Up to now, all the known Euclidean distance function algorithms are either excessively slow or inaccurate, and even Danielsson's method produces errors in some con gurations. We show that they are due to the local way distances are propagated in images by this algorithm. To remedy these drawbacks, an algorithm is introduced, which encodes the objects boundaries as chains and propagates these st...

| In this paper we apply the concepts of Vector Quantization (VQ) for the determination of arbitrary distance functions { a problem which has important applications in Logistics and Location Analysis. The input to our problem is the set of coordinates of a large number of nodes whose inter-node arbitrary \distances" have to be estimated. To render the problem interesting, non-trivial and realis...

We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove assorted theorems about the new reducibilities and about functions which have nonincreasing computable approximations. Finally, we show that the spectrum of the d...

Pitch modelling is considered to be an important factor in speech synthesis where the pitch contour plays a demonstrable role in the intelligibility and naturalness of synthesised speech. While quantitative models for pitch contours have been proposed previously, each of these have a fixed level of details and as such not all of them provide the basis either for automatic extraction of pitch mo...

This paper is concerned with the relations between the differential invariants of a smooth manifold embedded in the Euclidean space and the square of the distance function from the manifold. In particular, we are interested in curvature invariants like the mean curvature vector and the second fundamental form. We find that these invariants can be computed in a very simple way using the third or...

Let M be a simply connected complete Kähler manifold and N a closed complete totally geodesic complex submanifold of M such that every minimal geodesic in N is minimal in M . Let Uν be the unit normal bundle of N in M . We prove that if a distance function ρ is differentiable at v ∈ Uν , then ρ is also differentiable at −v.

This report will add some supplements to the recently finished report series on the distance function wavelets (DFW). First, we define the general distance in terms of the Riesz potential, and then, the distance function Abel wavelets are derived via the fractional integral and Laplacian. Second, the DFW Weyl transform is found to be a shifted Laplace potential DFW. The DFW Radon transform is a...

The edit distance between two graphs on the same labeled vertex set is the size of the symmetric difference of the edge sets. The distance between a graph, G, and a hereditary property, H, is the minimum of the distance between G and each G′ ∈ H with the same number of vertices. The edit distance function of H is a function of p ∈ [0, 1] and is the limit of the maximum normalized distance betwe...