The recognition of targets in IR scenes is complicated by the wide variety of appearances associated with different thermodynamic states. We represent variability in the thermal signatures of targets via an expansion in terms of "eigentanks" derived from a principal component analysis performed over the target's surface. Employing a Poisson sensor likelihood, or equivalently a likelihood based on Csiszar's I-divergence (a natural discrepancy measure for nonnegative images), yields a coupled set of nonlinear equations which must be solved to compute maximum a posteriori estimates of the thermodynamic expansion coefficients. We propose a weighted least-squares approximation to the Poisson loglikelihood for which the MAP estimates are solutions of linear equations. Bayesian model order estimation techniques are employed to choose the number of expansion coefficients; this prevents target models with numerous eigentanks in their representation from having an unfair advantage over simple target models. The Bayesian integral is approximated by Schwarz's application of Laplace's method of integration; this technique is closely related to Rissanen's minimum description length criteria. Our implementation of these techniques on Silicon Graphics computers exploits the flexible nature of their rendering engines. The implementation is illustrated in estimating the orientation of a tank and the optimum number of representative eigentanks for both simulated and real data.