A physics-based approach to detecting and classifying surface and sub-surface objects in longwave (thermal) infrared imagery is described. The main premise is to associate a heat capacity and effective depth with each voxel (or segment) in the image. An energy budget for the voxel then leads to a linear, first-order differential equation, in which the temperature is forced by fluxes in and out of the voxel (shortwave solar radiation, longwave radiation, sensible and latent turbulent heat exchanges with the atmosphere), while relaxing towards an equilibrium temperature determined by a weighted mean of the air and ground temperatures. Next, it is shown how this simplified model can be incorporated into maximum-likelihood and Bayesian classifiers to distinguish buried objects from their surroundings. In particular, a version of the Bayesian classifier is formulated that leverages the differing amplitude and phase response of a buried object over the diurnal cycle. These classifiers will be tested on experimental data in future work.
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