We have collected definitions and basic results for the (centered ball) density in metric space with respect to an arbitrary Hausdorff function. We have kept the definitions general: we do not assume the Hausdorff functions are continuous or blanketed, and we do not assume the metric space is a subset of Euclidean space. We discuss the covering measure (= centered Hausdorff measure) and packing...

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...

Removing the condition of symmetry in the notion of a fuzzy (pseudo)metric, in Kramosil and Michalek’s sense, one has the notion of a fuzzy quasi-(pseudo-)metric. Then for each fuzzy quasi-pseudo-metric on a set X we construct a fuzzy quasipseudo-metric on the collection of all nonempty subsets of X, called the Hausdorff fuzzy quasi-pseudo-metric. We investigate several properties of this struc...

We study properties of metric segments in the class all spaces considered up to an isometry, endowed with Gromov--Hausdorff distance. On isometry classes compact spaces, Gromov-Hausdorff distance is a metric. A segment that consists points lying between two given ones. By von Neumann--Bernays--Godel (NBG) axiomatic set theory, proper monster collection, e.g., collection cardinal sets. prove any...

Hausdorff metrics are used in geometric settings for measuring the distance between sets of points. They have been used extensively in areas such as computer vision, pattern recognition and computational chemistry. While computing the distance between a single pair of sets under the Hausdorff metric has been well studied, no results were known for the Nearest Neighbor problem under Hausdorff me...

We introduce the notion of the Gromov-Hausdorff fuzzy distance between two non-Archimedean fuzzy metric spaces (in the sense of Kramosil and Michalek). Basic properties involving convergence and the fuzzy version of the completeness theorem are presented. We show that the topological properties induced by the classic Gromov-Hausdorff distance on metric spaces can be deduced from our approach.

We study the infimum of the Hausdorff and Vietoris topologies on the hyperspace of a metric space. We show that this topology coincides with the supremum of the upper Hausdorff and lower Vietoris topologies if and only if the underlying metric space is either totally bounded or is a UC space.

We provide a supervised speech-independent voice recognition technique in this paper. In the feature extraction stage we propose a mel-cepstral based approach. Our feature vector classification method uses a special nonlinear metric, derived from the Hausdorff distance for sets, and a minimum mean distance classifier. Keywords—Text-independent speaker recognition, mel cepstral analysis, speech ...