Classically, the problem of object recognition has long been formulated as that of recognizing the instance of some object in a scene through information acquired from an image. This has motivated such questions as how to compute stable and effective representations for objects from image data and how to correctly identify an unknown object from its representation. Our interest, and the primary focus of this research, is how such decisions can be made in the presence of uncertainty and how one can explicitly represent and reason about the uncertainty. We have proposed a framework for parametric shape recognition based on a probabilistic model of inverse theory first introduced by Tarantola in [Tarantola:87]. The key result is a method for generating classifiers in the form of conditional probability densities in order to recognize an unknown from a set of reference models. Our procedure is automatic. Off-line, it invokes an autonomous process to estimate reference model parameters and their statistics. On-line, during measurement, it combines these with a priori context-dependent information, as well as the parameters and statistics estimated for an unknown object, into a single description. That description, a conditional probability density function, represents the likelihood of correspondence between the unknown and a particular reference model. The original context of this work was three-dimensional object recognition in which objects were represented by parametric shape descriptors and their uncertainties. Since then we have extended the approach to include parametric representations computed from other imaging modalities. Generally the process is the same. Object models are computed from a bottom-up analysis leading to a set of descriptors which form the basis for recognition. An experimental system has been implemented in which objects are represented by either single or multiple parametric models. These experiments have indicated that recognition performance is near perfect for cases in which most of the object is visible to the observer, and falls off gracefully (minimal false-positive response) when only partial information is available.