  Image segmentation is a fundamental task in the field of imaging and vision.
Supervised deep learning for segmentation has achieved unparalleled success
when sufficient training data with annotated labels are available. However,
annotation is known to be expensive to obtain, especially for histopathology
images where the target regions are usually with high morphology variations and
irregular shapes. Thus, weakly supervised learning with sparse annotations of
points is promising to reduce the annotation workload. In this work, we propose
a contrast-based variational model to generate segmentation results, which
serve as reliable complementary supervision to train a deep segmentation model
for histopathology images. The proposed method considers the common
characteristics of target regions in histopathology images and can be trained
in an end-to-end manner. It can generate more regionally consistent and
smoother boundary segmentation, and is more robust to unlabeled `novel'
regions. Experiments on two different histology datasets demonstrate its
effectiveness and efficiency in comparison to previous models.
