Designing Camera Networks by Convex Quadratic Programming

Abstract

Figure 1: Example result of our proposed optimal camera placement framework. In a particular scenario, the user inputs a 3D floorplan that can be generated by processing an overhead 2D floorplan using the user-friendly GUI we developed. After setting certain camera parameters (e.g. field-of-view and depth-of-field), our approach computes a placement solution that can either maximize 3D floorplan coverage with a limited number of cameras or minimize the number of cameras needed to cover the entire floorplan. Unlike other placement methods, our approach is computationally efficient because it solves a constrained convex quadratic program. It also allows pairwise camera interactions to be directly encoded, which is quite useful for multiview applications, such as 3D reconstruction and surveillance. AbstractIn this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport).

Interactive Camera Network Design Using a Virtual Reality Interface

“…A first modelling choice is to encode the notion that it is better for an environment point to be viewed by multiple cameras [2,3,5,14]. This corresponds to extending the previously defined function t to arbitrary functions.…”

“…Another modeling choice is to assign weights to viewpoints or/and environment points based on some notion of importance [2,10,14]. No weighting scheme can fundamentally change the problem structure as long as the weights remain positive.…”

“…The positive constant α and positive regularizer function r are used as a tool to discourage the optimizer to choose certain undesired camera configurations [2]. An example where this can be useful is a stereo reconstruction camera system.…”

“…Many practical problems can be formulated as an observation task, so it is no suprise that this problem has been studied extensively. For example, the design of surveillance systems for both large buildings and outdoor environments can be formulated as a camera network design problem [1,2]. In this formulation the objective is to maximize the camera coverage over a floorplan of the environment.…”

Placing Visual Sensors Using Heuristic Algorithms for Bridge Surveillance

“…Number of Camera Binary quadratic programming (BQP) [16] Min. Cost Particle swarm optimization (PSO) [17] In terms of objective functions, the maximization of coverage has been widely studied and many solution approaches have been suggested [2][3][4][7][8][9][11][12][13][14][15][16]. Furthermore, multi-objective problems, including maximizing coverage and visibility while minimizing the total cost, have been studied [10,11].…”