Calibrating Parameters of Cost Functionals

  • Laurent Younes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1843)


We propose a new framework for calibrating parameters of energy functionals, as used in image analysis. The method learns parameters from a family of correct examples, and given a probabilistic construct for generating wrong examples from correct ones. We introduce a measure of frustration to penalize cases in which wrong responses are preferred to correct ones, and we design a stochastic gradient algorithm which converges to parameters which minimize this measure of frustration. We also present a first set of experiments in this context, and introduce extensions to deal with data-dependent energies.


Learning variational method parameter estimation image reconstruction Bayesian image models 


  1. 1.
    R. Azencott, Image analysis and markov fields, in Proc. of the Int. Conf. on Ind. and Appl. Math, SIAM, Paris, 1987.Google Scholar
  2. 2.
    A. Benveniste, M. Métivier, AND P. Priouret, Algorithmes Adaptatifs et Approximations Stochastiques, Théorie et Application, Masson, 1987.Google Scholar
  3. 3.
    S. Geman AND D. Geman, Stochastic relaxation, gibbs distributions, and the bayesian restoration of images, IEEE Trans. PAMI, 6 (1984), pp. 721–741.zbMATHGoogle Scholar
  4. 4.
    J. J. Hopfield, iNeural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci USA, 79 (1982), pp. 2554–2558. Biophysics.CrossRefMathSciNetGoogle Scholar
  5. 5.
    D. Mumford and Shah, Optimal approximation by piecewise smooth functions and variational problems, Comm. Pure and Appl. Math., XLII (1988).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Laurent Younes
    • 1
  1. 1.CMLA (CNRS, URA 1611)Ecole Normale Supérieure de CachanCachan Cedex

Personalised recommendations