  Optical coherence tomography (OCT) is a noninvasive imaging modality which
can be used to obtain depth images of the retina. The changing layer
thicknesses can thus be quantified by analyzing these OCT images, moreover
these changes have been shown to correlate with disease progression in multiple
sclerosis. Recent automated retinal layer segmentation tools use machine
learning methods to perform pixel-wise labeling and graph methods to guarantee
the layer hierarchy or topology. However, graph parameters like distance and
smoothness constraints must be experimentally assigned by retinal region and
pathology, thus degrading the flexibility and time efficiency of the whole
framework. In this paper, we develop cascaded deep networks to provide a
topologically correct segmentation of the retinal layers in a single feed
forward propagation. The first network (S-Net) performs pixel-wise labeling and
the second regression network (R-Net) takes the topologically unconstrained
S-Net results and outputs layer thicknesses for each layer and each position.
Relu activation is used as the final operation of the R-Net which guarantees
non-negativity of the output layer thickness. Since the segmentation boundary
position is acquired by summing up the corresponding non-negative layer
thicknesses, the layer ordering (i.e., topology) of the reconstructed
boundaries is guaranteed even at the fovea where the distances between
boundaries can be zero. The R-Net is trained using simulated masks and thus can
be generalized to provide topology guaranteed segmentation for other layered
structures. This deep network has achieved comparable mean absolute boundary
error (2.82 {\mu}m) to state-of-the-art graph methods (2.83 {\mu}m).
