Differential epipolar constraint in mobile robot egomotion estimation

The estimation of camera egomotion is a well established problem in computer vision. Many approaches have been proposed based on both the discrete and the differential epipolar constraint. The discrete case is mainly used in self-calibrated stereoscopic systems, whereas the differential case deals with a unique moving camera. The article surveys several methods for mobile robot egomotion estimation covering more than 0.5 million samples using synthetic data. Results from real data are also given

A survey addressing the fundamental matrix estimation problem

Epipolar geometry is a key point in computer vision and the fundamental matrix estimation is the only way to compute it. This article surveys several methods of fundamental matrix estimation which have been classified into linear methods, iterative methods and robust methods. All of these methods have been programmed and their accuracy analysed using real images. A summary, accompanied with experimental results, is given

Generalized Higher-Order Voronoi Diagrams on Polyhedral Surfaces

We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a possibly non-convex polyhedral surface in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) on a polyhedral surface with obstacles. To obtain the discrete Voronoi diagrams our algorithms, exploiting hardware graphics capabilities, compute shortest path distances defined by the sites

View-dependent information theory quality measures for pixel sampling and scene discretization in flatland

In this paper, we present view-dependent information theory quality measures for pixel sampling and scene discretization in flatland. The measures are based on a definition for the mutual information of a line, and have a purely geometrical basis. Several algorithms exploiting them are presented and compare well with an existing one based on depth differences

Shape complexity based on mutual information

Shape complexity has recently received attention from different fields, such as computer vision and psychology. In this paper, integral geometry and information theory tools are applied to quantify the shape complexity from two different perspectives: from the inside of the object, we evaluate its degree of structure or correlation between its surfaces (inner complexity), and from the outside, we compute its degree of interaction with the circumscribing sphere (outer complexity). Our shape complexity measures are based on the following two facts: uniformly distributed global lines crossing an object define a continuous information channel and the continuous mutual information of this channel is independent of the object discretisation and invariant to translations, rotations, and changes of scale. The measures introduced in this paper can be potentially used as shape descriptors for object recognition, image retrieval, object localisation, tumour analysis, and protein docking, among others

Point sampling with uniformly distributed lines

In this paper we address the problem of extracting representative point samples from polygonal models. The goal of such a sampling algorithm is to find points that are evenly distributed. We propose star-discrepancy as a measure for sampling quality and propose new sampling methods based on global line distributions. We investigate several line generation algorithms including an efficient hardware-based sampling method. Our method contributes to the area of point-based graphics by extracting points that are more evenly distributed than by sampling with current algorithms

Good-visibility computation using graphics hardware

Aquesta tesi tracta del disseny, implementació i discussió d'algoritmes per resoldre problemes de visibilitat i bona-visibilitat utilitzant el hardware gràfic de l'ordinador. Concretament, s'obté una discretització dels mapes de multi-visibilitat i bona-visibilitat a partir d'un conjunt d'objectes de visió i un conjunt d'obstacles. Aquests algoritmes són útils tant per fer càlculs en dues dimensions com en tres dimensions. Fins i tot ens permeten calcular-los sobre terrenys.

Visibility and proximity on triangulated surfaces

En aquesta tesi es solucionen problemes de visibilitat i proximitat sobre superfícies triangulades considerant elements generalitzats. Com a elements generalitzats considerem: punts, segments, poligonals i polígons. Les estrategies que proposem utilitzen algoritmes de geometria computacional i hardware gràfic. Comencem tractant els problemes de visibilitat sobre models de terrenys triangulats considerant un conjunt d'elements de visió generalitzats. Es presenten dos mètodes per obtenir, de forma aproximada, mapes de multi-visibilitat. Un mapa de multi-visibilitat és la subdivisió del domini del terreny que codifica la visibilitat d'acord amb diferents criteris. El primer mètode, de difícil implementació, utilitza informació de visibilitat exacte per reconstruir de forma aproximada el mapa de multi-visibilitat. El segon, que va acompanyat de resultats d'implementació, obté informació de visibilitat aproximada per calcular i visualitzar mapes de multi-visibilitat discrets mitjançant hardware gràfic. Com a aplicacions es resolen problemes de multi-visibilitat entre regions i es responen preguntes sobre la multi-visibilitat d'un punt o d'una regió. A continuació tractem els problemes de proximitat sobre superfícies polièdriques triangulades considerant seus generalitzades. Es presenten dos mètodes, amb resultats d'implementació, per calcular distàncies des de seus generalitzades sobre superfícies polièdriques on hi poden haver obstacles generalitzats. El primer mètode calcula, de forma exacte, les distàncies definides pels camins més curts des de les seus als punts del poliedre. El segon mètode calcula, de forma aproximada, distàncies considerant els camins més curts sobre superfícies polièdriques amb pesos. Com a aplicacions, es calculen diagrames de Voronoi d'ordre k, i es resolen, de forma aproximada, alguns problemes de localització de serveis. També es proporciona un estudi teòric sobre la complexitat dels diagrames de Voronoi d'ordre k d'un conjunt de seus generalitzades en un poliedre sense pesos.

Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densities by generalizing the Aitchison geometry for compositions in the simplex into the set probability densities

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Central notations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform. In this way very elaborated aspects of mathematical statistics can be understood easily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating, combination of likelihood and robust M-estimation functions are simple additions/ perturbations in A2(Pprior). Weighting observations corresponds to a weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces formed by their posterior in the dual information space A2(Pprior). The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P. The discussion of A2(P) valued random variables, such as estimation functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Vertebrates Limb Geometry in the Simplex space

A novel metric comparison of the appendicular skeleton (fore and hind limb) of different vertebrates using the Compositional Data Analysis (CDA) methodological approach it’s presented. 355 specimens belonging in various taxa of Dinosauria (Sauropodomorpha, Theropoda, Ornithischia and Aves) and Mammalia (Prothotheria, Metatheria and Eutheria) were analyzed with CDA. A special focus has been put on Sauropodomorpha dinosaurs and the Aitchinson distance has been used as a measure of disparity in limb elements proportions to infer some aspects of functional morphology

A Negotiation Style Recommender Based on Computational Ecology in Open Negotiation Environments

The system described herein represents the first example of a recommender system in digital ecosystems where agents negotiate services on behalf of small companies. The small companies compete not only with price or quality, but with a wider service-by-service composition by subcontracting with other companies. The final result of these offerings depends on negotiations at the scale of millions of small companies. This scale requires new platforms for supporting digital business ecosystems, as well as related services like open-id, trust management, monitors and recommenders. This is done in the Open Negotiation Environment (ONE), which is an open-source platform that allows agents, on behalf of small companies, to negotiate and use the ecosystem services, and enables the development of new agent technologies. The methods and tools of cyber engineering are necessary to build up Open Negotiation Environments that are stable, a basic condition for predictable business and reliable business environments. Aiming to build stable digital business ecosystems by means of improved collective intelligence, we introduce a model of negotiation style dynamics from the point of view of computational ecology. This model inspires an ecosystem monitor as well as a novel negotiation style recommender. The ecosystem monitor provides hints to the negotiation style recommender to achieve greater stability of an open negotiation environment in a digital business ecosystem. The greater stability provides the small companies with higher predictability, and therefore better business results. The negotiation style recommender is implemented with a simulated annealing algorithm at a constant temperature, and its impact is shown by applying it to a real case of an open negotiation environment populated by Italian companies

Computing Distance Functions from Generalized Sources on Weighted Polyhedral Surfaces

We present algorithms for computing approximate distance functions and shortest paths from a generalized source (point, segment, polygonal chain or polygonal region) on a weighted non-convex polyhedral surface in which obstacles (represented by polygonal chains or polygons) are allowed. We also describe an algorithm for discretizing, by using graphics hardware capabilities, distance functions. Finally, we present algorithms for computing discrete k-order Voronoi diagrams

Single and multiple addition to C60. A computational chemistry study

Des del seu descobriment, a la molècula C60 se li coneixen una varietat de derivats segons el tipus de funcionalització amb propietats fisicoquímiques específiques de gran interès científic. Una sel·lecció de derivats corresponents a addicions simple o múltiple al C60 s'ha considerat en aquest treball d'investigació. L'estudi a nivell de química computacional de diversos tipus d'addició al C60 s'han portat a terme per tal de poder donar resposta a aspectes que experimentalment no s'entenen o són poc clars. Els sistemes estudiats en referència a l'addició simple al C60 han estat en primer lloc els monoiminoful·lerens, C60NR, (de les dues vies proposades per la seva síntesi, anàlisis cinètic i termodinàmic han ajudat a explicar els mecanismes de formació i justificar l'addició a enllaços tipus [5,6]), i en segon lloc els metanoful·lerens i els hidroful·lerens substituits, C60CHR i C60HR, (raons geomètriques, electròniques, energètiques i magnètiques justifiquen el diferent caràcter àcid ente ambdós derivats tenint en compte una sèrie de substituents R amb diferent caràcter electrònic donor/acceptor). Els fluoroful·lerens, C60Fn, i els epoxid ful·lerens, C60On, (anàlisi sistemàtic dels seus patrons d'addició en base a poder justificar la força que els governa han aportat dades complementàries a les poques que existeixen experimentalment al respecte).

Dihydrogen bonds: a study

Un pont de dihidrogen (dihydrogen bond,DHB) és un tipus de pont d'hidrogen atípic que s'estableix entre un hidrur metàl·lic i un donador de protons com un grup OH o NH. Els ponts de dihidrogen són claus en les característiques geomètriques i altres propietats de compostos que en presenten tan de molècules petites com el dímer de NH3BH3, com d'estructures superiors més complicades com complexes metàl·lics o sòlids. Poden ser útils aplicats a certes molècules o síntesis moleculars per a obtenir nous materials amb propietats o característiques fetes a mida. El treball d'aquesta tesi està orientat a millorar la comprensió dels ponts de dihidrogen, aprofundint en certs aspectes de la seva naturalesa atòmica/molecular utilitzant mètodes teòrics basats en la química física quàntica.