View based recognition methods such as those using eigenspace techniques have been successful for a number of recognition tasks Currently however such approaches are relatively limited in their ability to recognize objects which are partly hidden from view or occur against cluttered backgrounds In order to address these limitations we have developed a new view matching technique based on an eig...

The purpose of object matching is to decide the similarity between two objects. This paper introduces 24 possible distance measures based on the Hausdor distance between two point sets. These measures can be used to match two sets of edge points extracted from any two objects. Based on our experiments on synthetic images containing various levels of noise, we determined that one of these distan...

The rst mathematical model of the untyped lambda calculus was discovered by DANA SCOTT in the category of algebraic lattices and Scott continuous maps. The question then arises as to which other cartesian closed categories contain a model of the calculus. In this paper we show that any compact Hausdor model of the calculus must satisfy the property that the semantic map from the calculus to the...

Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...

We give a superconnection proof of Connes’ index theorem for proper cocompact actions of étale groupoids. This includes Connes’ general foliation index theorem for foliations with Hausdor¤ holonomy groupoid.

Consider a sequence fg d g converging uniformly on compact sets to g, where g and g d are meromorphic functions on C. We show that the Julia sets J(g d) converge to the Julia set J(g) in the Hausdorr metric, if the Fatou set F (g) is the union of basins of attraction of attracting periodic orbits and 1 2 J(g). This result is discussed for families of nite type depending on a parameter, which is...

Matching images based on a Hausdorr measure has become popular for computer vision applications. However, no probabilistic model has been used in these applications. This limits the formal treatment of several issues, such as feature uncertainties and prior knowledge. In this paper, we develop a probabilis-tic formulation of image matching in terms of maximum likelihood estimation that generali...

A lower bound of the Hausdorr dimension of certain self-aane sets is given. Moreover, this and other known bounds such as the box dimension are expressed in terms of solutions of simple equations involving the singular values of the aanities.

We report on a proof-checked version of Stone’s result on the representability of Boolean algebras via the clopen sets of a totally disconnected compact Hausdor↵ space. Our experiment is based on a proof verifier based on set theory, whose usability can in its turn benefit from fully formalized proofs of representation theorems akin to the one discussed in this note.