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The authors are interested in solving the problems of image estimation and image segmentation in a joint maximum a posteriori (MAP) framework. Due to the computational complexity and non-convexity of the problem, a continuation method which tracks the minima through the variation of a control parameter is used. The authors have found it useful to define two new processes; the gradient (GRAD) and gradient-magnitude (GMAG) processes. The line process can be obtained through a monotonic transformation of the GMAG process. Interactions are still added in the line process domain, and the concept of the uncertainty function is introduced to characterize the properties of the GMAG-line process transformation. Results obtained using two different transformations are compared.>
Rangarajan et al. (Tue,) studied this question.