Distributed Bayesian Filtering using Logarithmic Opinion Pool for Dynamic Sensor Networks

The discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented for the problem of tracking a target dynamic model using a time-varying network of heterogeneous sensing agents. In the DBF algorithm, the sensing agents combine their normalized likelihood functions in a distributed manner using the logarithmic opinion pool and the dynamic average consensus algorithm. We show that each agent's estimated likelihood function globally exponentially converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. We rigorously characterize the convergence, stability, and robustness properties of the DBF algorithm. Moreover, we provide an explicit bound on the time step size of the DBF algorithm that depends on the time-scale of the target dynamics, the desired convergence error bound, and the modeling and communication error bounds. Furthermore, the DBF algorithm for linear-Gaussian models is cast into a modified form of the Kalman information filter. The performance and robust properties of the DBF algorithm are validated using numerical simulations

Distributed Estimation using Bayesian Consensus Filtering

We present the Bayesian consensus filter (BCF) for tracking a moving target using a networked group of sensing agents and achieving consensus on the best estimate of the probability distributions of the target’s states. Our BCF framework can incorporate nonlinear target dynamic models, heterogeneous nonlinear measurement models, non-Gaussian uncertainties, and higher-order moments of the locally estimated posterior probability distribution of the target’s states obtained using Bayesian filters. If the agents combine their estimated posterior probability distributions using a logarithmic opinion pool, then the sum of Kullback–Leibler divergences between the consensual probability distribution and the local posterior probability distributions is minimized. Rigorous stability and convergence results for the proposed BCF algorithm with single or multiple consensus loops are presented. Communication of probability distributions and computational methods for implementing the BCF algorithm are discussed along with a numerical example

Mission-Aware Value of Information Censoring for Distributed Filtering

In this paper, we study the problem of distributed estimation with an emphasis on communication-efficiency. The proposed algorithm is based on a windowed maximum a posteriori (MAP) estimation problem, wherein each agent in the network locally computes a Kalman-like filter estimate that approximates the centralized MAP solution. Information sharing among agents is restricted to their neighbors only, with guarantees on overall estimate consistency provided via logarithmic opinion pooling. The problem is efficiently distributed using the alternating direction method of multipliers (ADMM), whose overall communication usage is further reduced by a value of information (VoI) censoring mechanism, wherein agents only transmit their primal-dual iterates when deemed valuable to do so. The proposed censoring mechanism is mission-aware, enabling a globally efficient use of communication resources while guaranteeing possibly different local estimation requirements. To illustrate the validity of the approach we perform simulations in a target tracking scenario

Second-order statistics analysis and comparison between arithmetic and geometric average fusion: Application to multi-sensor target tracking

Two fundamental approaches to information averaging are based on linear and logarithmic combination, yielding the arithmetic average (AA) and geometric average (GA) of the fusing data, respectively. In the context of multisensor target tracking, the two most common formats of data to be fused are random variables and probability density functions, namely v-fusion and f-fusion, respectively. In this work, we analyze and compare the second-order statistics (including variance and mean square error) of AA and GA in terms of both v-fusion and f-fusion. The case of weighted Gaussian mixtures representing multitarget densities in the presence of false alarms and missed detections (whose weight sums are not necessarily unit) is also considered, the result of which turns out to be significantly different from that of a single target. In addition to exact derivation, exemplifying analyses and illustrations are also provided.This work was supported in part by the Marie Skłodowska-Curie Individual Fellowship under Grant 709267, in part by Shaanxi Natural Fund under Grant 2018MJ6048, in part by the Northwestern Polytechnical University, and in part by Junta Castilla y León, Consejería de Educación and FEDER funds under project SA267P18

Decentralized Riemannian Particle Filtering with Applications to Multi-Agent Localization

The primary focus of this research is to develop consistent nonlinear decentralized particle filtering approaches to the problem of multiple agent localization. A key aspect in our development is the use of Riemannian geometry to exploit the inherently non-Euclidean characteristics that are typical when considering multiple agent localization scenarios. A decentralized formulation is considered due to the practical advantages it provides over centralized fusion architectures. Inspiration is taken from the relatively new field of information geometry and the more established research field of computer vision. Differential geometric tools such as manifolds, geodesics, tangent spaces, exponential, and logarithmic mappings are used extensively to describe probabilistic quantities. Numerous probabilistic parameterizations were identified, settling on the efficient square-root probability density function parameterization. The square-root parameterization has the benefit of allowing filter calculations to be carried out on the well studied Riemannian unit hypersphere. A key advantage for selecting the unit hypersphere is that it permits closed-form calculations, a characteristic that is not shared by current solution approaches. Through the use of the Riemannian geometry of the unit hypersphere, we are able to demonstrate the ability to produce estimates that are not overly optimistic. Results are presented that clearly show the ability of the proposed approaches to outperform current state-of-the-art decentralized particle filtering methods. In particular, results are presented that emphasize the achievable improvement in estimation error, estimator consistency, and required computational burden

