An efficient optimizer for simple point process models

Ahmed Gamal Eldin 1, 2, * Guillaume Charpiat 3 Xavier Descombes 2, 4 Josiane Zerubia 2, 5
* Corresponding author
1 LEAR - Learning and recognition in vision
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 ARIANA - Inverse problems in earth monitoring
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - SIS - Signal, Images et Systèmes
3 STARS - Spatio-Temporal Activity Recognition Systems
CRISAM - Inria Sophia Antipolis - Méditerranée
4 MORPHEME - Morphologie et Images
CRISAM - Inria Sophia Antipolis - Méditerranée , IBV - Institut de Biologie Valrose : U1091, Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : In this paper we discuss the main characteristics (that we consider to be essential) for the design of an efficient optimizer in the context of highly non-convex functions. We consider a specific model known as Marked Point Process (MPP). Given that the probability density is multimodal, and given the size of the configuration space, an exploration phase is essential at the beginning of the algorithm. Next, the fine details of the density function should be discovered. We propose efficient kernels to efficiently explore the different modes of the density, and other kernels to discover the details of each mode. We study the algorithm theoretically to express convergence speeds and to select its best parameters. We also present a simple and generic method to parallelize the optimization of a specific class of MPP models. We validate our ideas first on synthetic data of configurations of different sizes to prove the efficiency of the proposed kernels. Finally we present results on three different applications.
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Ahmed Gamal Eldin, Guillaume Charpiat, Xavier Descombes, Josiane Zerubia. An efficient optimizer for simple point process models. SPIE, Computational Imaging XI, Feb 2013, Burlingame, California, United States. ⟨10.1117/12.2009238⟩. ⟨hal-00801448⟩

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