Parallel Preprocessing for the Optimal Camera Placement Problem

Abstract

Abstract-This paper deals with the preprocessing needed for the optimal camera placement problem, which is stated as a unicost set covering problem (USCP). Distributed and massively parallel computations with graphics processing unit (GPU) are proposed in order to perform the reduction and visibility preprocessing respectively. An experimental study reports that a significant speedup can be achieved, and we give a general heterogeneous parallel approach that brings together these parallel computations. In addition to that, a set-based differential evolution (DE) method is applied to solve 10 instances of the considered problem, and promising results are reported.Index Terms-Distributed computing, graphics processing unit (GPU), optimal camera placement problem, preprocessing, set-based differential evolution (DE) algorithm, unicost set covering problem (USCP). I. INTRODUCTIONIntelligent video surveillance systems aim at monitoring areas of interest by using appropriate networks of cameras: the placement of these cameras is thus of great importance because of the requested quality of service and the deployment costs. Such an optimal camera placement problem can be stated as a decision problem in a discrete search space [1]: given the set of possible camera locations, find the optimal subset that can meet the operational requirements. In this work, the problem is modelled as a unicost set covering problem (USCP) together with a three-dimensional discretization of the monitored area.Firstly, the optimization process needs the following input data: the list of points to be covered, the list of possible camera locations, and the lists of points covered by each possible camera location. This so-called visibility preprocessing is performed according to the practical context, where the 3D setting avoids blind spot (with regard to a 2D model), but at the cost of a much larger computational effort [2]. For this reason, it is of high interest to design parallel approaches that can compute these input data within a reasonable time, so that larger problems can be optimized.Secondly, these input data can be reduced in order to speed up the optimizing process. The main reduction strategy is a variant of the so-called column domination test for non-unicost set covering problems [3] (sets that cover fewer points at the same cost can be removed, instead of those that cover the same points at a higher cost). It consists in Manuscript received October 27, 2017; revised December 12, 2017. This work was supported by the French Agence Nationale de la Recherche (ANR) as part of the OPMoPS project .The authors are with the LMIA Research Laboratory, Université de Haute-Alsace, Mulhouse, France (e-mail: mathieu.brevilliers@uha.fr, julien.lepagnot@uha.fr, julien.kritter@uha.fr, lhassane.idoumghar@uha.fr).discarding the so-called dominated camera locations: for each possible camera location , if another one can cover the same points as and some additional points, then is said to be dominated by and it can be removed from the set of availabl...

On the computational cost of the set cover approach for the optimal camera placement problem and possible set-cover-inspired trade-offs for surveillance infrastructure design

“…For 25 out of 32 instances however, CPLEX ranked first and reached optimality on 16. More importantly, it managed to find feasible solutions to all instances, something it could not always achieve on the OR-Library instances [4] or the toy instances used in [8,9]. Most of these sets are significantly smaller than the instances used in this paper when looking at |I| and |J |.…”