Context Exploitation in Data Fusion

Complex and dynamic environments constitute a challenge for existing tracking algorithms. For this reason, modern solutions are trying to utilize any available information which could help to constrain, improve or explain the measurements. So called Context Information (CI) is understood as information that surrounds an element of interest, whose knowledge may help understanding the (estimated) situation and also in reacting to that situation. However, context discovery and exploitation are still largely unexplored research topics. Until now, the context has been extensively exploited as a parameter in system and measurement models which led to the development of numerous approaches for the linear or non-linear constrained estimation and target tracking. More specifically, the spatial or static context is the most common source of the ambient information, i.e. features, utilized for recursive enhancement of the state variables either in the prediction or the measurement update of the filters. In the case of multiple model estimators, context can not only be related to the state but also to a certain mode of the filter. Common practice for multiple model scenarios is to represent states and context as a joint distribution of Gaussian mixtures. These approaches are commonly referred as the join tracking and classification. Alternatively, the usefulness of context was also demonstrated in aiding the measurement data association. Process of formulating a hypothesis, which assigns a particular measurement to the track, is traditionally governed by the empirical knowledge of the noise characteristics of sensors and operating environment, i.e. probability of detection, false alarm, clutter noise, which can be further enhanced by conditioning on context. We believe that interactions between the environment and the object could be classified into actions, activities and intents, and formed into structured graphs with contextual links translated into arcs. By learning the environment model we will be able to make prediction on the target\u2019s future actions based on its past observation. Probability of target future action could be utilized in the fusion process to adjust tracker confidence on measurements. By incorporating contextual knowledge of the environment, in the form of a likelihood function, in the filter measurement update step, we have been able to reduce uncertainties of the tracking solution and improve the consistency of the track. The promising results demonstrate that the fusion of CI brings a significant performance improvement in comparison to the regular tracking approaches

Parametric region-based foreround segmentation in planar and multi-view sequences

