Cooperative, Opportunistic Imaging within a Bayesian Distributed Constrained Optimization Framework

Cooperative, Opportunistic Imaging within a Bayesian Distributed Constrained Optimization Framework A. A. Morye, C. Ding, A. K. Roy-Chowdhury, J. A. Farrell Department of Electrical Engineering University of California, Riverside Abstract—This article considers the design of a network of pan, tilt, zoom (PTZ) cameras to obtain high resolution facial imagery through opportunistic imaging of moving targets within a surveillance area. Camera locations are assumed to be ﬁxed and known and the camera network is assumed to be connected. The number of targets is time-varying, often exceeding the number of cameras. The targets are free to maneuver within the surveillance area and to enter or leave the surveillance area through known doorway locations. The proposed solution involves distributed solution of a constrained, locally convex, optimization problem. The value function quantiﬁes the per target image quality. The tracking constraint is an upper bound on the uncertainty in the estimated horizontal position error of each target. At each time step, optimization is over the PTZ parameters for each camera in the network with the feasible parameter space deﬁned by the tracking constraint. All cameras optimize their PTZ parameters simultaneously by using information broadcast by neighboring cameras. At certain time steps, due to the conﬁguration of the targets relative to the cameras, and the fact that each camera may track many targets, the camera network may be able to achieve the tracking speciﬁcation with remaining degrees-of-freedom that can be used, by cameras at appropriate locations, to obtain high resolution facial images from desirable aspect angles. The challenge is to ﬁnd these time instants, the appropriate camera, and the appropriate parameter settings to capitalize on them. Ideally, the system would acquire at least one high-resolution image of each target in the region before the target leaves the region. The Bayesian approach automatically trades off maxi- mization of the objective versus risk (probability of losing track of a target). The solution involves a Bayesian formulation of the approach, design of the local and global objective functions and the inequality constraint set, and development of a Distributed Lagrangian Consensus algorithm that allows cameras to exchange information and asymptotically converge on a pair of primal-dual optimal solutions. This article presents the theoretical solution along with simulation results. I. I NTRODUCTION Camera sensor networks using static cameras that cover a wide-area may have low cost, but may also have low resolution imagery, may image uninteresting features or viewpoints, etc. Consequences of such scenarios are the increased difﬁculty of analysis of the collected video data and accumulation of vast quantities of unimportant imagery. These issues can be addressed by employing distributed pan, tilt, zoom (PTZ) camera sensor networks. Cameras with dynamically controllable PTZ parameters can be made to differentially focus on multiple regions of interest through dynamic camera parameter selection. Such an approach would Research supported by ONR under award no.: N000140910666 for the project titled ‘Distributed Dynamic Scene Analysis in a Self-Conﬁguring Multimodal Sensor Network’. provide improved performance and greater ﬂexibility while requiring less hardware. A prototypical application is a security screening checkpoint at the entrance lobby of a building. Over the course of each day a high volume of people ﬂow through the room. The room is equipped with a ﬁxed number of cameras while the number and location of people in the room varies with time. The objective of the camera network is to track (i.e., state estimation) all persons in the room at a speciﬁed accuracy level at all times and to capture high resolution images for certain persons in the room at opportunistically selected time instants. The challenges of such an application are development of algorithms to ensure accurate propagation of target-related information through the distributed network, analysis of the effect of changing network topology on solution convergence, and the design of objective functions suitable to solving the speciﬁed problem that also have the properties necessary to ensure convergence. All these factors inﬂuence the selection of an optimization strategy. In this paper, we formulate the problem within the Bayesian framework and utilize a dis- tributed constrained optimization approach to compute the optimal camera parameter settings that achieve the global cam- era network objective through optimization of local camera objectives. II. L ITERATURE R EVIEW Active vision [1], [2], [3] in a camera sensor network is a research area of great interest. Active computer vision systems have been applied to applications like automatic surveillance, simultaneous localization and mapping (SLAM), trajectory planning, etc. It involves research on cooperation and coordi- nation between many cameras in a network. Assumptions on the camera network topology play a major role in the problem solution; therefore recent work done on networks of vision sensors is important. A recent research surveyed [4] identiﬁes various computer vision problems that can be solved in a distributed fashion within a network topology. The article mentions the effects of nodes in the network with no measurement information and how such nodes may affect convergence properties of a distributed algorithm. An automated annealing approach for updating Lagrange multipliers to reduce dependence on agent inter-communication is provided in [5]. The method uses the probability collectives framework to generate a relation between game theory and statistical physics. The authors use