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Recent Advances in Learning and Control pp 65–78Cite as

On the Computation of Optimal Transport Maps Using Gradient Flows and Multiresolution Analysis

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 371))

Abstract

The optimal mass transport methodology has numerous applications in econometrics, fluid dynamics, automatic control, statistical physics, shape optimization, expert systems, and meteorology. Further, it leads to some beautiful mathematical problems. Motivated by certain issues in image registration, visual tracking and medical image visualization, we outline in this note a straightforward gradient descent approach for computing the optimal L 2 optimal transport mapping which may be easily implemented using a multiresolution scheme. We discuss the well-posedness of our scheme, and indicate how the optimal transport map may be computed on the sphere.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel

    Ayelet Dominitz & Allen Tannenbaum

  2. Department of Mathematics, University of Wisconsin, Madison, WI, 53706, USA

    Sigurd Angenent

  3. Schools of Electrical & Computer and Biomedical Engineering, Georgia Institute of Technolgy, Atlanta, GA, 30332-0250, USA

    Allen Tannenbaum

Authors
  1. Ayelet Dominitz
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  2. Sigurd Angenent
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  3. Allen Tannenbaum
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Editor information

Editors and Affiliations

  1. Département d’Ingénierie Mathématique, Université catholique de Louvain, avenue Georges Lemaître, 4, B-1348, Louvain-la-Neuve, Belgium

    Vincent D. Blondel PhD

  2. Information Systems Laboratory Department of Electrical Engineering, Stanford University, Stanford, CA, 94305-9510, USA

    Stephen P. Boyd PhD

  3. Bio-Mimetic Control Research Center, RIKEN (The Institute of Physical and Chemical Research), Anagahora, Shimoshidami, Moriyama-ku, Nagoya, 463-0003, Japan

    Hidenori Kimura PhD

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© 2008 Springer-Verlag Berlin Heidelberg

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Dominitz, A., Angenent, S., Tannenbaum, A. (2008). On the Computation of Optimal Transport Maps Using Gradient Flows and Multiresolution Analysis. In: Blondel, V.D., Boyd, S.P., Kimura, H. (eds) Recent Advances in Learning and Control. Lecture Notes in Control and Information Sciences, vol 371. Springer, London. https://doi.org/10.1007/978-1-84800-155-8_5

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  • DOI: https://doi.org/10.1007/978-1-84800-155-8_5

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84800-154-1

  • Online ISBN: 978-1-84800-155-8

  • eBook Packages: EngineeringEngineering (R0)

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