Coupled Markov random field models with phases as line field and region field

We investigate a boundary-based and a region-based coupled Markov random field model, both of which are useful in image restorations of gray-level images. In the conventional boundary-based and the conventional region-based coupled Markov random field models, both a line field and a region field take only two discrete states, 0 and 1. In the boundary-based coupled random field model, existence and nonexistence of the edge at each nearest-neighbor pair of pixels are denoted by 1 and 0, respectively. In the region-based coupled random field model, some different regions at each pixel are labeled by discrete numbers. We propose a boundary-based coupled Markov random field model with continuous line field and a region-based coupled Markov random field model with continuous segmentation field from a standpoint of a plane rotator model in statistical mechanics. The iterative algorithms for image restoration are constructed by using a mean-field approximation. We investigate how the proposed models produce a better quality of restored images.