Two novel probabilistic models for viewed angles and distances are derived using an observability sphere method. The method, which is based on the assumption that the prior probability density is isotropic for all viewing orientations, can be used for the computation of observation probabilities for object's aspects, features, and probability densities of their quantitative attributes. Using the sphere, it is discovered that the probability densities of viewed angles, distances, and even projected curvature have sharp peaks at their original values. From this peaking effect, it is concluded that in most cases, the values of angles and distances are being altered only slightly by the imaging process, and they can still serve as a strong cue for model-based recognition. The probabilistic models for 3-D object recognition from monocular images are used. To form the angular elements that are needed, the objects are represented by their linear features and specific points primitives. Using the joint density model of angles and distances, the probabilities of initial matching hypotheses and mutual information coefficients are estimated. These results are then used for object recognition by optimal matching search and stochastic labeling schemes. Various synthetic and real objects are recognized by this approach.
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