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Proceedings Article

Mathematical theories of shape: do they model perception?

[+] Author Affiliations
David Mumford

Harvard Univ. (USA)

Proc. SPIE 1570, Geometric Methods in Computer Vision, 2 (September 1, 1991); doi:10.1117/12.49981
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From Conference Volume 1570

  • Geometric Methods in Computer Vision
  • Baba C. Vemuri
  • San Diego, CA | July 21, 1991

abstract

The mathematics of shape has a long history in the fields of differential geometry and topology. But does this theory of shape address the central problem of vision: finding the best data structure plus algorithm for storing a shape and later recognizing the same and similar shapes. Several criteria may be used to evaluate this: does the data structure capture our intuitive idea of 'similarity'? does it allow reconstruction of typical shapes to compare with new input? One direction in which mathematics and vision have converged is toward multiscale analyses of visual signals and shapes. In other respects, however, the recognition process in animals shows features that still defy mathematical modeling.

© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Citation

David Mumford
"Mathematical theories of shape: do they model perception?", Proc. SPIE 1570, Geometric Methods in Computer Vision, 2 (September 1, 1991); doi:10.1117/12.49981; http://dx.doi.org/10.1117/12.49981


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