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

摘要

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. Application of the approach to spatially separated sensors is also presented.