Localization and Optimization Problems for Camera Networks

In the framework of networked control systems, we focus on networks of autonomous PTZ cameras. A large set of cameras communicating each other through a network is a widely used architecture in application areas like video surveillance, tracking and motion. First, we consider relative localization in sensor networks, and we tackle the issue of investigating the error propagation, in terms of the mean error on each component of the optimal estimator of the position vector. The relative error is computed as a function of the eigenvalues of the network: using this formula and focusing on an exemplary class of networks (the Abelian Cayley networks), we study the role of the network topology and the dimension of the networks in the error characterization. Second, in a network of cameras one of the most crucial problems is calibration. For each camera this consists in understanding what is its position and orientation with respect to a global common reference frame. Well-known methods in computer vision permit to obtain relative positions and orientations of pairs of cameras whose sensing regions overlap. The aim is to propose an algorithm that, from these noisy input data makes the cameras complete the calibration task autonomously, in a distributed fashion. We focus on the planar case, formulating an optimization problem over the manifold SO(2). We propose synchronous deterministic and distributed algorithms that calibrate planar networks exploiting the cycle structure of the underlying communication graph. Performance analysis and numerical experiments are shown. Third, we propose a gossip-like randomized calibration algorithm, whose probabilistic convergence and numerical studies are provided. Forth and finally, we design surveillance trajectories for a network of calibrated autonomous cameras to detect intruders in an environment, through a continuous graph partitioning problem

Asymptotic analysis of continuous opinion dynamics models under bounded confidence

This paper deals with the asymptotic behavior of mathematical models for opinion dynamics under bounded condence of Deuant-Weisbuch type. Focusing on the Cauchy Problem related to compromise models with homogeneous bound of condence, a general well-posedness result is provided and a systematic study of the asymptotic behavior in time of the solution is developed. More in detail, we prove a theorem that establishes the weak convergence of the solution to a sum of Dirac masses and characterizes the concentration points for dierent values of the model parameters. Analytical results are illustrated by means of numerical simulation

Asynchronous Distributed Calibration of Camera Networks

This work focuses on the problem of calibrating planar networks of cameras in a distributed fashion. The camera network is modeled by a graph, and along each edge a noisy relative angular measurement is available. The goal is to achieve the absolute orientation of each camera with respect to a fixed external reference frame, in order to be able to perform monitoring and patrolling tasks. The idea is to exploit the cycles in the graph, along which all relative measurements sum to zero, in order to eliminate the noise. We design a distributed algorithm for the cameras to autonomously calibrate and we adopt an asynchronous gossip-like communication protocol. The proposed algorithm is proved to converge, almost surely and in the mean square sense, to the set of angles with zero cycle error. Finally, numerical experiments are presented to compare the performance of the algorithm on different graph topologies

Finite-Field Consensus

This work studies consensus networks over finite fields, where agents process and communicate values from the set of integers f0; : : : ; p 1g, for some prime number p, and operations are performed modulo p. For consensus networks over finite fields we provide necessary and sufficient conditions on the network topology and weights to ensure convergence. For instance we show that, differently from the case of consensus networks over the field of real numbers, consensus networks over finite fields converge in finite time, and that properties of the agents interaction graph are not sufficient to ensure finitefield consensus. Finally, we discuss the application of finite-field consensus to distributed averaging in sensor network

Nouvelles droites et pouvoir en Europe

info:eu-repo/semantics/publishe

Autonomous calibration algorithms for planar networks of cameras

This paper deals with the problem of the angular calibration for a network of cameras, namely the problem of estimating a common orientation reference frame. In the proposed set-up each camera obtains noisy measurements of its relative orientation with respect to some other cameras. The set of measurements can be described by a graph having the cameras as nodes and having an edge between two cameras if a relative orientation measurement is available. The paper proposes a novel two-step algorithm based on a choice of a basis for the set of graph cycles. The first step consists in computing a set of integer numbers, which provides a first rough estimate of the orientations. The second step exploits this information to build up a suitable quadratic minimization problem. Two actual implementations, corresponding to two different basis of cycles, are described and compared in terms of the worst-case scenario. Finally, through numerical simulations the algorithm is compared with another algorithm proposed in the literature for solving the same problem

A hybrid model for opinion formation

This paper presents a hybrid model for opinion formation in a large group of agents exposed to the persuasive action of a small number of strong opinion leaders. The model is defined by coupling a finite difference equation for the dynamics of leaders opinion with a continuous integro-differential equation for the dynamics of the others. Such a definition stems from the idea that the leaders are few and tend to retain original opinions, so that their dynamics occur on a longer time scale with respect to the one of the other agents. A general well-posedness result is established for the initial value problem linked to the model. The asymptotic behavior in time of the related solution is characterized for some general parameter settings, which mimic distinct social scenarios, where different emerging behaviors can be observed. Analytical results are illustrated and extended through numerical simulation