Using an analytic analysis, we derive and solve the constraint equations obtained by folding the 2-spheres which are permuted under the outer automorphism groups of the toric graphs of affine ADE geometries in type II strings. We show that there are classes of solutions depending on the actions of on the elliptic curve E on which flat ADE bundles are fibred. We give two classes of four-dimensional N = 2 superconformal field theory solutions for affine BCFG geometries; one having the right space dimension but exhibiting mirror potentials with branch cuts and a second class sharing the main features with the solutions given by Mayr.

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The conventional PHD and CPHD lters presume that the probability (x) that a measurement will be collected from a target with state-vector x (the state-dependent probability of detection) is known a priori. However, in many applications this presumption is false. A few methods have been devised for estimating the probability of detection, but they typically presume that (x) is constant in both time and the region of interest. This paper introduces CPHD/PHD lters that are capable of multitarget track-before-detect operation even when probability of detection is not known and, moreover, when it is not necessarily constant, either temporally or spatially. Furthermore, these lters are potentially computationally tractable. We begin by deriving CPHD/PHD lter equations for the case when probability of detection is unknown but the clutter model is known a priori. Then, building on the results of a companion paper, we note that CPHD/PHD lters can be derived for the case when neither probability of detection or the background clutter are known.

Representing the image as a surface, an inhomogeneous diffusion algorithm is developed, evolving the surface at a speed proportional to its mean curvature, reducing noise while preserving image structure. An adaptive scaling parameter increases the speed of the diffusion. The properties of a discrete algorithm are demonstrated experimentally.

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AB STRACTThe inadequacy of the classic linear approach to edge detection and scale space filtering lies in the spatial averaging of the Laplacian. The Laplacian is the divergence of the gradient and thus is the divergence of both magnitude and direction. The divergence in magnitude characterizes edges and this divergence must not be averaged if the image structure is to be preserved. We introduce a new nonlinear filtering theory that that only averages the divergence of direction. This averaging keeps edges and lines intact as their direction is nondivergent. Noise does not have this nondivergent consistency and its divergent direction will be averaged. Higher order structures such as corners are singular points or inflection points in the divergence of direction and also will be averaged. Corners are intersection points of edges of nondivergent direction (or smooth curves of small divergence in direction) and their averaging will be limited. This approach provides a better compromise between noise removal and preservation of image structure. Experiments that verify and demonstrate the adequacy of this new theory are presented.