Exploitation of feature correlations in target classification using differential geometry: a numerical approach

Michael Patrick Cain; Myles Harthun; Todd W. Kinley; A. Todd Jurhs; Walton C. Gibson

doi:10.1117/12.477608

31 July 2002 Exploitation of feature correlations in target classification using differential geometry: a numerical approach

Michael Patrick Cain, Myles Harthun, Todd W. Kinley, A. Todd Jurhs, Walton C. Gibson

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Proceedings Volume 4729, Signal Processing, Sensor Fusion, and Target Recognition XI; (2002) https://doi.org/10.1117/12.477608
Event: AeroSense 2002, 2002, Orlando, FL, United States

Abstract

In classification problems where multiple features are extracted from the observations of one or more sensors, the features often exhibit some degree of correlation, or a functional relationship. Frequently, this is expected and arises because of the mapping between the parameters that define the object's equation of state and the sensor observables. Therefore, it is of interest to develop representations of the objects and classification algorithms that exploit the correlations between the features. An approach for developing these types of representations makes use of Differential Geometry. In this approach, the objects are represented as a mean surface in feature space. When the functional relationship between features can be expressed analytically, Differential Geometry is used to develop analytical expressions for class surfaces and classification algorithms. More complex problems require the use of numerical techniques. In this paper, some of the mathematical foundations of this approach are reviewed. In an example, tensor product non-uniform rational b-splines are employed to develop the description of class surfaces along with the associated metric tensor and geodesic equations, leading to classification algorithms. The resulting Surface Classifier performance is compared with that of a traditional Quadratic Classifier.

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Michael Patrick Cain, Myles Harthun, Todd W. Kinley, A. Todd Jurhs, and Walton C. Gibson "Exploitation of feature correlations in target classification using differential geometry: a numerical approach", Proc. SPIE 4729, Signal Processing, Sensor Fusion, and Target Recognition XI, (31 July 2002); https://doi.org/10.1117/12.477608

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KEYWORDS

Sensors

Optical spheres

Algorithm development

Data fusion

Feature extraction

Signal to noise ratio

Nose

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