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

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Presentation transcript:

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

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

3 Processing & Analysis of Geometric Shapes Introduction Dimensions of media

4 Processing & Analysis of Geometric Shapes Introduction Evolution of technology Analog eraDigital era

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

6 Processing & Analysis of Geometric Shapes Introduction Medical imaging

7 Processing & Analysis of Geometric Shapes Introduction Graphics & animation

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

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

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

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

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

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

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

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

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

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

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

21 Processing & Analysis of Geometric Shapes Introduction Formalities When?Thu 12:30-14:30 Where?Meyer 351 Who?Dr. Michael Bronstein 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