PCA Gaussianization for One-Class Remote Sensing Image Classification

摘要

The most successful one-class classification methods are discriminative approaches aimed at separating the class of interest from the outliers in a proper feature space. For instance, the support vector domain description (SVDD) has been successfully introduced for solving one-class remote sensing classification problems when scarce and uncertain labeled data is available. The success of this kernel method is due to that maximum margin nonlinear separation boundaries are implicitly defined, thus avoiding the hard and ill-conditioned problem of estimating probability density functions (PDFs). Certainly, PDF estimation is not an easy task, particularly in the case of high-dimensional PDFs such as is the case of remote sensing data. In high-dimensional PDF estimation, linear models assumed by widely used transforms are often quite restrictive to describe the PDF. As a result, additional non-linear processing is typically needed to overcome the limitations of the models. In this work we focus on the multivariate Gaussianization method for PDF estimation. The method is based on the Projection Pursuit Density Estimation (PPDE) technique.~1 The original PPDE procedure consists in iteratively project the data in the most non-Gaussian directions (like in ICA algorithms) and Gaussianizing them marginally. However, the extremely high computational cost associated to multiple ICA evaluations has prevented its practical use in high-dimensional problems such as those encountered in image processing. Here, we propose a fast alternative to iterative Gaussianization that makes it suitable for remote sensing applications while ensuring its theoretical convergence. Method's performance is successfully illustrated in the challenging problem of urban monitoring.