A Consistent Statistical Framework for Current-Based Representations of Surfaces

  • Benjamin Coulaud
  • Frédéric J. P. RichardEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9213)


In this paper, we deal with the statistical analysis of surfaces. To address this issue, we extend to a stochastic setting a surface representation by currents (Glaunès and Vaillant, 2005). This extension is inspired from the theory of generalized stochastic processes due to Itô (1954) and Gelfand and Vilenkin (1964). It consists of random linear forms defined on a space of vector fields. Upon this representation, we build a probabilistic model that allows us to describe the random variability of current-based representations of surfaces. For this model, we then propose estimators of a mean representant of a surface population, and the population variance. Finally, we establish the consistency of these estimators.


Vector Field Linear Form Maximum Likelihood Estimator Statistical Framework Surface Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373MarseilleFrance

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