This paper presents an unsupervised algorithm for learning a finite mixture model from multivariate data. This mixture model is based on the Dirichlet distribution, which offers high flexibility for modeling data. The proposed approach for estimating the parameters of a Dirichlet mixture is based on the maximum likelihood (ML) and Fisher scoring methods. Experimental results are presented for the following applications: estimation of artificial histograms, summarization of image databases for efficient retrieval, and human skin color modeling and its application to skin detection in multimedia databases.

We prove the existence and uniqueness of solution to the nonlinear local martingale problems for a large class of infinite systems of interacting diffusions. These systems, which we call the stochastic McKean-Vlasov limits for the approximating finite systems, are described as stochastic evolutions in a space of probability measures on T~ d and are obtained as weak limits of the sequence of empirical measures for the finite systems, which are highly correlated and driven by dependent Brownian motions. Existence is shown to hold under a weak growth condition, while uniqueness is proved using only a weak monotonicity condition on the coefficients. The proof of the latter involves a coupling argument carried out in the context of associated stochastic evolution equations in Hilbert spaces. As a side result, these evolution equations are shown to be positivity preserving. In the case where a dual process exists, uniqueness is proved under continuity of the coefficients alone. Finally, we prove that strong continuity of paths holds with respect to various Sobolev norms, provided the appropriate stronger growth condition is verified. Strong solutions are obtained when a coercivity condition is added on to the growth condition guaranteeing existence.

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The paper presents an approach for roads detection based on synthetic aperture radar (SAR) images and road databases. The vectors provided by the database are refined using active contours (snakes). In this framework, we firstly develop a restoration filter based on the frost filter achieving an acceptable compromise between speckle elimination and lines preserving. This is followed by a line plausibility calculation step which is used to deform the snake from its initial location toward the final solution. The snake is reformulated using finite elements method. The setting of the snake parameters is not an obvious problem especially when they are tuned by trial-and-error process. We propose a new automatic computational rule for the snake parameters. Our approach is validated by a series of tests on synthetic and SAR images.

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Abstract.In this paper of infinite systems of interacting measure-valued diffusions each with state space ¿^( [O, 1]), the set of probability measures on [0, 1], is constructed and analysed (Fleming-Viot systems). These systems arise as diffusion limits of population genetics models with infinitely many possible types of individuals (labelled by [0, 1]), spatially distributed over a countable collection of sites and evolving as follows. Individuals can migrate between sites and after an exponential waiting time a colony replaces its population by a new generation where the types are assigned by resampling from the empirical distribution of types at this site.It is proved that, depending on recurrence versus transience properties of the migration mechanism, the system either clusters as r -> oo , that is, converges in distribution to a law concentrated on the states in which all components are equal to some Su , « £ [0, 1], or the system approaches a nontrivial equilibrium state. The properties of the equilibrium states, respectively the cluster formation, are studied by letting a parameter in the migration mechanism tend to infinity and explicitly identifying the limiting dynamics in a sequence of different space-time scales. These limiting dynamics have stationary states which are quasi-equiiibria of the original system, that is, change only in longer time scales. Properties of these quasi-equilibria are derived and related to the global equilibrium process for large N. Finally we establish that the Fleming-Viot systems are the unique dynamics which remain invariant under the associated space-time renormalization procedure. 0. Introduction (a) Background and motivation. In the present paper, we construct a system consisting of countably many interacting Fleming-Viot processes. Each component takes values in the space of probability measures on a compact space, say [0, 1 ]. This model arises as the diffusion limit of the following model from population genetics. The population is spatially distributed among a collection of colonies in which there are individuals of various genetic types and these types are labelled via values in [0,1]. The types of individuals in the next generation in each colony are obtained by sampling according to the empirical frequency of current types within the colony. In addition individuals can migrate between colonies.

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