Two problems usually need to be dealt properly in edge detection:the conflict between the detection and localization goals at one scale

and the integration of edges at all different scales.An efficient way is to use multiscale MRF models.Edge position can be precisely localized due to the introduction of a line process

and edges at all different scales can be integrated by using any proper function of the line process.In this paper

a deterministic system of equations is deduced by applying GBF inequality to approximate the mean field

which explicitly expresses the interaction between edges and the influence of model parameters on edge detection results

and can be solved with less computational time.Experimental results by applying the algorithm to a few real images are also given.