Object recognition requires robust and stable features that are unique in feature space. Lie group analysis provides a constructive procedure to determine such features, called invariants, when they exist. Absolute invariants are rare in general, so quasi-invariants relax the restrictions required for absolute invariants and, potentially, can be just as useful in real-world applications. The paper develops the concept of a dominant-subspace invariant, a particular type of quasi-invariant, using the theory of Lie groups. A constructive algorithm is provided that fundamentally seeks to determine an integral submanifold which, in practice, is a good approximation to the orbit of the Lie group action. This idea is applied to the long-wave infrared problem and experimental results are obtained supporting the approach. Other application areas are cited.

An important issue in developing a model-based vision system is the specification of features that are invariant to viewing and scene conditions and also specific, i.e., the feature must have different values for different classes of objects. We formulate a new approach for establishing invariant features. Our 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 nonvisible spectrum. A new type of invariance called thermophysical invariance is defined. Features are defined such that they are functions of only the thermophysical properties of the imaged objects. The approach is based on a physics-based model that is derived from the principle of the conservation of energy applied at the surface of the imaged object.

We previously formulated a new approach for computing invariant features from infrared (IR) images. That 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 thermal state that affect images sensed in the nonvisible spectrum. In this paper, we extend the thermophysical algebraic invariance (TAI) formulation for the interpretation of uncalibrated infrared imagery and further reduce the information that is required to be known about the environment. Features are defined such that they are functions of only the thermophysical properties of the imaged objects. In addition, we show that the distribution of the TAI features can be accurately modeled by symmetric alpha-stable models. This approach is shown to yield robust classifier performance. Results on ground truth data and real infrared imagery are presented. The application of this scheme for site change detection is discussed.