Humans and other animals build up spatial knowledge of the environment on the basis of visual information and path integration. We compare three hypotheses about the geometry of this knowledge of navigation space: (a) 'cognitive map' with metric Euclidean structure and a consistent coordinate system, (b) 'topological graph' or network of paths between places, and (c) 'labelled graph' incorporat...

We extend the Theory of Computation on real numbers, continuous real functions, and bounded closed Euclidean subsets, to compact metric spaces (X, d): thereby generically including computational and optimization problems over higher types, such as the compact ‘hyper’ spaces of (i) nonempty closed subsets of X w.r.t. Hausdorff metric, and of (ii) equicontinuous functions on X . The thus obtained...

In this paper, we investigate the performance of a Soft-Input soft-Output decoding algorithm for LDPC codes that uses Euclidean distance as its metric, in the Rayleigh fading channel. It is found that its Bit Error Rate performance is close to that of traditional decoding algorithms like the SumProduct algorithm and its logarithmic version. Main characteristics of the proposed algorithm and its...

Vector median filtering is a well known technique for reducing noise in color images. These filters are defined on the basis of a suitable distance or similarity measure, being the most common used the Euclidean and City-Block distances. In this paper, a Fuzzy Metric, in the sense of George and Veeramani (1994), is defined and applied to color image filtering by means of a new Vector Median Fil...

This paper presents nonparametric two-sample bootstrap tests for means of random symmetric positive-definite (SPD) matrices, according to two different metrics: the Frobenius (or Euclidean) metric, inherited from the embedding of the set of SPD metrics in the Euclidean set of symmetric matrices, and the canonical metric, which is defined without an embedding and suggests an intrinsic analysis. ...

In binary images, the distance transformation (DT) and the geometrical medial axis are classic tools for shape analysis. In the digital geometry literature, recent articles have demonstrated that fast algorithms can be designed without any approximation of the Euclidean metric. The aim of the paper is to first give an overview of separable techniques to compute the distance transformation, the ...

A metric defined by Fine induces a topology on the unit interval which is strictly stronger than the ordinary Euclidean topology and which has some interesting applications in Walsh analysis. We investigate computability properties of a corresponding Fine representation of the real numbers and we construct a structure which characterizes this representation. Moreover, we introduce a general cla...

We investigate the action of imprecisely defined affine and Euclidean transformations and compute tolerance zones of points and subspaces. Tolerance zones in the Euclidean motion group are analyzed by means of linearization and bounding the linearization error via the curvatures of that group with respect to an appropriate metric.

The grid cells discovered in the rodent medial entorhinal cortex have been proposed to provide a metric for Euclidean space, possibly even hardwired in the embryo. Yet one class of models describing the formation of grid unit selectivity is entirely based on developmental self-organization, and as such it predicts that the metric it expresses should reflect the environment to which the animal h...

A definition of chirality based on group theory is presented. It is shown to be equivalent to the usual one in the case of Euclidean spaces, and it permits to define chirality in metric spaces which are not Euclidean. 2000 MSC code: 58D19 ; PACS code: 02.20.Bb