In this paper we survey some of the mathematical techniques that have led to useful new results in shape analysis and their application to a variety of object recognition tasks. In particular, we will show how these techniques allow one to solve a number of fundamental problems related to object recognition for configurations of point features under a generalized weak perspective model of image formation. Our approach makes use of progress in shape theory and includes the development of object-image equations for shape matching and the exploitation of shape space metrices (especially object-image metrics) to measure matching up to certain transformations. This theory is built on advanced mathematical techniques from algebraic and differential geometry which are used to construct generalized shape spaces for various projection and sensor models. That construction in turn is used to find natural metrics that express the distance (geometric difference) between two configurations of object features, two configurations of image features, or an object and an image pair. Such metrics are believed to produce the most robust tests for object identification; at least as far as the object's geometry is concerned. Moreover, these metrics provide a basis for efficient hashing schemes to do identification quickly, and they provide a rigorous foundation for error and statistical analysis in any recognition system. The most important feature of a shape theoretic approach is that all of the matching tests and metrics are independent of the choice of coordinates used to express the feature locations on the object or in the image. In addition, the approach is independent of the camera/sensor position and any camera/sensor parameters. Finally, the method is also independent of object pose or image orientation. This is what makes the results so powerful. Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/21/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx SPIE-IS&T/ Vol. 6508 65080E-2 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/21/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx SPIE-IS&T/ Vol. 6508 65080E-3 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/21/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx SPIE-IS&T/ Vol. 6508 65080E-5 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/21/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx SPIE-IS&T/ Vol. 6508 65080E-8 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/21/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

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.

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. This 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.

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