The Hausdorff distance measures the extent to which each point of a `model' set lies near some point of an `image' set and vice versa. Thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper we provide efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model. We focus primarily on the case in which the model is only allowed to translate with respect to the image. Then we consider how to extend the techniques to rigid motion (translation and rotation). The Hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived. The method is quite tolerant of small position errors as occur with edge detectors and other feature extraction methods. Moreover, we show how the method extends naturally to the problem of comparing a portion of a model against an i...

This paper represents a continuation of our programme [16, 13] of extending various concepts of general topology from the setting of Hausdorff (or, at most, 7^) spaces, in which they are usually embedded, to the larger classes of spaces we need to consider in the theory of computation.

. A new viewpoint of Topology, summarized under the name Convenient Topology, is considered in such a way that the structural deficiencies of topological and uniform spaces are remidied. This does not mean that these spaces are superfluous. It means exactly that a better framework for handling problems of a topological nature is used. In this context semiuniform convergence spaces play an essential role. They include not only convergence structures such as topological structures and limit space structures, but also uniform convergence structures such as uniform structures and uniform limit space structures, and they are suitable for studying continuity, Cauchy continuity and uniform continuity as well as convergence structures in function spaces, namely simple convergence, continuous convergence and uniform convergence. Several results are presented which cannot be obtained by using topological or uniform spaces respectively. Mathematics Subject Classifications (1991). 54A05, 54A20, 5...

Robert C. Flagg and Philipp Sunderhauf y University of Southern Maine fflagg,psunderg@usm.maine.edu December 12, 1995 Abstract If a posets lacks joins of directed subsets, one can pass to its ideal completion. But doing this means also changing the setting: The universal property of ideal completion of posets suggests that it should be regarded as a functor from the category of posets with monotone maps to the category of dcpos with Scott-continuous functions as morphisms. The same applies for the quantitative version of ideal completion suggested in the literature. As in the case of posets, it seems advantageous to consider a different topology with the completed spaces. We introduce Smyth completion as tool to automatically end up with the right topology after completing. 1 Introduction This paper is part of the ongoing foundational work on quantitative domain theory [Smy88, BBR95, Rut95, FW95, Wag94], which refines ordinary do- Supported by the Deutsche Forschungsgemeinschaf...