This question is meant to be a more technical question, so if I have phrased it as soliciting an opinion, any suggested language updates would be appreciated. 

I am relatively new to image processing, but have been looking at both the Convolutional Neural Networks literature on image segmentation, as well as the literature on graph cut and Mumford-Shah type approaches to image segmentation. I understand that graph cuts is a particular interpretation of the image segmentation problem, and that the Mumford-Shah functional is one implementation of penalty by which to identify the cut edges. I have yet to find a Convolutional Neural Network paper that references the Mumford-Shah approaches, and *vice versa*. 

Can anyone explain where Mumford-Shah approaches work better than CNNs, and where CNNs work better than Mumford-Shah. Are there particular domains in which one approach works better compared to the other--such as noisier backgrounds, etc. I realize that these questions are still open research areas. 

Graph cut ideas of course extend to problems outside of image processing, however I was wondering if anyone has directly compared the efficiency or prediction error of graph cut image segmentation versus CNNs? CNNs face a number of challenges in generalizing to problems outside of their training sets, but I have not seen how well graph-cut methods compare on the same datasets. 

It seems like the two literatures are proceeding in parallel, though of course there are obvious overlaps. 

Any suggestions would be appreciated.