  Segmenting the retinal vasculature entails a trade-off between how much of
the overall vascular structure we identify vs. how precisely we segment
individual vessels. In particular, state-of-the-art methods tend to
under-segment faint vessels, as well as pixels that lie on the edges of thicker
vessels. Thus, they underestimate the width of individual vessels, as well as
the ratio of large to small vessels. More generally, many crucial
bio-markers---including the artery-vein (AV) ratio, branching angles, number of
bifurcation, fractal dimension, tortuosity, vascular length-to-diameter ratio
and wall-to-lumen length---require precise measurements of individual vessels.
To address this limitation, we propose a novel, stochastic training scheme for
deep neural networks that better classifies the faint, ambiguous regions of the
image. Our approach relies on two key innovations. First, we train our deep
networks with dynamic weights that fluctuate during each training iteration.
This stochastic approach forces the network to learn a mapping that robustly
balances precision and recall. Second, we decouple the segmentation process
into two steps. In the first half of our pipeline, we estimate the likelihood
of every pixel and then use these likelihoods to segment pixels that are
clearly vessel or background. In the latter part of our pipeline, we use a
second network to classify the ambiguous regions in the image. Our proposed
method obtained state-of-the-art results on five retinal datasets---DRIVE,
STARE, CHASE-DB, AV-WIDE, and VEVIO---by learning a robust balance between
false positive and false negative rates. In addition, we are the first to
report segmentation results on the AV-WIDE dataset, and we have made the
ground-truth annotations for this dataset publicly available.
