We study the problem of computing a low-distortion embedding between two metric spaces. More precisely given an input metric space M we are interested in computing in polynomial time an embedding into a host space M ′ with minimum multiplicative distortion. This problem arises naturally in many applications, including geometric optimization, visualization, multi-dimensional scaling, network spa...

In this paper, we present a new and fast encoding algorithm (FEA) for vector quantization. The magnitude (sum of the components of a vector) feature of the vectors is used in this algorithm to improve the efficiency of searching. Sorting of the magnitude values enhances the searching. As the values are sorted, the searching can be terminated in advance to reduce the time needed to locate the re...

In 1733, Georges-Louis Leclerc, Comte de Buffon in France, set the ground of geometric probability theory by defining an enlightening problem: What is the probability that a needle thrown randomly on a ground made of equispaced parallel strips lies on two of them? In this work, we show that the solution to this problem, and its generalization to N dimensions, allows us to discover a quantized f...

(a) Input image (b) Scaling (c) Visibility map for (d) (d) Seam carving (e) Visibility map for (f) (f) Seam carving energy terms (distortion energy: absolute magnitude distance, nD = 1) (g) Visibility map for (h) (h) Distortion energy: absolute magnitude distance, nD = 1; unary with nU = 1 (i) Visibility map for (j) (j) Distortion energy: absolute magnitude distance, nD = 1; seam term: repeat c...

In remote sensing applications with large numbers of sensors, the global correlation structure of the sensor observations may not be known locally at the sensors. However, some knowledge of this correlation structure can enable the sensors to communicate collaboratively to avoid interference and combat channel noise. A model is proposed for the uncertainty in correlation structure, called a fad...

Lines are one of the basic primitives used by the perceptual system to analyze and interpret a scene. Therefore, line detection is a very important issue for the robustness and flexibility of Computer Vision systems. However, in the case of images showing a significant lens distortion, standard line detection methods fail because lines are not straight. In this paper we present a new technique ...

Background: The magnetic resonance imaging (MRI)-based radiotherapy planning method have been considered in recent years because of the advantages of MRI and the problems of planning with two images modality. The first step in MRI-based radiotherapy is to evaluate magnetic resonance (MR) images geometric distortion. Therefore, the present study aimed to evaluate system related geometric distort...

Suppose A is a finite set, let P be a discrete probability distribution on A, and let M be an arbitrary “mass” function on A. We give a precise characterization of the most efficient way in which An can be almost-covered using spheres of a fixed radius. An almost-covering is a subset Cn of A n, such that the union of the spheres centered at the points of Cn has probability close to one with res...