1 Analysis on Probabilistic View Coverage for Image Sensing – A Geometric Approach Fulu Li, Ramesh Raskar, Andrew Lippman The Media Laboratory, MIT, Cambridge, MA USA 02139 Email: {fulu, raskar, lip}@media.mit.edu Abstract In this paper we study the probabilistic view coverage problem for image sensing in wireless sensor networks. The view coverage of an image sensor network determines the quality of the surveillance services that an image sensor network can provide. In this paper, we present an indepth analysis on probabilistic view coverage in an image sensor network, where omnidirectional image sensors are randomly dropped to a given field and the locations of the image sensors may not be immediately known. We intend to answer the following question: if we randomly drop a given number of image sensors into a targeted field, what is the probability that a given area of interest can be effectively imaged and view-covered. The key to our analytical approach is to cast the probabilistic view coverage problem in wireless image sensor networks as a geometric one and then use the geometric techniques to find the solution. The analysis in this paper provides probabilistic assurance of the view coverage that one can expect for random dropping of omnidirectional image sensors into a given field. 1. Introduction As image sensing emerged as a hot research topic, the view coverage problem of an image sensor network with random dropping of image sensors, one of the fundamental issues for image sensor networks, has yet to be well explored. The view coverage of an image sensor network determines the quality of the monitoring services that an image sensor network can provide. With the advent of omnidirectional image sensors [12-14], image sensing has enabled a wide range of new applications such as object identification, localization and detection, etc. Existing work on coverage problems in wireless sensor networks focuses on the sensing coverage issues. The seminal work by Meguerdichian et al in [8] addressed the best sensing coverage problem in a sensor network using computational geometry techniques to find the best support path where the region of interest and the locations of the sensors are known a priori. Recent work in [2] studied a new type of sensing coverage problem in wireless sensor networks, termed as barrier coverage, where the sensors form a barrier for the intruders in a given belt region. In [2], Balister et al further derived the critical density needed to achieve barrier coverage and/or connectivity in such thin strips of finite length. While the sensing coverage problems [2,8] in wireless sensor networks have all been well explored, little has been known for the scenarios of probabilistic view coverage on some strategic spots within a given region such as boundaries and corners with random dropping of omnidirectional image sensors. In a hostile environment, e.g., battlefields, hazardous areas, forests, mountains, etc., where sensors can not be deployed manually, random dropping of sensors to a given targeted area is required and the locations of the sensors may not be known. In this paper we focus on the probabilistic view coverage of an image sensor network with random dropping of omnidirectional image sensors. The rest of the paper is organized as follows: we discuss the related work in Section 2; we present analytical results on probabilistic view coverage of image sensors in Section 3 and Section 4; the conclusions are given in Section 5. 2. The Related Work In the seminal sensing coverage work by by Meguerdichian et al [8], the authors presented an optimal polynomial time algorithms that uses Voronoi diagram and Delaunay triangulation techniques to solve the best support path and the maximal breach path problems across a given sensor field where the locations of the sensors are known a priori. In [7], Liu et al showed that mobility improves sensing coverage of wireless sensor networks. In [11], Wang et al examined the sensing coverage problem in hybrid networks with both static and mobile sensors. They addressed the trade-offs between mobility and density for sensing coverage in wireless sensor networks. In [9], the authors considered a grid-based sensor network and they derived necessary and efficient conditions for the grid network to cover a given region. The work in this paper is partly motivated by the ringtoss game described in [5] by Larsen and Marx. Players throw a ring onto a grid of squares. If the ring touches no lines, then the player wins a prize. In [4], the authors analyzed the redundancy of sensing areas in a wireless sensor network to achieve energy efficiency by minimizing the redundant sensing areas covered by neighboring sensors. As we address the problem of probabilistic view coverage of omnidirectional image sensors, to some extent the work in