Post on 21-Dec-2015
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
Shameless advertisement
Published by Springer Verlag
To appear in November 2007
Approximately 320 pages
Over 50 illustrations
Color figures