  Annotation is a major hurdle in the semantic segmentation of microscopy
images and volumes due to its prerequisite expertise and effort. This work
enables the training of semantic segmentation networks on images with only a
single point for training per instance, an extreme case of weak supervision
which drastically reduces the burden of annotation. Our approach has two key
aspects: (1) we construct a graph-theoretic soft-segmentation using individual
seeds to be used within a regularizer during training and (2) we use an
objective function that enables learning from the constructed soft-labels. We
achieve competitive results against the state-of-the-art in point-supervised
semantic segmentation on challenging datasets in digital pathology. Finally, we
scale our methodology to point-supervised segmentation in 3D fluorescence
microscopy volumes, obviating the need for arduous manual volumetric
delineation. Our code is freely available.
