A distance matrix D of order n is symmetric with elements idfj, where d,, = 0. D is Euclidean when the in(n 1) quantities dij can be generated as the distances between a set of n points, X (n X p), in a Euclidean space of dimension p. The dimensionality of D is defined as the least value of p = rank(X) of any generating X; in general p + 1 and p +2 are also acceptable but may include imaginary ...

In this paper, we rewrite the Minimal-Connected-Component (MCC) model in 2-D meshes in a fully-distributed manner without using global information so that not only can the existence of a Manhattan-distance-path be ensured at the source, but also such a path can be formed by routing-decisions made at intermediate nodes along the path. We propose the MCC model in 3-D meshes, and extend the corres...

A standard method to perform skeletonisation is to use a distance transform. Unfortunately such an approach has the drawback that only the Symmetric axis transform can be computed and not the more practical smoothed local symmetries or the more general symmetry set. Using singularity theory we introduce an extended distance transform which may be used to capture more of the symmetries of a shap...

Given a set T of n points in IR, a Manhattan Network G is a network with all its edges horizontal or vertical segments, such that for all p, q ∈ T , in G there exists a path (named a Manhattan path) of the length exactly the Manhattan distance between p and q. The Minimum Manhattan Network (MMN) problem is to find a Manhattan network of the minimum length, i.e., the total length of the segments...

The paper presents an analog, current-mode circuit that calculates a distance between the neuron weights vectors W and the input learning patterns X. The circuit can be used as a component of different self-organizing neural networks (NN) implemented in the CMOS technology. In Self-Organizing Maps (SOM) as well as in NNs using the Neural Gas or the Winner Takes All (WTA) learning algorithms, to...

A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer m ≥ 2, there are only finitely many non-geometric distance-regular graphs with smallest eigenvalue at least −m, diameter at least three and intersection number c2 ≥ 2.

In this paper, we present a new method for detecting curvilinear structures in a gray-scale image. The concept of skeleton extraction is introduced to detect more general structures such as tapering structures. A skeleton is extracted from the Euclidean distance map that is constructed based on the edge map of an input image. Then, skeletal points are classified into three types (RIDGE, RAVINE ...

Given a set T of n points in IR, a Manhattan Network G is a network with all its edges horizontal or vertical segments, such that for all p, q ∈ T , in G there exists a path (named a Manhattan path) of the length exactly the Manhattan distance between p and q. The Minimum Manhattan Network problem is to find a Manhattan network of the minimum length, i.e., the total length of the segments of th...