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.
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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