Foreground segmentation in video sequences is an important area of the image processing that attracts great interest among the scientist community, since it makes possible the detection of the objects that appear in the sequences under analysis, and allows us to achieve a correct performance of high level applications which use foreground segmentation as an initial step. The current Ph.D. thesis entitled Parametric Region-Based Foreground Segmentation in Planar and Multi-View Sequences details, in the following pages, the research work carried out within this eld. In this investigation, we propose to use parametric probabilistic models at pixel-wise and region level in order to model the di erent classes that are involved in the classi cation process of the di erent regions of the image: foreground, background and, in some sequences, shadow. The development is presented in the following chapters as a generalization of the techniques proposed for objects segmentation in 2D planar sequences to 3D multi-view environment, where we establish a cooperative relationship between all the sensors that are recording the scene. Hence, di erent scenarios have been analyzed in this thesis in order to improve the foreground segmentation techniques: In the first part of this research, we present segmentation methods appropriate for 2D planar scenarios. We start dealing with foreground segmentation in static camera sequences, where a system that combines pixel-wise background model with region-based foreground and shadow models is proposed in a Bayesian classi cation framework. The research continues with the application of this method to moving camera scenarios, where the Bayesian framework is developed between foreground and background classes, both characterized with region-based models, in order to obtain a robust foreground segmentation for this kind of sequences. The second stage of the research is devoted to apply these 2D techniques to multi-view acquisition setups, where several cameras are recording the scene at the same time. At the beginning of this section, we propose a foreground segmentation system for sequences recorded by means of color and depth sensors, which combines di erent probabilistic models created for the background and foreground classes in each one of the views, by taking into account the reliability that each sensor presents. The investigation goes ahead by proposing foreground segregation methods for multi-view smart room scenarios. In these sections, we design two systems where foreground segmentation and 3D reconstruction are combined in order to improve the results of each process. The proposals end with the presentation of a multi-view segmentation system where a foreground probabilistic model is proposed in the 3D space to gather all the object information that appears in the views. The results presented in each one of the proposals show that the foreground segmentation and also the 3D reconstruction can be improved, in these scenarios, by using parametric probabilistic models for modeling the objects to segment, thus introducing the information of the object in a Bayesian classi cation framework.La segmentaci on de objetos de primer plano en secuencias de v deo es una importante area del procesado de imagen que despierta gran inter es por parte de la comunidad cient ca, ya que posibilita la detecci on de objetos que aparecen en las diferentes secuencias en an alisis, y permite el buen funcionamiento de aplicaciones de alto nivel que utilizan esta segmentaci on obtenida como par ametro de entrada. La presente tesis doctoral titulada Parametric Region-Based Foreground Segmentation in Planar and Multi-View Sequences detalla, en las p aginas que siguen, el trabajo de investigaci on desarrollado en este campo. En esta investigaci on se propone utilizar modelos probabil sticos param etricos a nivel de p xel y a nivel de regi on para modelar las diferentes clases que participan en la clasi caci on de las regiones de la imagen: primer plano, fondo y en seg un que secuencias, las regiones de sombra. El desarrollo se presenta en los cap tulos que siguen como una generalizaci on de t ecnicas propuestas para la segmentaci on de objetos en secuencias 2D mono-c amara, al entorno 3D multi-c amara, donde se establece la cooperaci on de los diferentes sensores que participan en la grabaci on de la escena. De esta manera, diferentes escenarios han sido estudiados con el objetivo de mejorar las t ecnicas de segmentaci on para cada uno de ellos: En la primera parte de la investigaci on, se presentan m etodos de segmentaci on para escenarios monoc amara. Concretamente, se comienza tratando la segmentaci on de primer plano para c amara est atica, donde se propone un sistema completo basado en la clasi caci on Bayesiana entre el modelo a nivel de p xel de nido para modelar el fondo, y los modelos a nivel de regi on creados para modelar los objetos de primer plano y la sombra que cada uno de ellos proyecta. La investigaci on prosigue con la aplicaci on de este m etodo a secuencias grabadas mediante c amara en movimiento, donde la clasi caci on Bayesiana se plantea entre las clases de fondo y primer plano, ambas caracterizadas con modelos a nivel de regi on, con el objetivo de obtener una segmentaci on robusta para este tipo de secuencias. La segunda parte de la investigaci on, se centra en la aplicaci on de estas t ecnicas mono-c amara a entornos multi-vista, donde varias c amaras graban conjuntamente la misma escena. Al inicio de dicho apartado, se propone una segmentaci on de primer plano en secuencias donde se combina una c amara de color con una c amara de profundidad en una clasi caci on que combina los diferentes modelos probabil sticos creados para el fondo y el primer plano en cada c amara, a partir de la fi abilidad que presenta cada sensor. La investigaci on prosigue proponiendo m etodos de segmentaci on de primer plano para entornos multi-vista en salas inteligentes. En estos apartados se diseñan dos sistemas donde la segmentaci on de primer plano y la reconstrucci on 3D se combinan para mejorar los resultados de cada uno de estos procesos. Las propuestas fi nalizan con la presentaci on de un sistema de segmentaci on multi-c amara donde se centraliza la informaci on del objeto a segmentar mediante el diseño de un modelo probabil stico 3D. Los resultados presentados en cada uno de los sistemas, demuestran que la segmentacion de primer plano y la reconstrucci on 3D pueden verse mejorados en estos escenarios mediante el uso de modelos probabilisticos param etricos para modelar los objetos a segmentar, introduciendo as la informaci on disponible del objeto en un marco de clasi caci on Bayesiano

Event-based Vision: A Survey

Event cameras are bio-inspired sensors that differ from conventional frame cameras: Instead of capturing images at a fixed rate, they asynchronously measure per-pixel brightness changes, and output a stream of events that encode the time, location and sign of the brightness changes. Event cameras offer attractive properties compared to traditional cameras: high temporal resolution (in the order of microseconds), very high dynamic range (140 dB vs. 60 dB), low power consumption, and high pixel bandwidth (on the order of kHz) resulting in reduced motion blur. Hence, event cameras have a large potential for robotics and computer vision in challenging scenarios for traditional cameras, such as low-latency, high speed, and high dynamic range. However, novel methods are required to process the unconventional output of these sensors in order to unlock their potential. This paper provides a comprehensive overview of the emerging field of event-based vision, with a focus on the applications and the algorithms developed to unlock the outstanding properties of event cameras. We present event cameras from their working principle, the actual sensors that are available and the tasks that they have been used for, from low-level vision (feature detection and tracking, optic flow, etc.) to high-level vision (reconstruction, segmentation, recognition). We also discuss the techniques developed to process events, including learning-based techniques, as well as specialized processors for these novel sensors, such as spiking neural networks. Additionally, we highlight the challenges that remain to be tackled and the opportunities that lie ahead in the search for a more efficient, bio-inspired way for machines to perceive and interact with the world