Bayesian inference of thermodynamic state incorporating Schwarz-Rissanen complexity for infrared target recognition

Abstract

University of IllinoisCoordinated Science Laboratory1308 W. MainUrbana, Illinois 61801E-mail: lanterma@ifp.uiuc.eduAbstract. The recognition of targets in IR scenes is complicated by thewide variety of appearances associated with different thermodynamicstates. We represent variability in the thermal signatures of targets via anexpansion in terms of ‘‘eigentanks’’ derived from a principal componentanalysis performed over the target’s surface. Employing a Poisson sen-sor likelihood, or equivalently a likelihood based on Csiszar’sI-divergence (a natural discrepancy measure for nonnegative images),yields a coupled set of nonlinear equations which must be solved tocompute maximum a posterioriestimates of the thermodynamic expan-sion coefficients. We propose a weighted least-squares approximation tothe Poisson loglikelihood for which the MAP estimates are solutions oflinear equations. Bayesian model order estimation techniques are em-ployed to choose the number of expansion coefficients; this preventstarget models with numerous eigentanks in their representation fromhaving an unfair advantage over simple target models. The Bayesianintegral is approximated by Schwarz’s application of Laplace’s method ofintegration; this technique is closely related to Rissanen’s minimum de-scription length criteria. Our implementation of these techniques on Sili-con Graphics computers exploits the flexible nature of their renderingengines. The implementation is illustrated in estimating the orientation ofa tank and the optimum number of representative eigentanks for bothsimulated and real data.