In this paper, we describe a new region-based approach to active contours for segmenting images composed of two or three types of regions characterizable by a given statistic. The essential idea is to derive curve evolutions which separate two or more values of a predetermined set of statistics computed over geometrically determined subsets of the image. Both global and local image information ...

We investigate the extent of second order characterizable structures by extending Shelah’s Main Gap dichotomy to second order logic. For this end we consider a countable complete first order theory T . We show that all sufficiently large models of T have a characterization up to isomorphism in the extension of second order logic obtained by adding a little bit of infinitary logic if and only if...

Since 1969, the superstructure has been the usual approach to nonstandard analysis. The method used to measure the strength of a GDmodel Divine attribute, which is comparable to a human attribute, is, at least, partially expressible in terms of cardinality. In this paper, it is shown that for the non-atomic approach to superstructure construction such a cardinality does not have a set-theologic...

Global-as-view (GAV) constraints form a class of database constraints that has been widely used in the study of data exchange and data integration. Specifically, relationships between different database schemas are commonly described by a schema mapping consisting of a finite set of GAV constraints. Such schema mappings can be viewed as representations of an infinite set of data examples. We st...

The class of threshold functions is known to be characterizable by functional equations or, equivalently, by pairs of relations, which are called relational constraints. It was shown by Hellerstein that this class cannot be characterized by a finite number of such objects. In this paper, we investigate classes of threshold functions which arise as intersections of the class of all threshold fun...