Learning a Gaussian basis for spectra representation aimed at reflectance classification

In this paper, we present a method which aims at learning a Gaussian basis which can be used to represent the reflectance spectra in the image while yielding a high recognition rate when used as input to an SVM classifier. To do this, we view the reflectance spectra as a Gaussian mixture and depart from a maximum-likelihood formulation which allows the introduction of posterior probabilities as a means to computing the mixture weights. This formulation permits the update of the Gaussian basis parameters, i.e. means and variances, through a two-step iterative optimisation process reminiscent of the EM algorithm. The first step of the algorithm estimates the posterior probabilities whereas the second step employs the dual formulation of the SVM classifier to update the Gaussian parameters. As a result, our method learns the Gaussian basis for the reflectance in the image subject to the performance of the SVM. We provide results on skin recognition and ground cover classification on remote sensing data. We also compare our results with those obtained using a number of alternatives.