Distributed Topological Camera Selection Without Location Information

In this paper, a distributed algorithm, namely distributed topological camera selection, is proposed for selecting the minimum number of cameras to cover the entire area in the case that there is no location information. In order to relax the location information assumption, we propose an approach based on homology. We consider the nerve complex corresponding to the camera network and demonstrate how combinatorial Laplacian and topological properties of the network can be used to formulate the problem of selecting the minimum number of cameras for covering the entire space as an optimization problem. Proposed optimization problem works on the simplicial complex of the network and finds the least number of two-simplices that cover the entire area. Then, we propose a distributed algorithm using the subgradient method for this problem. Finally, we validate the algorithm via one experimental setup and evaluate the performance of the proposed algorithm by conducting simulations.