Our pattern theoretic approach to automatic target recognition for infrared scenes combines structured and unstructured representations: rigid, 3-D faceted models for known targets of interest and flexible, simply connected shapes to accommodate the unknown 'clutterers' that the algorithm may encounter. The radiant intensities of both kinds of targets form nuisance variables which are incorporated into the parameter space. Statistical inference proceeds by simulating hypothesized scenes and comparing them to the collected data via a likelihood function. For a given target pose, we derive closed-form expressions for estimates of the thermodynamic variables via a weighted least-squares approximation. Since the number of objects in the scene, both rigid and flexible, is unknown and must be estimated, the parameter space is a union of subspaces of varying dimension. Without constraints on the model order, scene descriptions may become too complex. We apply Rissanen's minimum description length (MDL) principle, which offers a mathematical foundation for balancing the brevity of descriptions against their fidelity to the data. For continuous parameters, the description length involves the log-determinant of the empirical Fisher information matrix. The relationship of Rissanen's MDL to Schwartz's application of Laplace's method of integration and to the Cramer-Rao bound are discussed. Examples of likelihood surfaces and associated complexity penalties are given for synthetic tank data. In these experiments, the minimum description length approach correctly deduces the number of thermodynamic parameters.