  For many segmentation tasks, especially for the biomedical image, the
topological prior is vital information which is useful to exploit. The
containment/nesting is a typical inter-class geometric relationship. In the
MICCAI Brain tumor segmentation challenge, with its three hierarchically nested
classes 'whole tumor', 'tumor core', 'active tumor', the nested classes
relationship is introduced into the 3D-residual-Unet architecture. The network
comprises a context aggregation pathway and a localization pathway, which
encodes increasingly abstract representation of the input as going deeper into
the network, and then recombines these representations with shallower features
to precisely localize the interest domain via a localization path. The
nested-class-prior is combined by proposing the multi-class activation function
and its corresponding loss function. The model is trained on the training
dataset of Brats2018, and 20% of the dataset is regarded as the validation
dataset to determine parameters. When the parameters are fixed, we retrain the
model on the whole training dataset. The performance achieved on the validation
leaderboard is 86%, 77% and 72% Dice scores for the whole tumor, enhancing
tumor and tumor core classes without relying on ensembles or complicated
post-processing steps. Based on the same start-of-the-art network architecture,
the accuracy of nested-class (enhancing tumor) is reasonably improved from 69%
to 72% compared with the traditional Softmax-based method which blind to
topological prior.
