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Michael Bronstein

Computational metric geometry: an old new tool in image sciences. Michael Bronstein. tracking. retrieval. categorization. restoration. alignment. detection. /recognition. Similarity. Raffaello Santi, School of Athens , Vatican. Shape similarity and correspondence. Correspondence.

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Michael Bronstein

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  1. Computational metric geometry: an old new tool in image sciences Michael Bronstein

  2. tracking retrieval categorization restoration alignment detection /recognition Similarity

  3. Raffaello Santi, School of Athens, Vatican

  4. Shape similarity and correspondence Correspondence Similarity Metric space Metric space Correspondence quality = metric distortion Gromov-Hausdorff distance = Minimum possible correspondence distortion

  5. Invariance Rigid Scale Inelastic Topology Elastic Choice of the metric prescribes the invariance

  6. Non-rigid shape analysis and synthesis Correspondence Morphing Retrieval BBK

  7. Self-similarity and symmetry Permutation Raviv & BBK 2007

  8. Metric learning Data space Embedding space Min distortion on training set of examples with known

  9. Video copy detection Lightsaber Luke vs Vader – Starwars classic Star Wars DVD copy Star Wars pirated copy BBK 2010

  10. Challenges • Theoretical • Approximate symmetry notion: group-like structure • Comparing data from different spaces • Computational • Efficient solution of minimum distortion correspondence problems • (Gromov-Hausdorffdistance) • Efficient algorithms for embedding into interesting metric spaces • Applications • Problems that can be formulated in terms of metric geometry

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