Coupled Markov random field (MRF) models have been proposed so far for visual image processing. These are classified into boundary- and region-based models, where hidden variables that determine the interaction between the units corresponding to image pixels are given by line and label processes, respectively. In this paper, we have investigated a region-based coupled MRF model with phase variables as the hidden variables, and have modified the model for applications to coarse image-region segmentation by replacing some nonlinear functions in the update equations of the intensity and label processes with piecewise linear (PWL) functions. Using PWL functions facilitates VLSI implementation of coupled MRF models, and also makes their performance improved. We have verified that the modified region-based MRF model is superior to the resistive-fuse network, which is one of the boundary-based MRF models. We also propose an improvement of the modified region-based MRF model by introducing a new parameter, and evaluate the model performance in coarse image region segmentation.