Hyper-Parameter in Hidden Markov Random Field

Hidden Markov random field(HMRF) is one of the most common model for image segmentation which is an important preprocessing in many imaging devices. The HMRF has unknown hyper-parameters on Markov random field to be estimated in segmenting testing images. However, in practice, due to computational complexity, it is often assumed to be a fixed constant. In this paper, we numerically show that the segmentation results very depending on the fixed hyper-parameter, and, if the parameter is misspecified, they further depend on the choice of the class-labelling algorithm. In contrast, the HMRF with estimated hyper-parameter provides 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.