We introduce a novel and general approach for digitalization of line segments in the plane that satisfies a set of axioms naturally arising from Euclidean axioms. In particular, we show how to derive such a system of digital segments from any total order on the integers. As a consequence, using a well-chosen total order, we manage to define a system of digital segments such that all digital seg...

Why do we study Is the a acoustic structure in which we are interested to use it for communication? Certainly, belongs to a natural class of acoustic patterns about which we know very little, nam'ely, structured over time by mechanical events--such as a footstep on hand paper, a glass bottle bouncing or breaking communication) 0 If we knew more about the temporally and ly distributed acoustic p...

In this paper, we answer the question: Given a collection of compact sets, can one decide in polynomial time whether there exists a convex body whose boundary intersects every set in the collection? We prove that already when the sets are segments in the plane, deciding existence of a convex stabber is NP-complete. On the positive side, we give a polynomial-time algorithm (in the full paper) to...

In several image applications, it is necessary to retrieve specific line segments born a potentially very large set. In this paper, we consider the problem of indexing straight line segments to enable efficient retrieval of all line segments that (i) go through a specified point, or (ii) intersect a specified line segment. We propose a data organization, based on the Hough transform, that can b...

Denote by B the n-dimensional unit ball centred at o. It is known that in every lattice packing of B there is a cylindrical hole of infinite length whenever n ≥ 3. As a counterpart, this note mainly proves the following result: For any fixed , > 0, there exist a periodic point set P (n, ) and a constant c(n, ) such that B + P (n, ) is a packing in R, and the length of the longest segment contai...

Geometric spanner is a fundamental structure in computational geometry and plays an important role in many geometric networks design applications. In this paper, we consider a generalization of the classical geometric spanner problem (called segment spanner): Given a set S of disjoint 2-D segments, find a spanning network G with minimum size so that for any pair of points in S, there exists a p...

We report on first annotation experiments on narrative segments. Narrative segments are a pragmatic intermediate layer that allows studying more complex narratological phenomena. Our experiments show that segmenting on limited context information alone is difficult. High interannotator agreement on this task can be achieved by coupling the segmentation with summarization and aligning parts of t...

Properties of homogeneous segment sets are investigated in this paper. A universal characterization of homogeneous sets is presented in the form of a polynomial algorithm which decides whether or not a set S is homogeneous with respect to S∗. It is shown that any set of homogeneous segments can be reduced to the uniquely determined minimal base and a polynomial algorithm solving this task is pr...

We consider the following singularly perturbed Neumann problem ε∆u− u+ u = 0 , u > 0 in Ω, ∂u ∂ν = 0 on ∂Ω, where p > 2 and Ω is a smooth and bounded domain in R2. We construct a new class of solutions which consist of large number of spikes concentrating on a segment of the boundary which contains a strict local minimum point of the mean curvature function and has the same mean curvature at th...

Given a system S of simple continuous curves (``strings'') in the plane, we can define a graph GS as follows. Assign a vertex to each curve, and connect two vertices by an edge if and only if the corresponding two curves intersect. GS is called the intersection graph of S. Not every graph is an intersection graph of a system of curves [EET76] (see Fig. 1 for a simple example). This implies that...