Analysis of invariants for thermophysical models in infrared image understanding

Object recognition requires robust and stable features that are unique in feature space. Stable long-wave infrared features are invariant to transformations that may be a function of viewing aspect, ambient temperature, wind speed, and solar insolation. Uniqueness guarantees a one-to-one correspondence between feature values and the objects to be recognized. Currently, many features are selected based on intuition and heuristics. Since the extracted features are the foundation upon which the entire object recognition system is built, the limitations of a system cannot be determined and robustness cannot be guaranteed. An improved method for defining classifier features is required---a method that involves more science and less art.;Lie group analysis can determine (absolute) invariant functions for classification in object recognition problems. The mathematics of Lie groups is discussed and its application to the thermophysical model is illustrated. Lie group analysis is used to determine the simplest non-trivial function that has a constant value on the set of all roots of a conservation equation (which determines a manifold). The goal is to use this function for classification. Since the form of the conservation equation remains the same, with only the coefficients changing for different objects, the set of roots will differ depending on the object being viewed. An invariant function of the conservation equation (with the coefficients as parameters) yields different values based upon which object is currently observed. Lie group analysis is used to prove that the thermophysical model is the simplest invariant.;Quasi-invariants are a generalization of absolute invariants. Non-trivial absolute invariants are generally rare. Because the restrictions required for absolute invariance are relaxed, quasi-invariants are more common. These types of functions could be just as useful as absolute invariants in practice. A constructive algorithm is developed to find a particular type of quasi-invariant called a Dominant-Subspace Invariant (DSI). Experimental results validate the approach.;The following approach is unique in the field since it considers not just surface reflection and surface geometry in the specification of invariant features, but it also takes into account internal object composition and state which affect images sensed in the non-visible spectrum. The approach utilizes a physics-based model that is derived from the principle of the conservation of energy (COE) applied at the surface of the imaged object.