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Aggregation Of Boundary Points Into Solid Models

We consider the problem of aggregating the information provided by sensors such as range finders and its applications to scene modelling. This information consists of collections of three-dimensional points which form a discrete subspace of the objects-to-free-space boundaries within the world to be modelled. The ultimate goal is to obtain a valid surface model which can in turn be transformed into an efficient volumetric representation for solid interference detection algorithms. We first relate our work to that of other researchers, and we then show that surface connectivity is a non-trivial but essential element of a valid representation. To that end, we introduce a formal definition for model validity which we use to guide the process of aggregating the different views and we provide a proof of its correctness under stated assumptions. We eventually suggest heuristic methods for extending our approach when the strict validity conditions do not suffice to construct a perceptually consistent model. Finally, we quickly introduce the topological problems posed by objects non-homeomorphic to spheres, such as multi-holed tori. The methods we develop do not depend on the physical nature of the sensing technique. For example, our results can also be used from data obtained by stereo analysis and to some extent by haptic sensing.