A new, probabilistic approach for inferring 3-D volumetric primitives from a single 2-D view is presented. This recognition relies on the assumption that every object can be decomposed into component parts that belong to a finite set or alphabet of volumetric primitives (geons). For each possible primitive from the permissible set, a conditional probability function is computed. This law specifies the probability of obtaining the primitive given an observable 2- D measure or feature. The distribution functions are determined by simulation, on the basis of a representative number of random projections of the primitives. The measures themselves are chosen in such a way that they can easily be extracted from real images and their discriminative power for the volumetric primitive inference is high. Examples illustrate the proposed approach.