Pottmann Analysis (Computer vision) Synthesis (Computer graphics)

10. 10 Numerical geometry of non-rigid shapes Introduction 8:30 – 8:45Introduction 8:45 – 9:25Basic geometry 9:25 – 9:35Break 9:35 – 10:20Numerical 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

11. 11 Numerical geometry of non-rigid shapes Introduction Shameless advertisement Published by Springer Verlag To appear in November 2007 Approximately 320 pages Over 50 illustrations Color figures