Weight Parameter Optimization by the Ho–Kashyap Algorithm in MRF Models for Supervised Image Classification

In the context of remote-sensing image analysis, Markov random field (MRF) models play an important role, due to their ability to integrate the use of contextual information associated with the image data in the analysis process, through the definition of suitable energy functions. However, especially when dealing with MRF models for supervised classification, the estimation of the parameters characterizing an MRF model is still an open issue, which is typically addressed by using time-expensive interactive "trial-and-error" procedures. In this paper, by focusing on a broad class of MRF models, in which the energy functions can be expressed as linear combinations of distinct contributions (e.g., representing different typologies of contextual interactions), an automatic supervised procedure for the optimization of the weight parameters of the combinations is proposed. Formulating the parameter-estimation problem as the solution of a system of linear inequalities, the problem is solved by extending to the present context the Ho-Kashyap algorithm, which is typically applied by the pattern-recognition community in computing linear discriminant functions for binary classification. The method is validated experimentally on three different (both single-date and multitemporal) datasets, which are endowed with distinct MRF models formalizing the spatial contextual information associated with a single remote-sensing image and/or the spatio-temporal contextual information associated with an image sequence