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Computer Vision Panel Board on Mathematical Sciences Workshop on The Interface Between Computer Science & Mathematical Sciences April 28-29, 2000, NAS, Washington DC

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The Panelists Jitendra Malik (CS, Berkeley) 25 mins A Brief Overview of Computer Vision Larry Davis (CS, Maryland) 15 mins Challenges to Computer Vision Guillermo Sapiro (EE, Minnesota) 15 mins Mathematics in Image Processing, Computer Vision and Computer Graphics Tony Chan (Math, UCLA) Moderator

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Rapporteur Stan Osher (Math, UCLA)

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Websites Workshop Presentations: www.cs.umd.edu/users/oleary/nasworkshop.html General Computer Vision: www.cs.cmu.edu/~cil/vision.html

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Abstract View of Computer Vision 2D Images3D World CG CV

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Major Computer Vision Tasks Object Representation Reconstruction Segmentation Recognition Control Learning

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Major Challenges Incomplete information Ill-posedness Motion Multiple Images of Same Scene Textures Occlusion Illumination

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Math in Computer Vision Geometry (projections, shapes, level sets, …) Probability/Statistics (estimation under uncertainty) Analysis/PDE (wavelets, curvature flows, diffusion, …) Computational Math (fast algorithms) Discrete Math (graph theory, …) Topology (deformable shapes, …) Algebra (symmetry, uniqueness….) Mathematical Physics (light, reflectance, radiosity,..)

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