Spherical Classification of Remote Sensing Data

Real data are often characterized by high dimensional feature vectors. However, such data contain redundant information that may not be beneficial for analysis algorithms. As such, feature transformation arises in related fields of study, including geoscientific applications, as a means to capture the few characteristics that are useful for pattern analysis algorithms. In this study, we investigate the transformation of remote sensing images to a coordinate system that preserves local pixel relationships on a constant curvature space. The transformation is performed using the spherical embedding method. Based on the properties of spherical surfaces and their relationship with local tangent spaces, we further propose two geometrical spherical nearest neighbor metrics for classification. As part of experimental validation, results on modeling multi-class multispectral and hyperspectral data using the proposed spherical Mahalanobis nearest neighbor rule and the spherical discriminant adaptive nearest neighbor rule are presented. The results indicate that the proposed metrics yield better classification accuracies on lower dimensional spherical surfaces. This promising outcome serves as a motivation for further development of new models to analyze remote sensing images in spherical manifolds.