  While convolutional neural networks (CNNs) trained by back-propagation have
seen unprecedented success at semantic segmentation tasks, they are known to
struggle on out-of-distribution data. Markov random fields (MRFs) on the other
hand, encode simpler distributions over labels that, although less flexible
than UNets, are less prone to over-fitting. In this paper, we propose to fuse
both strategies by computing the product of distributions of a UNet and an MRF.
As this product is intractable, we solve for an approximate distribution using
an iterative mean-field approach. The resulting MRF-UNet is trained jointly by
back-propagation. Compared to other works using conditional random fields
(CRFs), the MRF has no dependency on the imaging data, which should allow for
less over-fitting. We show on 3D neuroimaging data that this novel network
improves generalisation to out-of-distribution samples. Furthermore, it allows
the overall number of parameters to be reduced while preserving high accuracy.
These results suggest that a classic MRF smoothness prior can allow for less
over-fitting when principally integrated into a CNN model. Our implementation
is available at https://github.com/balbasty/nitorch.
