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1 Numerical geometry of non-rigid shapes Introduction Introduction Alexander Bronstein, Michael Bronstein © 2008 All rights reserved. Web: tosca.cs.technion.ac.il - Do you see that cloud, that’s almost in shape like a camel? - By the mass, and ’t is like a camel, indeed. - Methinks, it is like a weasel. - It is backed like a weasel. - Or, like a whale? - Very like a whale. Shakespeare, Hamlet

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2 Numerical geometry of non-rigid shapes Introduction Welcome to non-rigid world

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3 Numerical geometry of non-rigid shapes Introduction Non-rigid shapes everywhere Articulated shapes Volumetric medical data Computer graphics models Two-dimensional shapes

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4 Numerical geometry of non-rigid shapes Introduction Rock Paper Scissors Rock-Scissors-Paper Roccia, carta, forbici

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5 Numerical geometry of non-rigid shapes Introduction Hands Rock Paper Scissors Rock-Scissors-Paper

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6 Numerical geometry of non-rigid shapes Introduction Deformation-invariant similarity Define a class of deformations Find properties of the shape which are invariant under the class of deformations and discriminative (uniquely describe the shape) Define a shape distance based on these properties

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7 Numerical geometry of non-rigid shapes Introduction Invariance Rigid motion Elastic deformation Inelastic deformation

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8 Numerical geometry of non-rigid shapes Introduction Similarity and correspondence CORRESPONDENCESIMILARITY

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9 Numerical geometry of non-rigid shapes Introduction Analysis and synthesis Elephant image: courtesy M. Kilian and H. Pottmann SYNTHESISANALYSIS

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10 Numerical geometry of non-rigid shapes Introduction Landscape “HORSE” Image processingGeometry processing Pattern recognition Computer vision Computer graphics 2D world3D world

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11 Numerical geometry of non-rigid shapes Introduction Thorny path Via dolorosa

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12 Numerical geometry of non-rigid shapes Introduction Course in a nutshell Analysis and synthesis of non-rigid shapes Archetype problems: shape similarity and correspondence Metric geometry as a common denominator Tools from geometry, algebra, optimization, numerical analysis, statistics, and data analysis. Practical numerical methods MATLAB tutorials Applications in computer vision, pattern recognition, computer graphics, and geometry processing

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13 Numerical geometry of non-rigid shapes Introduction Material Excerpts from the book On paper Online tosca.cs.technion.ac.il/book Problems Solutions Lecture slides Software Links Tutorials Data

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