Basics of random fields
Aly A. Farag · Cambridge University Press eBooks · 2014
Introduction This chapter describes the basics of random fields with focus on models that have been useful for image synthesis, filtering, segmentation, and registration. There is a vast literature on the subject. Besag [6.1], Geman and Geman [6.2], Derin and Elliott [6.3], and Dubes and Jain [6.4] are among the accessible literature in this area. Various books and monograms exist as well. Rue and Held [6.5], and Adler and Taylor [6.6] deal with some basics of random fields, and Blake et al . [6.7] contains examples of applied work on the random field in image analysis and computer vision. From an algorithmic point of view, Dubes and Jain [6.4] is excellent introductory reading. In simple terms, a random field is a random process in which the index set is multidimensional. As random variables are the building blocks of random processes, they are also the basic ingredients of random fields. To introduce the subject of random fields, we provide examples of random experiments that produce outputs in one or more dimensions.