Computer Vision

2014 Edition
| Editors: Katsushi Ikeuchi

Variational Analysis

  • Bastian Goldluecke
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-31439-6_683

Synonyms

Related Concepts

Definition

In mathematics, the term variational analysis usually denotes the combination and extension of methods from convex optimization and the classical calculus of variations to a more general theory [5]. However, in computer vision literature, the term is frequently encountered as just a synonym for calculus of variations. This branch of mathematics deals with the minimization of functionals, which are real-valued functions on infinite-dimensional spaces, most frequently spaces of functions.

Background

In the continuous world view, images are modeled as functions on a domain \(\Omega\subset{\mathbb R}{n}\)

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References

  1. 1.
    Attouch H, Buttazzo G, Michaille G (2006) Variational analysis in Sobolev and BV spaces. MPS-SIAM series on optimization. Society for Industrial and Applied Mathematics, PhiladelphiaGoogle Scholar
  2. 2.
    Chambolle A, Caselles V, Cremers D, Novaga M, Pock T (2010) An introduction to total variation for image analysis. Radon Ser Comput Appl Math 9:263–340MathSciNetGoogle Scholar
  3. 3.
    Gelfand IM, Fomin SV (2003) Calculus of variations. Dover publications reprint of the 1963 edn. Dover Publications Inc., Mineola, NYGoogle Scholar
  4. 4.
    Luenberger D (1969) Optimization by vector space methods. Wiley, New YorkzbMATHGoogle Scholar
  5. 5.
    Rockafellar RT, Wets R (2005) Variational analysis. Springer, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Bastian Goldluecke
    • 1
  1. 1.Department of Computer Science, Technische universität MünchenMünchenGermany