We consider the following problem: two parties have each a private function, for example one that outputs the party’s preferences on a set of alternatives; they wish to compute the distance between their functions without any of the parties revealing its function to the other. The above problem is extremely important in the context of social, political or business networks, whenever one wishes ...

The edit distance between two graphs on the same labeled vertex set is the symmetric difference of the edge sets. The edit distance function of hereditary property, H, is a function of p ∈ [0, 1] and is the limit of the maximum normalized distance between a graph of density p and H. This paper uses localization, for computing the edit distance function of various hereditary properties. For any ...

This paper is presented as an undergraduate honors thesis by Christopher Severs under the supervision of Professor Jeffrey Remmel at UCSD. The aim of the project was to read material about permutation statistics and generating functions for the ring of symmetric functions and then address a problem not covered in the literature to date. In working on this project the author gained a much better...

The goal of this article is to develop a framework for large margin classification in metric spaces. We want to find a generalization of linear decision functions for metric spaces and define a corresponding notion of margin such that the decision function separates the training points with a large margin. It will turn out that using Lipschitz functions as decision functions, the inverse of the...

In this chapter, we present distance mapping, a technique for adding small-scale displacement mapping to objects in a pixel shader. We treat displacement mapping as a ray-tracing problem, beginning with texture coordinates on the base surface and calculating texture coordinates where the viewing ray intersects the displaced surface. For this purpose, we precompute a three-dimensional distance m...

We present algorithms for computing some distance functions between two (possibly intersecting) polygons, both in the convex and nonconvex cases. The interest for such distance functions comes from applications in robot vision, pattern recognition and contour fitting. We present a linear sequential algorithm and an optimal EREW·PRAM parallel algorithm for the case when the input polygons are co...

Distance functions are at the core of numerous computer vision and machine learning tasks. For example, a multiple view geometry application (such as homography estimation), often includes a descriptor matching step. First, small image patches are selected. Then, descriptors (vectors) are computed to describe these patches. To decide if two descriptors (from two different images) are from the s...

This paper is concerned with the simulation of the Partial Diierential Equation (PDE) driven evolution of a closed surface by means of an implicit representation. In most applications, the natural choice for the implicit representation is the signed distance function to the closed surface. Osher and Sethian propose to evolve the distance function with a Hamilton-Jacobi equation. Unfortunately t...