  Segmentation of multiple surfaces in medical images is a challenging problem,
further complicated by the frequent presence of weak boundary and mutual
influence between adjacent objects. The traditional graph-based optimal surface
segmentation method has proven its effectiveness with its ability of capturing
various surface priors in a uniform graph model. However, its efficacy heavily
relies on handcrafted features that are used to define the surface cost for the
"goodness" of a surface. Recently, deep learning (DL) is emerging as powerful
tools for medical image segmentation thanks to its superior feature learning
capability. Unfortunately, due to the scarcity of training data in medical
imaging, it is nontrivial for DL networks to implicitly learn the global
structure of the target surfaces, including surface interactions. In this work,
we propose to parameterize the surface cost functions in the graph model and
leverage DL to learn those parameters. The multiple optimal surfaces are then
simultaneously detected by minimizing the total surface cost while explicitly
enforcing the mutual surface interaction constraints. The optimization problem
is solved by the primal-dual Internal Point Method, which can be implemented by
a layer of neural networks, enabling efficient end-to-end training of the whole
network. Experiments on Spectral Domain Optical Coherence Tomography (SD-OCT)
retinal layer segmentation and Intravascular Ultrasound (IVUS) vessel wall
segmentation demonstrated very promising results. All source code is public to
facilitate further research at this direction.
