Institute for Systems Research
Permanent URI for this communityhttp://hdl.handle.net/1903/4375
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Item The Inverse Conductivity Problem and the Hyperbolic X-Ray Transform(1993) Berenstein, Carlos A.; Tarabusi, E. Casadio; ISRIt is shown here how the approximate inversion algorithm of Barber & Brown for the linearized inverse conductivity problem in the disk can be interpreted exactly in terms of the X-ray transform with respect to the Poincare metric and of suitable convolution operators.Item Structure of Divisible Discrete Random Sets and Their Randomized Superpositions(1991) Sidiropoulos, N.; Baras, John S.; Berenstein, Carlos A.; ISRIn this paper, we present an axiomatic formulation of Discrete Random Sets, and extend Choquet's uniqueness result to obtain a recursive procedure for the computation of the underlying event- space probability law, given a consistent Discrete Random Set specification via its generating functional. Based on this extension, we investigate the structure of Discrete Random Set models that enjoy the properties of independent decomposition/superposition, and present a design methodology for deriving models that are guaranteed to be consistent with some underlying event-space probability law. These results pave the way for the construction of various interesting models, and the solution of statistical inference problems for Discrete Random Sets.Item Bayesian Hypothesis Testing for Boolean Random Sets with Radial Convex Primary Grains Using Morphological Skeleton Transforms(1991) Sidiropoulos, N.; Baras, John S.; Berenstein, Carlos A.; ISRWe consider the problem of binary hypothesis testing for planar Boolean random sets with radial convex primary grains. We show that this problem is equivalent to the problem of binary hypothesis testing for Poisson points on a subset of R cube . The log-likelihood ratio for Poisson points can therefore be applied to observation points on this subset of R cube. Several interesting results pertaining to the asymptotic performance of the log-likelihood ratio for Poisson points are known. A major difficulty with this approach is that the test is based on observation points on a subset of R cube, and is not directly given in terms of the observation of a realization of a Boolean random set. An efficient means of mapping realizations of planar Boolean random sets to corresponding realizations of Poisson point processes on this subset of R cube is needed in order to implement the test. We show that this can be achieved via a class of morphological transformations known as morphological skeleton transforms. These transforms are flexible shape-size analysis tools based on elementary morphological and set-theoretic operations. This is the principal contribution of this paper.Item Exact, Recursive, Inference of Event Space Probability Law for Discrete Random Sets with Applications(1991) Sidiropoulos, N.; Baras, John S.; Berenstein, Carlos A.; ISRIn this paper we extend Choquet's result to obtain a recursive procedure for the computation of the underlying event-space probability law for Discrete Random Sets, based on Choquet's capacity functional. This is an important result, because it paves the way for the solution of statistical inference problems for Discrete Random Sets. As an example, we consider the Discrete Boolean Random Set with Radial Convex Primary Grains model, compute its capacity functional, and use our procedure to obtain a recursive solution to the problem of M-ary MAP hypothesis testing for the given model. The same procedure can be applied to the problem of ML model fitting. Various important probability functionals are computed in the process of obtaining the above results.