The method of regularization was described in Section 2.4 with regard to image flow segmentation. This type of global image processing can also be used to find edges, via more general surface reconstruction. (In fact, regularization was used with individual images before it was used with image sequences.) These methods tend to be computationally expensive.
In  Blake and Zisserman used a weak membrane model which has many similarities to the work described earlier. The elements of the cost functional are the smoothness of the estimated surface, the quality of the fit of the estimated surface to the original data and the ``line processes'', i.e., the discontinuities in the membrane. This method does not pick up fine complicated detail very well.
In  Geiger and Girosi extend this approach to cope with sparse data. In  Nordström uses a similar approach from the viewpoint of anisotropic diffusion. Thus rather than solving one global equation, local diffusion is performed iteratively (using similar cost function elements to those mentioned above to control the anisotropy) to achieve image reconstruction. Image edges can be extracted at some stage in the iterative procedure, before the image is homogenized.
In  Tan et. al. use a slightly different approach from that of surface reconstruction followed by edge extraction. Firstly, the image is processed with dissimilarity enhancement to enhance edges, and non-maximum suppression is performed. The enhancement is typically region dissimilarity when standard edge finding is to be performed, but texture preprocessing can be used instead to find texture boundaries. Then, minimization is performed to find the best global edge configuration, using five elements for the cost functional; a cost for edge curvature, a cost for region dissimilarity (with edge pixels contributing zero cost), a cost for the number of edge points, a cost for edge fragmentation (i.e., related to the number of edge ends and isolated points), and a cost for edge thickness. As with other minimization methods, the relative weighting of the different terms in the cost functional is difficult to reliably optimize.