The solar corona is the origin of very dynamic events that are mostly produced in active regions (AR) and coronal holes (CH). The exact location of these large-scale features can be determined by applying image-processing approaches to extreme-ultraviolet (EUV) data. We here investigate the problem of segmentation of solar EUV images into ARs, CHs, and quiet-Sun (QS) images in a firm Bayesian way. On the basis of Bayes’ rule, we need to obtain both prior and likelihood models. To find the prior model of an image, we used a Potts model in non-local mode. To construct the likelihood model, we combined a mixture of a Markov–Gauss model and non-local means. After estimating labels and hyperparameters with the Gibbs estimator, cellular learning automata were employed to determine the label of each pixel. We applied the proposed method to a Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) dataset recorded during 2011 and found that the mean value of the filling factor of ARs is 0.032 and 0.057 for CHs. The power-law exponents of the size distribution of ARs and CHs were obtained to be −1.597 and −1.508, respectively, with the maximum likelihood estimator method. When we compare the filling factors of our method with a manual selection approach and the SPoCA algorithm, they are highly compatible.