The estimation of h\"olderian regularity using genetic programming

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@InProceedings{Trujillo:2010:gecco,
  author =       "Leonardo Trujillo and Pierrick Legrand and 
                 Jacques Levy-Vehel",
  title =        "The estimation of h{\"{o}}lderian regularity using
                 genetic programming",
  booktitle =    "GECCO '10: Proceedings of the 12th annual conference
                 on Genetic and evolutionary computation",
  year =         "2010",
  editor =       "Juergen Branke and Martin Pelikan and Enrique Alba and 
                 Dirk V. Arnold and Josh Bongard and 
                 Anthony Brabazon and Juergen Branke and Martin V. Butz and 
                 Jeff Clune and Myra Cohen and Kalyanmoy Deb and 
                 Andries P Engelbrecht and Natalio Krasnogor and 
                 Julian F. Miller and Michael O'Neill and Kumara Sastry and 
                 Dirk Thierens and Jano {van Hemert} and Leonardo Vanneschi and 
                 Carsten Witt",
  isbn13 =       "978-1-4503-0072-8",
  pages =        "861--868",
  keywords =     "genetic algorithms, genetic programming, Signal
                 regularity, Holder exponent",
  month =        "7-11 " # jul,
  organisation = "SIGEVO",
  address =      "Portland, Oregon, USA",
  URL =          "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.220.3708",
  URL =          "http://hal.inria.fr/docs/00/53/89/43/PDF/t10fp182-trujillo.pdf",
  DOI =          "doi:10.1145/1830483.1830641",
  publisher =    "ACM",
  publisher_address = "New York, NY, USA",
  abstract =     "This paper presents a Genetic Programming (GP)
                 approach to synthesise estimators for the pointwise
                 Holder exponent in 2D signals. It is known that
                 irregularities and singularities are the most salient
                 and informative parts of a signal. Hence, explicitly
                 measuring these variations can be important in various
                 domains of signal processing. The point wise Holder
                 exponent provides a characterisation of these types of
                 features. However, current methods for estimation
                 cannot be considered to be optimal in any sense.
                 Therefore, the goal of this work is to automatically
                 synthesise operators that provide an estimation for the
                 Holderian regularity in a 2D signal. This goal is posed
                 as an optimisation problem in which we attempt to
                 minimize the error between a prescribed regularity and
                 the estimated regularity given by an image operator.
                 The search for optimal estimators is then carried out
                 using a GP algorithm. Experiments confirm that the
                 GP-operators produce a good estimation of the Holder
                 exponent in images of multifractional Brownian motions.
                 In fact, the evolved estimators significantly
                 outperform a traditional method by as much as one order
                 of magnitude. These results provide further empirical
                 evidence that GP can solve difficult problems of
                 applied mathematics.",
  notes =        "Also known as \cite{1830641} GECCO-2010 A joint
                 meeting of the nineteenth international conference on
                 genetic algorithms (ICGA-2010) and the fifteenth annual
                 genetic programming conference (GP-2010)",
}

Genetic Programming entries for Leonardo Trujillo Pierrick Legrand Jacques Levy-Vehel

Citations