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Instance-level quantification of kidney functional units is essential for morphometric analysis, yet most publicly available pathology datasets provide only semantic segmentation annotations, where adjacent structures of the same class are merged into single regions. This prevents reliable instance-level analysis and limits downstream quantitative studies. Existing heuristic post-processing methods often yield suboptimal instance separation, particularly in crowded and adherent regions, while deep learning-based instance segmentation approaches typically require intensive instance-level annotations that are costly and labor-intensive to obtain. We propose MORI-Seg, a deep learning framework that enables instance segmentation without requiring instance-level annotations. Instead of heuristic splitting or instance supervision, MORI-Seg learns morphology-aware geometric representations directly from semantic masks by jointly modeling object-centric distance fields and boundary-band representations to encode interior structure and contact interfaces. A class-conditioned feature disentanglement module further promotes intra-instance coherence and inter-instance separation. Under semantic-only supervision, MORI-Seg decomposes connected semantic regions into distinct instance masks in an end-to-end manner. Experiments demonstrate improved instance separation accuracy and more reliable morphometric quantification compared with classical post-processing pipelines and representative semantic-to-instance learning approaches. The official implementation is publicly available at this https URL.