  Deep neural networks have achieved tremendous success in various fields
including medical image segmentation. However, they have long been criticized
for being a black-box, in that interpretation, understanding and correcting
architectures is difficult as there is no general theory for deep neural
network design. Previously, precision learning was proposed to fuse deep
architectures and traditional approaches. Deep networks constructed in this way
benefit from the original known operator, have fewer parameters, and improved
interpretability. However, they do not yield state-of-the-art performance in
all applications. In this paper, we propose to analyze deep networks using
known operators, by adopting a divide-and-conquer strategy to replace network
components, whilst retaining its performance. The task of retinal vessel
segmentation is investigated for this purpose. We start with a high-performance
U-Net and show by step-by-step conversion that we are able to divide the
network into modules of known operators. The results indicate that a
combination of a trainable guided filter and a trainable version of the Frangi
filter yields a performance at the level of U-Net (AUC 0.974 vs. 0.972) with a
tremendous reduction in parameters (111,536 vs. 9,575). In addition, the
trained layers can be mapped back into their original algorithmic
interpretation and analyzed using standard tools of signal processing.
