基于星凸性与空间关联性，单次完成多类生物对象的实例分割。

Biomedical images often contain objects known to be spatially correlated or nested due to their inherent properties, leading to semantic relations. Examples include cell nuclei being nested within eukaryotic cells and colonies growing exclusively within their culture dishes. While these semantic relations bear key importance, detection tasks are often formulated independently, requiring multi-shot analysis pipelines. Importantly, spatial correlation could constitute a fundamental prior facilitating learning of more meaningful representations for tasks like instance segmentation. This knowledge has, thus far, not been utilised by the biomedical computer vision community. We argue that the instance segmentation of two or more categories of objects can be achieved in parallel. We achieve this via two architectures HydraStarDist (HSD) and the novel (HSD-WBR) based on the widely-used StarDist (SD), to take advantage of the star-convexity of our target objects. HSD and HSD-WBR are constructed to be capable of incorporating their interactions as constraints into account. HSD implicitly incorporates spatial correlation priors based on object interaction through a joint encoder. HSD-WBR further enforces the prior in a regularisation layer with the penalty we proposed named Within Boundary Regularisation Penalty (WBR). Both architectures achieve nested instance segmentation in a single shot. We demonstrate their competitiveness based on $IoU_R$ and AP and superiority in a new, task-relevant criteria, Joint TP rate (JTPR) compared to their baseline SD and Cellpose. Our approach can be further modified to capture partial-inclusion/-exclusion in multi-object interactions in fluorescent or brightfield microscopy or digital imaging. Finally, our strategy suggests gains by making this learning single-shot and computationally efficient.