Ambiguity in the solution of inverse problems arises when data are insufficient to define a unique solution (i.e., the problem is ill-posed). Data fusion has the potential to reduce this ambiguity by using other sensory data that complement the original data. This paper examines the application of data fusion to limited-angle computed tomography (CT) to resolve ambiguity. While CT in its conven...

We show that for generic sliced spacetimes global hyperbolicity is equivalent to space completeness under the assumption that the lapse, shift and spatial metric are uniformly bounded. This leads us to the conclusion that simple sliced spaces are timelike and null geodesically complete if and only if space is a complete Riemannian manifold.

We address the problem identifying the K best point-to-point simple paths connecting a given pair of nodes in a directed network with arbitrary lengths. The main result in this paper is the proof that a path tree containing the kth point-to-point shortest simple path can be obtained by using one of the previous (k-1) path trees containing each one of the previous (k-1) best point-to-point short...

Various forms of shortest path planning (SPP) have been studied by numerous researchers. Although SPP is generally regarded as a solved problem in 2D space, few of the existing 2D solutions can be applied to 3D. Since many real-world applications are based on 3D or higher space, this deficiency severely limits the applicability of 2D solutions. In this paper, we present a new method of partitio...

We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the timeand space-like geodesics and invariant 1-form on the space of null geodesics. We prove a Poncelet-type theorem for null geodesics on the ellipsoid: if such a geodesic ...

We consider the problem of computing k shortest paths in a two-dimensional environment with polygonal obstacles, where the jth path, for 1  j  k, is the shortest path in the free space that is also homotopically distinct from each of the first j 1 paths. In fact, we consider a more general problem: given a source point s, construct a partition of the free space, called the kth shortest path m...