A unified framework for MAP estimation in remote sensing image segmentation

A complete framework is proposed for applying the maximum a posteriori (MAP) estimation principle in remote sensing image segmentation. The MAP principle provides an estimate for the segmented image by maximizing the posterior probabilities of the classes defined in the image. The posterior probability can be represented as the product of the class conditional probability (CCP) and the class prior probability (CPP). In this paper, novel supervised algorithms for the CCP and the CPP estimations are proposed which are appropriate for remote sensing images where the estimation process might to be done in high-dimensional spaces. For the CCP, a supervised algorithm which uses the support vector machines (SVM) density estimation approach is proposed. This algorithm uses a novel learning procedure, derived from the main field theory, which avoids the (hard) quadratic optimization problem arising from the traditional formulation of the SVM density estimation. For the CPP estimation, Markov random field (MRF) is a common choice which incorporates contextual and geometrical information in the estimation process. Instead of using predefined values for the parameters of the MRF, an analytical algorithm is proposed which automatically identifies the values of the MRF parameters. The proposed framework is built in an iterative setup which refines the estimated image to get the optimum solution. Experiments using both synthetic and real remote sensing data (multispectral and hyperspectral) show the powerful performance of the proposed framework. The results show that the proposed density estimation algorithm outperforms other algorithms for remote sensing data over a wide range of spectral dimensions. The MRF modeling raises the segmentation accuracy by up to 10% in remote sensing images.