We propose a general unsupervised multiscale featurebased approach towards image segmentation. Clusters in the feature space are assumed to be properties of underlying classes, the recovery of which is achieved by the use of the mean shift procedure, a robust non-parametric decomposition method. The subsequent classification procedure consists of Bayesian multiscale processing which models the ...

This paper concerns the derivation of kinetic models for high frequency scalar wave fields propagating in random media. The kinetic equations model the propagation in the phase space of the energy density of a wave field or the correlation function of two wave fields propagating in two possibly different media. Dispersive effects due to e.g. spatial and temporal discretizations, which are model...

We study a mean-field model for a clustering process that may be described informally as follows. At each step a random integer k is chosen with probability pk, and the smallest cluster merges with k randomly chosen clusters. We prove that the model determines a continuous dynamical system on the space of probability measures supported in (0,∞), and we establish necessary and sufficient conditi...

The paper studies stochastic integration with respect to Gaussian processes and fields. It is more convenient to work with a field than a process: by definition, a field is a collection of stochastic integrals for a class of deterministic integrands. The problem is then to extend the definition to random integrands. An orthogonal decomposition of chaos space of the random field leads to two suc...

We obtain a representation theorem for Banach space valued Gaussian random variables as integrals against a white noise. As a corollary we obtain necessary and sufficient conditions for the existence of a white noise representation for a Gaussian random field indexed by a measure space. We then show how existing theory for integration with respect to Gaussian processes indexed by [0, 1] can be ...

We propose a data replication scheme on a random apollonian P2P overlay that benefits from the small world and scale free properties. The proposed algorithm features a replica density estimation and a space filling mechanism designed to avoid redundant messages. Not only it provides uniform replication of the data stored into the network but it also improves on classical flooding approaches by ...

Transport processes in groundwater systems with spatially heterogeneous properties often exhibit anomalous behavior. Using first-order approximations in velocity fluctuations we show that anomalous superdiffusive behavior may result if velocity fields are modeled as superpositions of random space functions with correlation structures consisting of linear combinations of short-range correlations...

For a given metric space (S, d), let us use the term “standard σ-field” to denote the σ-field S of subsets of S generated by the open balls (in the metric d). A function f : S×S×S× . . .→ S is “measurable” (with respect to S) if for every set A ∈ S one has that f−1(A) is a member of S×S×S×. . . , the product σ-field on S × S × S × . . . . Suppose B is a separable real Banach space. Suppose (Ω,F...

In the high-level operations of computer vision it is taken for granted that image features have been reliably detected. This paper addresses the problem of feature extraction by scale-space methods. There has been a strong development in scale-space theory and its applications to low-level vision in the last couple of years. Scale-space theory for continuous signals is on a firm theoretical ba...