Quantifying the Resolution Ceiling of Prototype-Based Few-Shot Segmentation on Sub-Centimetre Pulmonary Nodules: A Training-Free Geometric Analysis.

Background/Objectives: Prototype-based few-shot segmentation is validated almost entirely on centimetre-scale abdominal organs; on pulmonary nodules, 70% of which are less than 10 mm in size, accuracy degrades sharply. We seek to determine how much of that degradation is geometric rather than methodological. Methods: No published method is trained or evaluated here. For any model whose prediction is a union of whole feature grid cells, the attainable Dice coefficient is bounded exactly by a single ratio ρ of the lesion diameter to the grid cell extent; bilinear upsampling relaxes it rather than removing it. We measured this bound on the 50% consensus masks of 2614 LIDC-IDRI nodules, quantified lesion preservation under six mask-handling policies, and swept a training-free implementation across fifteen input geometries. Results: Using SSL-ALPNet's configuration, no whole-cell decision at that grid can exceed 19.0% Dice on the 5-8 mm band, which holds 44.6% of nodules, compared with 63-85% on abdominal organs. The governing size is the slice's equal-area diameter, i.e., a median of 69% of the nominal value, which overstates the bound by 11.5 points. A lung mask used to erase rather than to locate destroys the lesion it should help find; hard masking removes more than half of 11.7% of the 180 nodules (95% CI 7.8-17.2). The swept implementation tracks the ceiling (r = 0.74 per episode), attaining 69% of the ceiling at the derived 32 mm tile compared with 8% at full-chest input; at a fixed cell size, it peaks at the encoder's training resolution. Conclusions: Much of the reported deficit is bounded by representation geometry rather than by modelling quality. We provide a lesion-preserving formulation and derive the tile size from measurement rather than via a chosen margin.