This paper introduces STARDIST, a novel method for cell detection in microscopy images using star-convex polygons as a shape representation. Traditional methods often use axis-aligned bounding boxes, which can lead to segmentation errors in crowded cell images. STARDIST predicts star-convex polygons for each pixel, which better represent the roundish shapes of cell nuclei and avoid the need for shape refinement. The method uses a U-Net-based neural network to predict both object probabilities and polygon distances. Object probabilities are defined as the normalized Euclidean distance to the nearest background pixel, while polygon distances are computed along predefined radial directions. Non-maximum suppression is used to select the final set of polygons. The method is evaluated on three datasets: TOY, TRAGEN, and DSB2018. Results show that STARDIST outperforms existing methods, especially in crowded cell scenarios, and is more efficient in terms of parameters and training complexity. The method is particularly effective in handling overlapping and partially visible cells, making it suitable for cell tracking applications. STARDIST achieves high accuracy for moderate IoU thresholds and performs well on real-world fluorescence microscopy images. The method is competitive with state-of-the-art instance segmentation methods like Mask R-CNN but has a much simpler architecture and fewer parameters.This paper introduces STARDIST, a novel method for cell detection in microscopy images using star-convex polygons as a shape representation. Traditional methods often use axis-aligned bounding boxes, which can lead to segmentation errors in crowded cell images. STARDIST predicts star-convex polygons for each pixel, which better represent the roundish shapes of cell nuclei and avoid the need for shape refinement. The method uses a U-Net-based neural network to predict both object probabilities and polygon distances. Object probabilities are defined as the normalized Euclidean distance to the nearest background pixel, while polygon distances are computed along predefined radial directions. Non-maximum suppression is used to select the final set of polygons. The method is evaluated on three datasets: TOY, TRAGEN, and DSB2018. Results show that STARDIST outperforms existing methods, especially in crowded cell scenarios, and is more efficient in terms of parameters and training complexity. The method is particularly effective in handling overlapping and partially visible cells, making it suitable for cell tracking applications. STARDIST achieves high accuracy for moderate IoU thresholds and performs well on real-world fluorescence microscopy images. The method is competitive with state-of-the-art instance segmentation methods like Mask R-CNN but has a much simpler architecture and fewer parameters.