1 Numerical geometry of non-rigid shapes A journey to non-rigid world objects Introduction non-rigid Alexander Bronstein Michael Bronstein Numerical geometry.

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Presentation transcript:

1 Numerical geometry of non-rigid shapes A journey to non-rigid world objects Introduction non-rigid Alexander Bronstein Michael Bronstein Numerical geometry of

2 Numerical geometry of non-rigid shapes A journey to non-rigid world Welcome to non-rigid world

3 Numerical geometry of non-rigid shapes A journey to non-rigid world Rock Paper Scissors Rock, paper, scissors

4 Numerical geometry of non-rigid shapes A journey to non-rigid world Hands Rock Paper Scissors Rock, paper, scissors

5 Numerical geometry of non-rigid shapes A journey to non-rigid world Invariant similarity SIMILARITY TRANSFORMATION

6 Numerical geometry of non-rigid shapes A journey to non-rigid world Rigid Elastic TopologicalInelastic Invariance

7 Numerical geometry of non-rigid shapes A journey to non-rigid world Invariant correspondence CORRESPONDENCE TRANSFORMATION

8 Numerical geometry of non-rigid shapes A journey to non-rigid world Analysis and synthesis Elephant image: courtesy M. Kilian and H. Pottmann SYNTHESISANALYSIS

9 Numerical geometry of non-rigid shapes A journey to non-rigid world Landscape “HORSE” Image processingGeometry processing Pattern recognition Computer vision Computer graphics 2D world3D world

10 Numerical geometry of non-rigid shapes A journey to non-rigid world Additional reading Excerpts from the book On paper Online tosca.cs.technion.ac.il/book Problems Solutions Lecture slides Software Links Tutorials Data Springer, October 2008

11 Numerical geometry of non-rigid shapes A journey to non-rigid world Two perspectives Computer vision Features and local descriptors Metric geometry Shapes as metric spaces