An attempt is made to unify several approaches to image segmentation in early vision under a common framework. The energy function, or Markov random field, formalism is very attractive since it enables the assumptions used to be explicitly stated in the energy functions, and it can be extended to deal with many other problems in vision. It is shown that specified discrete formulations for the energy function are closely related to the continuous formulation. When the mean field (MF) theory approach is used, several previous attempts to solve these energy functions are effectively equivalent. By varying the parameters of the energy functions, one can obtain a class of solutions and several nonlinear diffusion approaches to image segmentation. The theory is developed for image segmentation, but it can be applied equally well to image or surface reconstruction (where the data are sparse).