Maximizing full-view target coverage in camera sensor networks

Abstract

Traditional target coverage only ensures monitoring of targets. However, as people’s security awareness increases, the requirement for target coverage also increases from monitoring to identification. Thus full-view coverage model is proposed to guarantee that any facing direction of a target could be covered. Based on this coverage model, we study the maximum full-view target coverage problem in camera sensor networks, where each camera sensor has P working directions, aiming at maximizing the number of full-view covered targets by scheduling the working directions of camera sensors. To solve this problem, we design a $(1-\frac{1}{e})$-approximation algorithm based on pipage rounding and an efficient heuristic algorithm. Finally, simulation results are presented to demonstrate the performance of our algorithms.

Introduction

Coverage problem is one of the most fundamental problems in wireless sensor networks, which reflects how well a region is monitored. The emergence of camera sensors adds new vitality to this topic, because they can provide much richer information about monitoring environment through videos or images. Such sensor networks have wide application perspective in many fields, such as military reconnaissance, environment monitoring, intelligent transportation, medical care, industrial control and disaster management [1].

In most of the previous studies, sensors are based on omnidirectional sensing model, in which the sensing region of a sensor is abstracted as a disk, and whether a target is covered only depends on its location. Afterwards directional sensing models are proposed [2], [3], [4]. Compared with omnidirectional sensors, directional sensors have limited angle of sensing range, and the sensing region of a directional sensor is modeled as a sector, which not only depends on its location but also depends on its orientation. The camera sensor is a special kind of directional sensor, which may generate very different views of the same target [5].

With people’s safety consciousness increasing gradually, new demands on capturing clear profile of targets have risen beyond traditional coverage of simply detecting them [6]. For example, when a criminal suspect appears in the crowded public places, it needs camera surveillance system to obtain enough facial information of the criminal suspect to confirm his or her identity. Against this background, full-view coverage is introduced in camera sensor networks to satisfy the security requirement [5]. Previous studies, such as [5], [7], [8], [9], [10], on full-view coverage mainly focus on the sensing model with one fixed working direction, which leads to a waste of sensing resources. One intuitive way is to utilize the sensors with rotation ability to improve the utilization of sensors instead of leaving them idle. Besides, in many practical applications, such as wildlife monitoring and battlefield surveillance, camera sensors are randomly deployed by airplanes, and camera sensors initially deployed may not be sufficient to provide full-view coverage for all targets, thus it needs to schedule camera sensors to full-view cover as many targets as possible. However, most of the existing efforts on full-view coverage focus on how to judge a region or targets are full-view covered, and there still lack of efficient algorithms with theoretical bounds to schedule camera sensors to realize full-view coverage. Take that into account, based on the full-view coverage model, we study the maximum full-view target coverage problem (MFTC) in camera sensor networks, where each camera sensor has P working directions with mutually disjoint sensing sectors combined to generate a circle and can rotate to cover different sensing sectors. Our goal is to maximize the number of full-view covered targets by scheduling the working directions of camera sensors. To solve this problem, we design a $(1-\frac{1}{e})$-approximation algorithm and an efficient heuristic algorithm. In particular no study, to our knowledge, has considered the MFTC problem in uniformly randomly distributed camera sensor networks, where every camera sensor has P disjoint working directions.

Several difficulties make our issue challenging. First, every camera sensor has P working directions and can rotate its orientation around the center, thus the working direction of each camera sensor can vary from one sensing sector to another. Since at any time at most one working direction of each sensor can be activated, it induces conflict among targets covered by different working directions of the same camera sensor. Second, unlike traditional target coverage, full-view target coverage requires that, for any facing direction of targets, there is always at least one camera sensor obtaining the positive images of those targets (formal definition is given in Section 3.1), which makes the coverage relationship between camera sensors and targets more complicated. Further, in order to achieve full-view coverage of targets, camera sensors need to cooperatively turn to specific working directions at the same time.

Due to the aforementioned challenges, we solve the MFTC problem incrementally. For ease of handling, two new concepts are introduced, basic full-view cover set (BFCS) and normal full-view cover set (NFCS) (formal definitions are given in Section 3.1). We first design FindBFCSs algorithm to find out all BFCSs for targets. Considering that different targets may be full-view covered by some of the same working directions, we construct NFCSs based on BFCSs by ConstrustNFCSs algorithm. Then we formulate the MFTC problem as an optimization problem selecting some NFCSs, which are not in conflict with each other, such that the total number of full-view covered targets is maximized. To make the problem tractable, we formalize the optimization problem as an integer programming problem, and further relax it into a linear programming problem. We can obtain an optimal solution to the linear programming optimization in polynomial time. After that we develop an approximation algorithm applying the pipage rounding method to convert the optimal solution into an integer solution, which yields a feasible solution for the MFTC problem with $(1-\frac{1}{e})$ performance ratio. Besides, we also design an efficient heuristic algorithm to address the MFTC problem.

The rest of this paper is organized as follows. Section 2 briefly reviews related research. Section 3 defines the camera sensor network model, the full-view coverage model and the MFTC problem. Section 4 presents an approximation algorithm and an efficient heuristic algorithm to solve the MFTC problem. Section 5 presents simulation results of our algorithms. Section 6 concludes the paper.