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First European Congress of Mathematics pp 187–224Cite as

Pattern Theory: A Unifying Perspective

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Part of the book series: Progress in Mathematics ((PM,volume 3))

Abstract

The term “Pattern Theory” was introduced by Ulf Grenander in the 70s as a name for a field of applied mathematics which gave a theoretical setting for a large number of related ideas, techniques and results from fields such as computer vision, speech recognition, image and acoustic signal processing, pattern recognition and its statistical side, neural nets and parts of artificial intelligence (see [Grenander 76–81]). When I first began to study computer vision about ten years ago, I read parts of this book but did not really understand his insight. However, as I worked in the field, every time I felt I saw what was going on in a broader perspective or saw some theme which seemed to pull together the field as a whole, it turned out that this theme was part of what Grenander called pattern theory. It seems to me now that this is the right framework for these areas, and, as these fields have been growing explosively, the time is ripe for making an attempt to reexamine recent progress and try to make the ideas behind this unification better known. This article presents pattern theory from my point of view, which may be somewhat narrower than Grenander’s, updated with recent examples involving interesting new mathematics.

Suppported in part by NSF Grant DMS 91-21266 and by the Geometry Center, University of Minnesota, a STC funded by NSF, DOE and Minnesota Technology Inc.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    David Mumford

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  1. David Mumford
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Editor information

Editors and Affiliations

  1. Laboratoire de Mathématiques Fondamentales, Université Pierre et Marie Curie, 4, place Jussieu, 75252, Paris Cedex 05, France

    Anthony Joseph  & Rudolf Rentschler  & 

  2. The Weizmann Institute of Science, 76100, Rehovot, Israel

    Anthony Joseph

  3. Mathématiques Bâtiment 425, Université de Paris-Sud, 91405, Orsay Cedex, France

    Fulbert Mignot

  4. Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, 4, place Jussieu, 75252, Paris Cedex, France

    François Murat

  5. Laboratoire de Statistique Médicale, Université Paris V, 45, rue des Saints Pères, 75270, Paris Cedex, France

    Bernard Prum

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© 1994 Birkhäuser Verlag

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Mumford, D. (1994). Pattern Theory: A Unifying Perspective. In: Joseph, A., Mignot, F., Murat, F., Prum, B., Rentschler, R. (eds) First European Congress of Mathematics . Progress in Mathematics, vol 3. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9110-3_6

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  • DOI: https://doi.org/10.1007/978-3-0348-9110-3_6

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9911-6

  • Online ISBN: 978-3-0348-9110-3

  • eBook Packages: Springer Book Archive

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