Video cameras are widely applied to inspect and/or monitor interesting objects and scenes remotely and automatically [1, 2]. Often, to cover a large area, multiple cameras are connected together to form a camera/video network. By acting as an integrated unit, the camera network provides a much larger field of view (FOV) coverage than any single camera that constitutes it. However, the distribution of cameras (locations and orientations) will influence greatly the total FOV coverage of the camera network. With a fixed number of cameras, an optimal arrangement—putting cameras at the right locations and orientations—will produce the largest FOV coverage. It subsequently maximizes the effectiveness of the camera network deployment. This optimization problem has been studied by, for example, computer vision researchers from slightly different perspectives, such as 3D reconstruction [3, 4], target surveillance [5, 6].

The camera network FOV coverage optimization is defined as the using fewest possible cameras to monitor/inspect a fixed area or maximizing the FOV coverage of a network with fixed number of cameras. At present, the video camera is still an expensive sensor (not only in terms of financial cost but also in terms of bandwidth and computation power needed for transmitting and processing its output). That is why the coverage optimization has attracted a lot of research attention [7]. The oldest coverage optimization may be the Art Gallery Problem (AGP) [8]. The goal of AGP is to determine a minimal number of guards and their positions, so that all important sites in a polygon area can be fully under supervision. Because the human guards have no eyesight limitations (in comparison to the limited FOV of video cameras), applying AGP directly to camera networks is difficult. Erdem and Sclaroff [9] defined a camera placement problem similar to AGP, but with a more realistic camera model. For solving this problem, they proposed a 0-1 integer program model for the placement and then adopted a bound and branch approach. However, it is very difficult, if not impossible, to globally optimize the formed mathematical model when the problem size becomes large. To avoid this problem, Hsieh et al. [10] limited themselves to several special types of scenarios (lanes and circles) and one type of cameras (omni directional).

Recently, more considerations from real applications are taken into account. For instance, unlike the previous mentioned papers trying to minimize the overlapping FOV, Yao et al. [11] suggested that in some applications an overlapping FOV between the cameras is necessary. One such example is the object tracking. The trajectory of an object should be maintained across different camera views. For this purpose a sufficient uniform overlap between neighboring cameras' FOVs should be secured so that camera handover can be successful and automated. They proposed sensor-planning methods which add the handoff rate analysis. Zhao and Cheung [12] studied how to arrange the cameras for tracking visual tags. Their model incorporates realistic camera models, occupant traffic models, self-occlusion, and mutual occlusion possibilities.

The above-mentioned papers are about the full plan for deploying cameras in a network, where both location and orientation of each camera can be determined before constructing the network. Recently, Tao et al. [13, 14] studied another type of coverage optimization problem. In their system, the cameras were randomly spread over an area, the location of each camera could not be changed, but the orientation of each camera can be freely adjusted. Their system can be applied for military purposes where hundreds of cameras with wireless sensors are scattered by an airplane and quickly form a camera network to monitor a wide area. For large camera networks this system is more practical because in most situations the mounting locations are limited by the physical possibilities. Tao et al. proposed a potential field-based coverage enhancing algorithm (PFCEA) for solving this problem. In PFCEA, the FOV of each camera is regarded as a virtual particle and can be repelled by other cameras. The virtual force idea first appeared in [15], where it was used to deploy omni directional sensors. In [13, 14], if the virtual torque on the FOV of a camera is not zero, the camera will adapt its angle accordingly. They found the coverage of the camera network was maximized when the network reached an equilibrium.

In this paper, we base ourselves on the problem model and application of [13, 14]. Whereas, to overcome the disadvantage of the PFCEA algorithm (to be explained in Section 4), we propose to use particle swarm optimization (PSO) as the optimization engine. PSO was proposed by Kennedy and Eberhart to model birds flocking and fish schooling for food [16]. It is welcomed in practice, because it is easy to implement, needs few parameters, and does not require the objective function to be differentiable [17]. PSO has attracted a lot of research attentions in recent years. It has been successfully applied in, for example, training of neural networks [18], control of the reactive power and voltage [19], and cutting and packing problems [20]. We will show that PSO is also very effective for the camera network coverage problem. It can achieve global optimization. To prove its superior performance, we conduct an extensive comparison between PSO and PFCEA through several experiments. Further, we will theoretically analyze the optimization feasibility under different situations. We therefore find a new effective way for optimizing the camera network coverage problem that is much better than previous approaches. On the other hand, we explore a new field of applying the PSO algorithm.

Conci and Lizzi [21] also reported on the placement of cameras using PSO. In their method, they assumed a Rayleigh distribution for characterizing the distance of the object and a Gaussian distribution for modeling the horizontal camera FOV, and, their work mainly focused on an indoor environment where the number of cameras is small and the PSO performance is not an issue. Our work, on the contrary, is more intended for applications discussed in [13, 14] where hundreds of cameras or more are randomly distributed in an unknown area. Therefore we focus more on the performance of the algorithm and the relationships between the coverage improvement and the scale of the network. This makes our work complementary to [21].

The paper is organized as follows. We first define our problem model in Section 2. We then introduce our PSO algorithm in detail in Section 3. Subsequently, we experimentally show the superior performance of our PSO algorithm and make comparisons to the PFCEA in Section 4. We then give discussions about the results in Section 5, and finally, we conclude the paper in Section 6.