  We present a joint graph convolution-image convolution neural network as our
submission to the Brain Tumor Segmentation (BraTS) 2021 challenge. We model
each brain as a graph composed of distinct image regions, which is initially
segmented by a graph neural network (GNN). Subsequently, the tumorous volume
identified by the GNN is further refined by a simple (voxel) convolutional
neural network (CNN), which produces the final segmentation. This approach
captures both global brain feature interactions via the graphical
representation and local image details through the use of convolutional
filters. We find that the GNN component by itself can effectively identify and
segment the brain tumors. The addition of the CNN further improves the median
performance of the model by 2 percent across all metrics evaluated. On the
validation set, our joint GNN-CNN model achieves mean Dice scores of 0.89,
0.81, 0.73 and mean Hausdorff distances (95th percentile) of 6.8, 12.6, 28.2mm
on the whole tumor, core tumor, and enhancing tumor, respectively.
