Let P be a simple polygon of n vertices and let S be a set of N points lying in the interior of P . A geodesic disk GD(p, r) with center p and radius r is the set of points in P that have a geodesic distance ≤ r from p (where the geodesic distance is the length of the shortest polygonal path connection that lies in P ). In this paper we present an output sensitive algorithm for finding all N ge...

In this paper, we present a clustering-based color indexing scheme for effective amd efficient image retrieval, which is essentially an exploration on the application of clustering technique to image retrieval. In our approach, the color features are clustered automatically using a color clustering algorithm twice (called two-level clustering processing) and two color feature summarizations are...

Let E be an elliptic curve over a finite field Fq of q elements and x(P ) to denote the x-coordinate of a point P = (x(P ), y(P )) ∈ E. Let ⊕ denote the group operation in the Abelian group E(Fq) of Fq -rational points on E. We show that for any sets R,S ⊆ E(Fq) at least one of the sets { x(R)+ x(S): R ∈R, S ∈ S} and {x(R⊕ S): R ∈R, S ∈ S} is large. This question is motivated by a series of rec...

We describe a new method for computing a dense displacement eld from a time-sequence of 2D or 3D images. It consists in minimizing an energy deened on the space of correspondence functions. This energy is divided into two terms, one term which matches contour points and particularly high curvature points, and one regularization term which constrains the continuity of the eld. We introduce an ad...

We improve the best known lower bounds on the distance between two points of a Morse cluster in R, with ρ ∈ [4.967, 15]. Our method is a generalization of the one applied to the Lennard-Jones potential in [2], and it also leads to improvements of lower bounds for the energy of a Morse cluster. Some of the numerical results have been announced in [1].

This paper extends the result of Steele [6, 5] on the worst-case length of the Euclidean minimum spanning tree EMST and the Euclidean minimum insertion tree EMIT of a set of n points S ⊂ R. More precisely, we show that, if the weight w of an edge e is its Euclidean length to the power of α, the following quantities ∑ e∈EMST w(e) and ∑ e∈EMIT w(e) are both worst-case O(n 1−α/d), where d is the d...