Robust Construction of the Camera Network Complex for Topology Recovery

While performing tasks such as estimating the topology of camera network coverage or coordinate-free object tracking and navigation, knowledge of camera position and other geometric constraints about the environment are considered unnecessary. Instead, topological information captured by the construction of a simplicial representation called the $CN$-Complex can be utilized to perform these tasks. This representation can be thought of as a generalization of the so-called vision graph of a camera network. The construction of this simplicial complex consists of two steps: the decomposition of the camera coverage through the detection of occlusion events, and the discovery of overlapping areas between the multiple decomposed regions. In this paper, we present an algorithm for performing both of these tasks in the presence of multiple targets and noisy observations. The algorithm exploits temporal correlations of the detections to estimate probabilities of overlap in a distributed manner. No correspondence, appearance models, or tracking are utilized. Instead of applying a single threshold on the probabilities, we analyze the persistence of the topological features in our representation through a filtration process. We demonstrate the validity of our approach through simulation and an experimental setup.