We devise a segmentation scheme aimed at extracting edge information from speckled images using a maximum likelihood edge detector. The scheme is based on finding a threshold for the probability density function of the summing average field over a neighborhood set and, in a general context, is founded on a likelihood random field model (LRFM). A rigorous stochastic analysis is used to derive an exact expression for the cumulative density function of the likelihood of the averaging sum image. Based on this, an accurate probability of error is derived and the performance of the scheme is analyzed. The segmentation performs reasonably well for both simulated and real images. The LRFM scheme is also compared with standard edge detection methods to quantify the significant gains obtained from the optimized edge detector. The importance of this work lies in the development of a stochastic-based segmentation, allowing an accurate quantification of the probability of false detection. Nonvisual quantification and misclassification in speckled images, such as synthetic aperture radar and medical ultrasound, is relatively new and is of interest to remote sensing human observers and clinicians.