Efficient simulation for positioning and utilizing of multiple cameras

Abstract

This paper proposes the efficient camera placement method that considers spatial information and gives priorities of spaces in the viewpoint of people moving pattern. To efficiently cover realistic environments, camera performance and installation cost are included in our model. Simulation results show that the proposed placement method not only optimally determines the number of cameras but also coordinates the position and orientation of cameras in a utility-maximized way. Furthermore, this paper can provide a near optimal solution at a very low computational cost based on peak detection and Kullback–Leibler divergence concepts. The proposed method is evaluated and compared in terms of the computational cost and the coverage rate with the greedy approach.

Introduction

As the demands for video surveillance increase to find criminals and prevent crimes, a camera placement technology has been highlighted as a solution for increasing the performance of surveillance system in a cost-efficient way [1]. Security professionals as well as closed-circuit television (CCTV) designers, network engineers and installers are immersed in adopting such placement technologies [2], [3]. For example, CCTV Design Software [4] and VideoCAD [5] tools were developed for determining camera placement based on the number of installable cameras, target scene shots, and lens focal length. These tools determine camera’s positions not in an optimized or quantitative way but in a heuristic way. However, spatio–temporal patterns of people moving (or concentration), created by characteristics of building space as well as people moving in real building environments, as well as camera-specific characteristics leave room for camera’s positions to be determined in an optimized way. Therefore, it is crucial not only to explicate accurate spatio–temporal model and camera-specific characteristics but also, considering them, design camera placement methods of video surveillance systems.

People movement model refinements for building environments have been discussed by the measurement campaigns of paths traveled by people in real building environments. The measurement data have unveiled that one path traveled consists of a sequence of accessible points between starting and destination points. Since building’s walls act as obstacles in paths, the paths are usually not direct lines between starting and destination points. A large amount of measurement data for people movement paths has been fitted by A^∗ algroithm [6], which are based on heuristic search and graph search algorithms. However, people movement model itself is not still insufficient for efficient camera placement methods.

Camera placement problem has its root in art gallery problem (AGP) [7], a well-studied visibility problem of computational geometry, whose goal is determine the minimum number of guards with their positions such that each wall is observed by at least one guard. The advent of CCTV technology has replaced guards by cameras with the AGP unchanged in cameras’ placement problem. The seminal work of [8], [9], [10], [11], [12], [13] laid early foundations on camera placement methods, which determines the number of cameras with their positions in an optimized or quantitative way, and is classified by its approach: a task-specific camera placement [10] considering a set of specific actions to be only observed, defined as tasks; camera specification-based placement [11] considering camera-specific characteristics such as overlapped field of views (FOVs), installation cost, and quality of recorded data; and optimization-based placement [8], [9], [14], [15] applying optimization methods, such as integer programming or linear programming to solving optimal placement problems. In the prior work [12], [13], we presented a camera placement approach minimizing occlusion with considering space coverage and cost constraints. However, efficient simulation methods were not considered. In other words, the previous methods were implemented based on the greedy approach. Unfortunately, a straightforward implementation of the greedy approach is expensive and not scalable.

A key challenge in this context is to determine the placement of sensors that provides high coverage at low cost, resilience to sensor failures, and tradeoffs between various resources. In this paper, we propose an efficient method based on peak detection and Kullback–Leibler (KL) divergence concepts for placing cameras. We consider a utility-based efficient camera placement method using people movement model. Specifically, we model spatio–temporal randomness of people movement in a building according to extended A^∗ algorithm with a building map and people moving patterns. In the extended A^∗ algorithm, two-dimensional grid for building floor map and eight different directions for people moving are considered. We then consolidate people movement into cameras’ FOV property with accounting for visibility-based utility and develop a utility-based camera placement method that determines cameras’ setup places reflecting two-dimensional utility matrix information on a building floor. The main contributions of this paper are as follows: (1) integrating utility and setup cost; (2) modeling people movement; (3) maximizing the views of objects under the constraint of a limited number of cameras; (4) considering an efficient camera placement method for high real-time performance; and (5) evaluating the performance of the proposed algorithm with the following camera setups: field of view is limited, depth of field is finite, and angle is finite.

The rest of this paper is organized as follows. People movement model is explained in Section 2. The optimal camera placement method is presented in Section 3. Numerical results are presented in Section 4 and conclusions are finally given in Section 5.