AbstractAn edge‐detection method based on Markov random field and statistical estimation is proposed. Compound Gauss‐Markov random fields are used as the image model, and the edge‐detection problem was formulated as the maximum a posteriori probability (MAP) estimation problem which can determine the estimated value of line process from the observed value of intensity process. the simulated annealing (SA) method and iterative conditional model (ICM) method are well known as relaxation methods for such types of problems. However, a large amount of calculations is needed in the SA method and convergence to local optimum solution is a major problem in the ICM method.This paper determines the MAP estimation solution using the method of mean field annealing (MFA), which has shown good results for the combinatorial optimization problem. Moreover, since in this method the shape and continuity of the detected edge changes with the model parameters of compound Gauss‐Markov random field, parameter estimation is an important problem.In the previous research, those parameter estimation methods have been studied where parameters determined from experience have been used or parameters are estimated using the edges traced by a human being. This paper proposes the method of automatic parameter estimation from the observed image based on the maximum likelihood (ML) criterion. Moreover, the gradient descent method and expectation maximization (EM) algorithm are used to calculate the actual ML solution.