This paper introduces a supervised discriminant Hausdorff distance that fits into the framework for automatic face analysis and recognition proposed in [1]. Our proposal relies solely on face shape variation contrarily to most of the successful model-based approaches, and results show comparable performance to them. The whole framework is based in a new set of Hausdorff measures and defines fac...

We show that for every Lebesgue measurable function f : [0, 1] → R there exists a compact set C of Hausdorff dimension 1/2 such that f is of bounded variation on C, and there exist compact sets Cα of Hausdorff dimension 1−α such that f is Hölder-α on Cα (0 < α < 1). These answer questions of M. Elekes, which were open even for continuous functions f . Our proof goes by defining a discrete Hausd...

*Correspondence: [email protected] Department of Mathematics, İstanbul Commerce University, Sütlüce/Beyoğlu, İstanbul, Turkey Abstract Das (Proc. Camb. Philos. Soc. 67:321-326, 1970) proved that every conservative Hausdorff matrix is absolutely kth power conservative. Savaş and Rhoades (Anal. Math. 35:249-256, 2009) proved the result of Das for double Hausdorff summability. In this paper we...

A sequential space (X,T) is called minimal sequential if no sequential topology on X is strictly weaker than T . This paper begins the study of minimal sequential Hausdorff spaces. Characterizations ofminimal sequential Hausdorff spaces are obtained using filter bases, sequences, and functions satisfying certain graph conditions. Relationships between this class of spaces and other classes of s...

In the paper, we introduce the concepts of dynamic object identification and verification using video. A generalized Hausdorff metric, which is more robust to noise and allows a confidence interpretation, is suggested for the identification and verification problem. Parameters from sensor motion compensation procedure are incorporated into the search step such that the Hausdorff metric based ma...

Let A and B be two sets of balls in Rd, d = 2, 3. We measure similarity between A and B by computing the minimum Hausdorff distance between A+ t and B, where the minimum is taken either over all vectors t ∈ Rd or over the vectors t such that A+t and B do not intersect. These problems arise in measuring similarity between the shapes of two proteins. We propose a number of exact and approximation...

Based on the work of Abercrombie [1], Barnea and Shalev [3] gave an explicit formula for the Hausdorff dimension of a group acting on a rooted tree. We focus here on the binary tree T . Abért and Virág [2] showed that there exist finitely generated (but not necessarily level-transitive) subgroups of AutT of arbitrary dimension in [0, 1]. We give the first deterministic construction of finitely ...

By de Vries duality, the category of compact Hausdorff spaces is dually equivalent to the category of de Vries algebras (complete Boolean algebras endowed with a proximity-like relation). We provide an alternative “modal-like” duality by introducing the concept of a Gleason space, which is a pair (X,R), where X is an extremally disconnected compact Hausdorff space and R is an irreducible equiva...

This paper discusses one method of producing fractals, namely that of iterated function systems. We first establish the tools of Hausdorff measure and Hausdorff dimension to analyze fractals, as well as some concepts in the theory of metric spaces. The latter allows us to prove the existence and uniqueness of fractals as fixed points of iterated function systems. We discuss the connection betwe...

Let X be a Hausdorff space and A EX a continuum. A is said to be a Universal Subcontinuum (USC) if AH\B is connected for every continuum B EX. Let a be a collection of USC's of a Hausdorff space. Then a is said to have the finite partition property if a has a decomposition into a finite number of subcollections each having the finite intersection property. A result due to W. J. Gray [l] can be ...