  Existing joint optic disc and cup segmentation approaches are developed
either in Cartesian or polar coordinate system. However, due to the subtle
optic cup, the contextual information exploited from the single domain even by
the prevailing CNNs is still insufficient. In this paper, we propose a novel
segmentation approach, named Cartesian-polar dual-domain network (DDNet), which
for the first time considers the complementary of the Cartesian domain and the
polar domain. We propose a two-branch of domain feature encoder and learn
translation equivariant representations on rectilinear grid from Cartesian
domain and rotation equivariant representations on polar grid from polar domain
parallelly. To fuse the features on two different grids, we propose a
dual-domain fusion module. This module builds the correspondence between two
grids by the differentiable polar transform layer and learns the feature
importance across two domains in element-wise to enhance the expressive
capability. Finally, the decoder aggregates the fused features from low-level
to high-level and makes dense predictions. We validate the state-of-the-art
segmentation performances of our DDNet on the public dataset ORIGA. According
to the segmentation masks, we estimate the commonly used clinical measure for
glaucoma, i.e., the vertical cup-to-disc ratio. The low cup-to-disc ratio
estimation error demonstrates the potential application in glaucoma screening.
