Topology, To What End?

There have been a number of approaches to build topological models of multi-camera networks. The idea is to represent, in some useful and relatively simple mathematical way, the relationship — usually meaning the overlap — between the fields of view of the cameras. To date, it seems as though all such methods fall into two basic types.

On one hand, we have the motion-based methods, which are typically targeted at tracking applications. Ellis et al. temporally correlate objects transiting between adjacent fields of view, after establishing each camera’s entry and exit zones. Similarly, Mandel et al. correlate simultaneous motion between views to establish overlap. Detmold et al. propose the exclusion algorithm, which is basically the opposite and potentially more robust: if there is motion in one view, and not in another, then those views cannot overlap (initially all views are assumed to overlap). Farrell and Davis present a slightly different model, dubbed the transition model, which focuses even more on tracking as it expresses the probability of transitions between views; this is also determined from observations of motion.

On the other hand, we have the feature-based methods, typically used as a precursor to or substitute for multi-camera calibration. Devarajan and Radke first proposed the vision graph without specifying an automated means of obtaining it; they later approached this topic in Cheng et al. using distributed matching of SIFT features. Kurillo et al. also use common features to build their vision graph for calibration. In my ICDSC 2008 paper, the vision graph is a theoretical upper limit for the grouping and calibration graphs, which are built from 3D feature matches via registration. Kulkarni et al. use a calibration target to explicitly match spatial points, and build an actual tessellation of 3D space to represent the range and degree of overlap of the cameras’ fields of view. Finally, Lobaton et al. use scene features (in their case, bisecting lines indicating wall delineations) to construct their algebraic topological model, which is proposed as a substitute for full calibration in certain (unspecified) secondary applications.

So is generic topological information about multi-camera networks only useful for tracking and calibration, the two problem areas that appear to have spawned every topological model in the literature? Are there any other applications that simply don’t have any convenient information of their own for building such models?

Mar 19th, 2010
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