1. 1 Processing & Analysis of Geometric Shapes Introduction Processing and Analysis of Geometric Shapes Department of Electrical Engineering – Technion Spring 2010

2. 2 Processing & Analysis of Geometric Shapes Introduction Introduction © Alexander & Michael Bronstein, 2006-2009 © Michael Bronstein, 2010 tosca.cs.technion.ac.il/book 048921 Advanced topics in vision Processing and Analysis of Geometric Shapes EE Technion, Spring 2010

3. 3 Processing & Analysis of Geometric Shapes Introduction Dimensions of media

4. 4 Processing & Analysis of Geometric Shapes Introduction 1880 19001920196019802000 1940 1990 Evolution of technology Analog eraDigital era

5. 5 Processing & Analysis of Geometric Shapes Introduction Human-machine-interfaces

6. 6 Processing & Analysis of Geometric Shapes Introduction Medical imaging

7. 7 Processing & Analysis of Geometric Shapes Introduction Graphics & animation

8. 8 Processing & Analysis of Geometric Shapes Introduction Landscape “HORSE” Image processingGeometry processing Pattern recognition Computer vision Computer graphics 2D world3D world

9. 9 Processing & Analysis of Geometric Shapes Introduction Shapes vs images GeometrySamplingParametrization Euclidean (flat) Non-Euclidean (curved) Global Local“Uniform” is not well-defined Uniform Cartesian

10. 10 Processing & Analysis of Geometric Shapes Introduction Shapes vs images RepresentationDeformations Array of pixels Cloud of points, mesh, etc, etc. Rotation, affine, projective, etc. Wealth of non-rigid deformations

11. 11 Processing & Analysis of Geometric Shapes Introduction Non-rigid world from macro to nano Animals Organs Micro- organisms Proteins Nano- machines

12. 12 Processing & Analysis of Geometric Shapes Introduction Rock Paper Scissors Rock, paper, scissors

13. 13 Processing & Analysis of Geometric Shapes Introduction Hands Rock Paper Scissors Rock, paper, scissors

14. 14 Processing & Analysis of Geometric Shapes Introduction Similarity and correspondence Structure Correspondence Correspondence quality = structure similarity (distortion) Similarity Minimum possible correspondence distortion

15. 15 Processing & Analysis of Geometric Shapes Introduction Similarity and correspondence Structure Similarity Minimum possible correspondence distortion Transformation Invariant similarity

16. 16 Processing & Analysis of Geometric Shapes Introduction Elastic Rigid Transformations InelasticTopological Scale Missing data

17. 17 Processing & Analysis of Geometric Shapes Introduction SimilarityPartial similarity Topics ? Symmetry StructureStructural similarity Correspondence Shape Analysis

18. 18 Processing & Analysis of Geometric Shapes Introduction Topics “ ” “ ” Metric spaces Embeddings Local featuresGeometric words& expressions Shape Representation

19. 19 Processing & Analysis of Geometric Shapes Introduction Topics Calculus of shapes = + 1 2 1 2 Morphing Editing Filtering Shape Synthesis & Processing

20. 20 Processing & Analysis of Geometric Shapes Introduction Tools Metric and differential geometry Fast marching Multidimensional scaling Iterative closes point algorithms Spectral methodsConvex optimization

21. 21 Processing & Analysis of Geometric Shapes Introduction Formalities When?Thu 12:30-14:30 Where?Meyer 351 Who?Dr. Michael Bronstein (mbron@cs.technion.ac.il) Grading50% homework 50% final project Webhttp://tosca.cs.technion.ac.il/book/course_technion10.html FacebookNumerical geometry of non-rigid shapes ReferenceA. M. Bronstein, M. M. Bronstein, R. Kimmel, Numerical geometry of non-rigid shapes, Springer 2008 Various papers in the field