  Nucleus segmentation is a challenging task due to the crowded distribution
and blurry boundaries of nuclei. Recent approaches represent nuclei by means of
polygons to differentiate between touching and overlapping nuclei and have
accordingly achieved promising performance. Each polygon is represented by a
set of centroid-to-boundary distances, which are in turn predicted by features
of the centroid pixel for a single nucleus. However, using the centroid pixel
alone does not provide sufficient contextual information for robust prediction
and thus degrades the segmentation accuracy. To handle this problem, we propose
a Context-aware Polygon Proposal Network (CPP-Net) for nucleus segmentation.
First, we sample a point set rather than one single pixel within each cell for
distance prediction. This strategy substantially enhances contextual
information and thereby improves the robustness of the prediction. Second, we
propose a Confidence-based Weighting Module, which adaptively fuses the
predictions from the sampled point set. Third, we introduce a novel Shape-Aware
Perceptual (SAP) loss that constrains the shape of the predicted polygons.
Here, the SAP loss is based on an additional network that is pre-trained by
means of mapping the centroid probability map and the pixel-to-boundary
distance maps to a different nucleus representation. Extensive experiments
justify the effectiveness of each component in the proposed CPP-Net. Finally,
CPP-Net is found to achieve state-of-the-art performance on three publicly
available databases, namely DSB2018, BBBC06, and PanNuke. Code of this paper is
available at \url{https://github.com/csccsccsccsc/cpp-net
