We present a novel method for representing and evolving objects of arbitrary dimension. The method, called the Vector Distance Function (VDF) method, uses the vector that connects any point in space to its closest point on the object. It can deal with smooth manifolds with and without boundaries and with shapes of diierent dimensions. It can be used to evolve such objects according to a variety...

We describe linear-time algorithms for solving a class of problems that involve transforming a cost function on a grid using spatial information. These problems can be viewed as a generalization of classical distance transforms of binary images, where the binary image is replaced by an arbitrary function on a grid. Alternatively they can be viewed in terms of the minimum convolution of two func...

Suppose each of n men and n women is located at a point in a metric space. A woman ranks the men in order of their distance to her from closest to farthest, breaking ties at random. Œe men rank the women similarly. An interesting problem is to use these ranking lists and €nd a stable matching in the sense of Gale and Shapley. Œis problem formulation naturally models preferences in several real ...

In this paper we review computational techniques for efficiently computing distance functions and geodesics, thereby addressing optimal trajectory problems. These techniques are based on solving the Eikonal equation. Following [30] we first describe how we can numerically solve this equation in a Cartesian grid in O(N) operations, N being the number of grid points. This optimal run-time cost is...

This paper deals with the basic notions of k-tautimmersions . These notions come from two special cases; that is, tight and taut immersions. Tight and taut based on high and distance functions respectively and their basic notions are normal bundle, endpoint map, focal point, critical normal. We generalize hight and distance functions to cylindrical function and define basic notions of k-taut ...

Picking up exactly one member from each of the nonperiodic cyclic equivalence classes of an (n, k + 1) Reed-Solomon code E over GF(q) gives a code, E”, which has bounded Hamming correlation values and the self-synchronizing property. The exact size of E” is shown to be t Cdln p(d)~~~+[$], where p(d) is the Miibius function, [z] is the integer part of 5, and the summation is over all the divisor...