Computer Vision

2014 Edition
| Editors: Katsushi Ikeuchi

Variational Analysis

  • Bastian Goldluecke
Reference work entry


Related Concepts


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.


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

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    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
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    Gelfand IM, Fomin SV (2003) Calculus of variations. Dover publications reprint of the 1963 edn. Dover Publications Inc., Mineola, NYGoogle Scholar
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    Luenberger D (1969) Optimization by vector space methods. Wiley, New YorkzbMATHGoogle Scholar
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    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