An approach is presented to 3-D primitive reconstruction that is independent of the selection of volumetric primitives used to model objects. The approach first takes an arbitrary set of 3-D volumetric primitives and generates a hierarchical aspect representation based on the projected surfaces of the primitives; conditional probabilities capture the ambiguity of mappings between levels of the hierarchy. The integration of object-centered and viewer-centered representations provides the indexing power of 3-D volumetric primitives, while supporting a 2-D matching paradigm for primitive reconstruction. Formulation of the problem based on grouping the image regions according to aspect is presented. No domain dependent heuristics are used; the authors exploit only the probabilities inherent in the aspect hierarchy. For a given selection of primitives, the success of the heuristic depends on the likelihood of the various aspects; best results are achieved when certain aspects are more likely, and fewer primitives project to a given aspect.
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