  Most recent semantic segmentation methods train deep convolutional neural
networks with fully annotated masks requiring pixel-accuracy for good quality
training. Common weakly-supervised approaches generate full masks from partial
input (e.g. scribbles or seeds) using standard interactive segmentation methods
as preprocessing. But, errors in such masks result in poorer training since
standard loss functions (e.g. cross-entropy) do not distinguish seeds from
potentially mislabeled other pixels. Inspired by the general ideas in
semi-supervised learning, we address these problems via a new principled loss
function evaluating network output with criteria standard in "shallow"
segmentation, e.g. normalized cut. Unlike prior work, the cross entropy part of
our loss evaluates only seeds where labels are known while normalized cut
softly evaluates consistency of all pixels. We focus on normalized cut loss
where dense Gaussian kernel is efficiently implemented in linear time by fast
Bilateral filtering. Our normalized cut loss approach to segmentation brings
the quality of weakly-supervised training significantly closer to fully
supervised methods.
