Hyper-Parameter in Hidden Markov Random Field

Abstract Hidden Markov random eld(HMRF) is one of the most common model for image segmentation which is animportant preprocessing in many imaging devices. The HMRF has unknown hyper-parameters on Markovrandom eld to be estimated in segmenting testing images. However, in practice, due to computational com-plexity, it is often assumed to be a xed constant. In this paper, we numerically show that the segmentationresults very depending on the xed hyper-parameter, and, if the parameter is misspeci ed, they further de-pend on the choice of the class-labelling algorithm. In contrast, the HMRF with estimated hyper-parameterprovides consistent segmentation results regardless of the choice of class labelling and the estimation method.Thus, we recommend practitioners estimate the hyper-parameter even though it is computationally complex. Keywords: Hidden Markov random eld, hyper-parameter, image segmentation. 1. Introduction Segmentation is a process which divides an image into several homogeneous regions, whereas clas-sification matches an unknown image with a known image in the database. Despite their apparentdifference, classifiers are often used for segmenting an image with the name of context-based clas-sifier.A context-based classifier partitions the whole image into many sub-blocks and classifies each sub-block into one of the classes in the database. In doing so, a difficulty arises in obtaining smoothboundaries, which is often a trait of the true segmentation. To obtain smooth boundaries, hiddenMarkov models(HMM) have often been proposed, in which the spatial coherence between sub-blocksis modelled by the Markovian random field (Geman and Geman, 1984; Besag, 1986; Li and Gray,1999; Li