-Extraction of two-dimensional object locations using current techniques is a computationally intensive process. In this paper a parallel algorithm is presented that can specify the location of objects from edge streaks produced by an edge operator. Best-first searches are carried out in a number of non-interacting and localized edge streak spaces. The outcome of each search is a hypothesis. Ea...

In 1956, quantum physicist N. Bogoliubov discovered the edge-ofthe-wedge theorem, a theorem used to analytically continue a function through the boundary of a domain under certain conditions. We discuss an analogous phenomenon, a wedge-of-the-edge theorem, for the boundary values of Pick functions, functions from the polyupperhalf plane into the half plane. We show that Pick functions which hav...

This paper shows that the continuous shearlet transform, a novel directional multiscale transform recently introduced by the authors and their collaborators, provides a precise geometrical characterization for the boundary curves of very general planar regions. This study is motivated by imaging applications, where such boundary curves represent edges of images. The shearlet approach is able to...

This paper presents a 3D-mesh segmentation algorithm based on a learning approach. A large database of manually segmented 3D-meshes is used to learn a boundary edge function. The function is learned using a classifier which automatically selects from a pool of geometric features the most relevant ones to detect candidate boundary edges. We propose a processing pipeline that produces smooth clos...

Since edge detection is in the forefront of image processing for object detection, it is crucial to have a good understanding of edge detection algorithms. The reason for this is that edges form the outline of an object. An edge is the boundary between an object and the background, and indicates the boundary between overlapping objects. This means that if the edges in an image can be identified...

A streamlined flat plate (herein ‘aerofoil’) containing a small rectangular cavity on one side was experimentally found to produce aerofoil tones (rather than cavity tones) under certain flow conditions. To clarify the responsible mechanism, the effect of sinusoidal acoustic forcing on the boundary layer was investigated by placing a loudspeaker downstream of the aerofoil. Velocity fluctuations...

We examine, from a geometrical point of view, the dynamics of a relativistic extended object with loaded edges. In the case of a Dirac-Nambu-Goto [DNG] object with DNG edges, the worldsheet m generated by the parent object is, as in the case without boundary, an extremal timelike surface in spacetime. Using simple variational arguments, we demonstrate that the worldsheet of each edge is a const...

We show in the context of Einstein gravity that the removal of a spatial region leads to the appearance of an infinite set of observables and their associated edge states localized at its boundary. Such a boundary occurs in certain approaches to the physics of black holes like the one based on the membrane paradigm. The edge states can contribute to black hole entropy in these models. A “comple...

Edge is the boundary between an object and the background, and identifies the boundary between overlapping and non-over lapping objects. This means that if the edges in an image can be identified accurately, all of the objects can be located and basic properties such as area, perimeter, and shape can be measured. Here fuzzy logic based image processing is used for accurate and noise free edge d...

We develop an adaptive finite element method for island dynamics in epitaxial growth. We study a step-flow model, which consists of an adatom (adsorbed atom) diffusion equation on terraces of different height; thermodynamic boundary conditions on terrace boundaries including anisotropic line tension; and the normal velocity law for the motion of such boundaries determined by a two-sided flux, t...