  Although the preservation of shape continuity and physiological anatomy is a
natural assumption in the segmentation of medical images, it is often neglected
by deep learning methods that mostly aim for the statistical modeling of input
data as pixels rather than interconnected structures. In biological structures,
however, organs are not separate entities; for example, in reality, a severed
vessel is an indication of an underlying problem, but traditional segmentation
models are not designed to strictly enforce the continuity of anatomy,
potentially leading to inaccurate medical diagnoses. To address this issue, we
propose a graph-based approach that enforces the continuity and connectivity of
anatomical topology in medical images. Our method encodes the continuity of
shapes as a graph constraint, ensuring that the network's predictions maintain
this continuity. We evaluate our method on two public benchmarks on retinal
vessel segmentation, showing significant improvements in connectivity metrics
compared to traditional methods while getting better or on-par performance on
segmentation metrics.
