Invariants of the LWIR thermophysical model

Abstract

The temperature of a surface viewed by a long-wave infrared camera can be predicted by a thermophysical model (a conservation of energy statement at the surface of a unit volume). However this prediction currently requires at least 24 hours of previous imagery in order to estimate the parameters of the model. Absolute invariants, relative invariants, and quasi-invariants provide three possible methods for circumventing this obstacle. Lie group analysis is a fundamental tool for systematically exploring invariance and for finding the appropriate transformations groups. This paper discusses the relevant parts of Lie group analysis and uses them to find the transformation groups and absolute invariants of the thermophysical model. The goal is to recognize objects based upon a composition of materials that are identified using invariant features of infrared imagery.