Statistics and estimation theory is enriched with techniques derived from differential geometry. This establishes the increasing topic of information geometry. This allows new insights into these classical topics. Differential geometry offers a wide spectrum of applications within statistic inference and estimation theory. Especially, many topics of information theory can be interpreted in a ge...

A natural partial ordering exists on all weighted games and, more broadly, on all linear games. We describe several properties of the partially ordered sets formed by these games and utilize this perspective to enumerate proper linear games with one generator. We introduce a geometric approach to weighted voting by considering the convex polytope of all possible realizations of a weighted game ...

We present a new definition of optimality intervals for the parametric right-hand side linear programming (parametric RHS LP) Problem r = m i n { c r x l A x = b + 2b, x > 0}. We then show that an optimality interval consists eifher of a breakpoint or the open interval between two consecutive breakpoints of the continuous piecewise linear convex function ~o(2). As a consequence, the optimality ...

Integration over a domain, such as a Euclidean space or a Riemannian manifold, is a fundamental problem across scientific fields. Many times, the underlying domain is only accessible through a discrete approximation, such as a set of points sampled from it, and it is crucial to be able to estimate integral in such discrete settings. In this paper, we study the problem of estimating the integral...

In general, excessive colorimetric and geometric errors in multi-view images induce visual fatigue to users. Various works have been proposed to reduce these errors, but conventional works have only been available for stereoscopic images while requiring cumbersome additional tasks, and often showing unstable results. In this paper, we propose an effective multi-view image refinement algorithm. ...

Lecture notes for the Geometry, Mechanics and Control 8th Intl. Young Researchers Workshop 2013 held in Barcelona. This document presents the mathematical framework that has been developed in the field of computational anatomy in the last fifteen years. We will focus in particular on the use of right-invariant metrics on diffeomorphism groups and its recent developments.

Relevance is a central concept in Information Retrieval (IR). It is used to work out effectiveness measures for IR systems, i.e. measures to express how well (or bad) an IR system performs; classical measures are precision, recall, fallout. It is shown that the empirical relation P=NR/x (P=precision, R=recall, N=total number of relevant documents, x=the number of retrieved documents) can be for...

This paper deals with changes of the geometric field of view on speed perception. This study has been carried out using the SAAM dynamic driving simulator (Arts et Métiers ParisTech). SAAM provides motion cues thanks to a 6 DOF electromechanical platform and is equipped with a cylindrical screen of 150°. 20 subjects have reproduced 2 speeds (50 km/h and 90 km/h) without knowing the numerical va...

We recall the basic idea of an algebraic approach to learning Bayesian network (BN) structures, namely to represent every BN structure by a certain (uniquely determined) vector, called a standard imset. The main result of the paper is that the set of standard imsets is the set of vertices (= extreme points) of a certain polytope. Motivated by the geometric view, we introduce the concept of the ...

We present a geometric view on bilingual lexicon extraction from comparable corpora, which allows to re-interpret the methods proposed so far and identify unresolved problems. This motivates three new methods that aim at solving these problems. Empirical evaluation shows the strengths and weaknesses of these methods, as well as a significant gain in the accuracy of extracted lexicons.