Topo-Morphological Edge Logits Field for 3D Dental Proposal Generation and Instance Segmentation

Automatic tooth segmentation is essential for computer-aided diagnosis and treatment planning in dentistry. Proposal generation plays a pivotal role in accurately delineating instance boundaries and is critical for improving segmentation accuracy. However, existing methods suffer from dispersive offset bias, spatial information loss, and spillover-induced centroid shift, all of which are difficult to alleviate in Euclidean space. This limitation commonly leads to missed detections or excessive merging of instances, particularly in cases of missing or crowded teeth. To overcome these issues, we introduce a novel proposal generation framework based on Topological Morphological Clustering (TMC), which integrates edge logits fields with topological morphology. The key insight is that morphological erosion applied to tooth and edge masks enables the separation of individual tooth instances. To further enhance the continuity of tooth-tooth edges, we design an edge enhancement module that fuses the alpha-shape algorithm with our proposed KNN-based iterative contour approximation (KNN-ICA) method, thereby constructing a supplementary geometric edge logits field. Extensive experiments show that our method achieves superior detection performance over existing proposal generation techniques, and outperforms prior instance segmentation methods on two public benchmarks. Our code is available at https://github.com/jfzhuang314/TMELFNet.