Numerical geometry of nonrigid shapes Introduction Alexander Bronstein

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

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

4 Numerical geometry of non-rigid shapes Introduction Rock, scissors, paper Rock Paper Scissors

5 Numerical geometry of non-rigid shapes Introduction Extrinsic vs intrinsic similarity Extrinsic similarity n Are the shapes congruent? n Invariant only to rigid transformations n Classical solution: ICP Intrinsic similarity n Do the shapes have the same metric structure? n Invariant to isometric deformations

Numerical geometry of non-rigid shapes Introduction 6 Invariants n Which properties describe the shape and which result from deformation? n Invariants: geometric properties preserved by deformations n Deformation-invariant similarity

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

Numerical geometry of non-rigid shapes Introduction If it doesn’t fit, you must acquit Photo: AP OJ Simpson measuring the glove that appeared as an evidence in the court 8

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

10 Numerical geometry of non-rigid shapes Introduction Schedule n 8: 30 – 8: 45 Introduction n 8: 45 – 9: 25 Basic geometry n 9: 25 – 9: 35 Break n 9: 35 – 10: 20 Numerical geometry Alex n 10: 20 – 11: 05 Multidimensional scaling n 11: 05 – 11: 15 Break Michael n 11: 15 – 11: 50 Non-rigid similarity n 11: 50 – 12: 15 Non-rigid correspondence n 12: 15 – 12: 25 Conclusion n 12: 25 – 12: 30 Q&A Alex

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