In this paper, we propose a novel two step shape classification approach consisting of a description and a discrimination phase. In the description phase, curvature features are extracted from the shape and are utilized to build a Hidden Markov Model (HMM). The HMM provides a robust Maximum Likelihood (ML) description of the shape. In the discrimination phase, a weighted likelihood discriminant...

Geometric deformable models based on the level set method have become very popular in the last several years. To overcome an inherent limitation in accuracy while maintaining computational efficiency, adaptive grid techniques using local grid refinement have been developed for use with these models. This strategy, however, requires a very complex data structure, yields large numbers of contour ...

In this note, we use the Feynman-Kac formula to derive a moment representation for the 2D parabolic Anderson model in small time, which is related to the intersection local time of planar Brownian motions.

Using two sets of high-precision Monte Carlo data for the twodimensional XY model in the Villain formulation on square L×L lattices, the scaling behavior of the susceptibility χ and correlation length ξ at the Kosterlitz-Thouless phase transition is analyzed with emphasis on multiplicative logarithmic corrections (lnL)−2r in the finite-size scaling region and (ln ξ)−2r in the high-temperature p...

In this paper we introduce a PDE system which aims at describing the dynamics of a dispersed phase of particles moving into an incompressible perfect fluid, in two space dimensions. The system couples a Vlasov-type equation and an Euler-type equation: the fluid acts on the dispersed phase through a gyroscopic force whereas the latter contributes to the vorticity of the former. First we give a D...

We prove a chaos expansion for the 2D parabolic Anderson Model in small time, with the expansion coefficients expressed in terms of the density function of the annealed polymer in a white noise environment.

We present a model of biofilm growth in a long channel where the biomass is assumed to have the rheology of a viscous polymer solution. We examine the competition between growth and erosion-like surface detachment due to the flow. A particular focus of our investigation is the effect of the biofilm growth on the fluid flow in the pores, and the issue of whether biomass can grow sufficiently to ...