  Automatic detection and segmentation of cells and nuclei in microscopy images
is important for many biological applications. Recent successful learning-based
approaches include per-pixel cell segmentation with subsequent pixel grouping,
or localization of bounding boxes with subsequent shape refinement. In
situations of crowded cells, these can be prone to segmentation errors, such as
falsely merging bordering cells or suppressing valid cell instances due to the
poor approximation with bounding boxes. To overcome these issues, we propose to
localize cell nuclei via star-convex polygons, which are a much better shape
representation as compared to bounding boxes and thus do not need shape
refinement. To that end, we train a convolutional neural network that predicts
for every pixel a polygon for the cell instance at that position. We
demonstrate the merits of our approach on two synthetic datasets and one
challenging dataset of diverse fluorescence microscopy images.
