  Segmentation is an essential operation of image processing. The convolution
operation suffers from a limited receptive field, while global modelling is
fundamental to segmentation tasks. In this paper, we apply graph convolution
into the segmentation task and propose an improved \textit{Laplacian}.
Different from existing methods, our \textit{Laplacian} is data-dependent, and
we introduce two attention diagonal matrices to learn a better vertex
relationship. In addition, it takes advantage of both region and boundary
information when performing graph-based information propagation. Specifically,
we model and reason about the boundary-aware region-wise correlations of
different classes through learning graph representations, which is capable of
manipulating long range semantic reasoning across various regions with the
spatial enhancement along the object's boundary. Our model is well-suited to
obtain global semantic region information while also accommodates local spatial
boundary characteristics simultaneously. Experiments on two types of
challenging datasets demonstrate that our method outperforms the
state-of-the-art approaches on the segmentation of polyps in colonoscopy images
and of the optic disc and optic cup in colour fundus images.
