Density-Guided Variational Semantic Field Recovery for Open-Vocabulary 3D Part Segmentation

Point–text matching based methods for open-vocabulary 3D part segmentation di- rectly convert prompt-conditioned responses into part predictions, making them vulnerable to low-density semantic outliers and boundary-mixed responses in the underlying semantic field. To address this issue, we formulate the task as prompt- conditioned semantic field recovery before final prediction and propose DGV- SFR. First, density-guided semantic denoising moves unreliable point states to- ward local prompt-consistent high-density modes while suppressing propagation across risky part boundaries. Second, a unified variational Dirichlet–Wiener cor- rection jointly models the nonparametric posterior semantic surface and point- wise uncertainty, and evolves uncertain states on this surface under boundary and anchor constraints. The recovered semantic field is finally used for standard masked point–text matching, preserving the original open-vocabulary prediction interface. Experiments on standard benchmarks show that DGV-SFR achieves state-of-the-art average performance, improving a strong point–text matching baseline by approximately 4.1 mIoU. Further ablations, calibration analysis, and boundary-missing stress tests show that the recovered field reduces low-density er- rors, improves uncertainty calibration, and better preserves segmentation quality when local boundary evidence is incomplete.