Phase as a Strong Prior: Surgical Phase Feature Modulation for Vessel Recognition in Complex Surgical Videos

Surgical procedures unfold in stereotypical phases, and the anatomy exposed at any moment is strongly conditioned on the current surgical phase. This work investigates whether the surgical phase constitutes a sufficiently informative prior for fine-grained anatomical segmentation and, if so, how such a prior should be incorporated into a segmentation foundation model. We study this problem on key vessel segmentation in laparoscopic gastrectomy, using the LapGC-KVAD-30 dataset (30 procedures, 8 surgical phases, 15 vessel classes, case-level splits). A diagnostic experiment shows that the phase label alone predicts 15-class vessel presence with a macro-F1 of 0.810, whereas image-only prediction with a compact convolutional network remains near chance (macro-F1 0.136), indicating that the phase prior dominates appearance for vessel presence. Motivated by this observation, we inject the phase prior as feature-level modulation: the proposed Phase-FiLM maps the phase embedding to channel-wise scale and shift parameters that modulate the SAM2 image features before the mask decoder. On binary vessel segmentation, Phase-FiLM improves the test mean Dice from $0.5892\pm 0.0190$ to $0.6245\pm 0.0103$ over three seeds (mean gain $+3.5$ points), outperforming the no-phase baseline on every seed, and yields consistent gains across two backbones (SAM2-L $+3.1$ points; MedSAM2-T $+7.9$ points). The improvements concentrate in the data-scarce dissection phases, where single-phase training collapses (S4: 0.320 vs. 0.428). Robustness analysis shows the method remains beneficial down to a break-even phase-recognition accuracy of 82.6%, within the 85-92% range reported for current surgical phase recognizers. Substituting an incorrect phase at test time collapses performance to 0.4212, indicating that the improvement arises from genuine exploitation of phase information rather than from increased model capacity. These results suggest that, in phase-structured procedures, workflow priors are most effectively incorporated as multiplicative feature modulation.