Search results for "Random compact set"
showing 4 items of 4 documents
Random attractors for stochastic lattice systems with non-Lipschitz nonlinearity
2011
In this article, we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an additive noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems, we prove the existence of a random compact global attractor.
On the Analysis of a Random Interleaving Walk–Jump Process with Applications to Testing
2011
Abstract Although random walks (RWs) with single-step transitions have been extensively studied for almost a century as seen in Feller (1968), problems involving the analysis of RWs that contain interleaving random steps and random “jumps” are intrinsically hard. In this article, we consider the analysis of one such fascinating RW, where every step is paired with its counterpart random jump. In addition to this RW being conceptually interesting, it has applications in testing of entities (components or personnel), where the entity is never allowed to make more than a prespecified number of consecutive failures. The article contains the analysis of the chain, some fascinating limiting proper…
Resuming Shapes with Applications
2004
Many image processing tasks need some kind of average of different shapes. Frequently, different shapes obtained from several images have to be summarized. If these shapes can be considered as different realizations of a given random compact set, then the natural summaries are the different mean sets proposed in the literature. In this paper, new mean sets are defined by using the basic transformations of Mathematical Morphology (dilation, erosion, opening and closing). These new definitions can be considered, under some additional assumptions, as particular cases of the distance average of Baddeley and Molchanov. The use of the former and new mean sets as summary descriptors of shapes is i…
Modeling of female human body shapes for apparel design based on cross mean sets
2014
This paper is concerned with a method to build prototypes of human bodies that can be used for apparel design. One of the most important issues in the apparel development process is to define a sizing system to provide a good fitting for the majority of the population. Since anthropometric measures do not present the same linear growth with size in each dimension, it is very important to find a prototype that represents as accurately as possible each class in the sizing system. In this paper we propose a method based on the concept of random compact mean set to define prototypes in apparel design. From a cloud of 3D points obtained with a 3D scanner a solid that represents the human body is…