Although every implementation of a recent high frequency multiple scattering solver has displayed a frequency independent operation count, its numerical analysis yet remains as a challenging open problem. This is, in part, due to the absence of detailed information on the uniform asymptotic expansions of multiple scattering iterations. Here we address precisely this issue for a collection of co...

-In this paper we use the parameteric polar representation to extend the application of edge directional information from circle to ellipse extraction. As a result we obtain a mapping which decomposes the parameter space required for ellipse extraction into two independent sub-spaces and one final histogram accumulator. The mapping includes the tangent of the angle of the first and second direc...

Differential operators have been widely used for multiscale geometric descriptions of images. The efficient computation of these differential operators is always desirable. Moreover, it has not been clear whether such representations are invertible. For certain applications, it is usually required that such representations should be invertible so that one can facilitate the processing of inform...

We provide a corrected proof of [4, Theorem 2.2], which preserves the validity of the theorem exactly under those assumptions as stated in the original paper. 1. Corrigendum. This Corrigendum concerns the proof of [4, Theorem 2.2]. In the original proof we used [1, Theorem 2.4] and [3, Proposition 3.2], which require more restrictive conditions than necessary. We provide here an elementary maxi...

We compare the performance of Directional Derivatives features for automatic speech recognition when extracted from different time-frequency representations. Specifically, we use the short-time Fourier transform, Mel-frequency, and Gammatone spectrograms as a base from which we extract spectrotemporal modulations. We then assess the noise robustness of each representation with varied number of ...

We study the nodal set of the Steklov eigenfunctions on the boundary of a smooth bounded domain in Rn – the eigenfunctions of the Dirichlet-to-Neumann map Λ. For a bounded Lipschitz domain Ω ⊂ Rn, this map associates to each function u defined on the boundary ∂Ω, the normal derivative of the harmonic function on Ω with boundary data u. Under the assumption that the domain Ω is C2, we prove a do...

This paper proposes an extension of edge detectors based on second-order differential operators to the case of multiple band (color) images. To this end, we deline a local directional measure of multispectral contrast. A definition of edge point is then given, as the location of a directional maximum of the contrast function. Extremal contrast edges are defined, as loci of zero crossing points ...

Directional drilling systems generate complex curved boreholes in the earth’s crust for the exploration and harvesting of oil, gas and geothermal energy. In practice, boreholes drilled with such systems often show instability-induced borehole spiraling, which negatively affects the borehole quality and increases drag losses while drilling. This paper presents a dynamic state-feedback controller...

Let M be a compact manifold with smooth boundary. We study the heat content asymptotics on M defined by a time dependent heat source and time dependent boundary conditions. We adopt the following notational conventions: let M be a compact Riemannian manifold with smooth boundary ∂M , let ∆ = δd be the scalar Laplacian on M , let x be a point of the interior of M , let y be a point of the bounda...

K e y w o r d s A c o u s t i c scattering, Boundary value problems, Potential theory, Explicit solution, Cuts, Cracks, Screens. 1. I N T R O D U C T I O N In the jump problem for the Helmholtz equation outside cuts in a plane we specie" the jump of the solution and the jump of its normal derivative at the cuts. This problem is closely related to the Dirichlet and Neumann problems outside cuts ...