  We present a differentiable model that infers explicit boundaries, including
curves, corners and junctions, using a mechanism that we call boundary
attention. Boundary attention is a boundary-aware local attention operation
that, when applied densely and repeatedly, progressively refines a field of
variables that specify an unrasterized description of the local boundary
structure in every overlapping patch within an image. It operates in a
bottom-up fashion, similar to classical methods for sub-pixel edge localization
and edge-linking, but with a higher-dimensional description of local boundary
structure, a notion of spatial consistency that is learned instead of designed,
and a sequence of operations that is end-to-end differentiable. We train our
model using simple synthetic data and then evaluate it using photographs that
were captured under low-light conditions with variable amounts of noise. We
find that our method generalizes to natural images corrupted by real sensor
noise, and predicts consistent boundaries under increasingly noisy conditions
where other state-of-the-art methods fail.
