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<p>An approach to the recovery of 3-D volumetric primitives from a single 2-D image is presented. The approach first takes a set of 3-D volumetric modeling 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. From a region segmentation of the input image, the authors present a formulation of the recovery problem based on the grouping of the regions into aspects. No domain-independent heuristics are used; only the probabilities inherent in the aspect hierarchy are exploited. Once the aspects are recovered, the aspect hierarchy is used to infer a set of volumetric primitives and their connectivity. As a front end to an object recognition system, the approach provides the indexing power of complex 3-D object-centered primitives while exploiting the convenience of 2-D viewer-centered aspect matching; aspects are used to represent a finite vocabulary of 3-D parts from which objects can be constructed.</p>
3D shape recovery; pattern recognition; 3D volumetric primitives; picture processing; projected primitive surfaces; distributed aspect matching; hierarchical aspect representation; conditional probabilities; region segmentation; probabilities; connectivity; vocabulary; pattern recognition; picture processing; probability

A. Pentland, A. Rosenfeld and S. Dickinson, "3-D Shape Recovery Using Distributed Aspect Matching," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 14, no. , pp. 174-198, 1992.
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