Metric Positional Encoding in Transformer-Based 3D Medical Image Segmentation Under Controlled Spacing Changes

In 3D computed tomography segmentation, differences in voxel spacing mean that equal separations on the voxel grid correspond to different physical distances. Many Transformers incorporate positional encodings because self-attention does not explicitly represent position. However, index-based encodings do not express these distances. Whether metric coordinates improve performance or the response to resampling remains unclear. We evaluated this effect using a factorial UNETR design that combined index or physical coordinates with additive Fourier encoding or 3D RoPE. In KiTS23, we evaluated 391 patients across three folds; 117 were resampled to inter-slice spacings of 3, 4, and 5 mm. Control conditions varied the supplied spacing without altering the image. We repeated the RoPE comparison after training the models from scratch on AMOS22-CT. Among the 117 eligible KiTS23 cases, the metric variants responded to the supplied spacing, but no average advantage in Surface Dice change after resampling was demonstrated (contrast: −0.0029; 95% CI: −0.0104 to 0.0043). In 38 eligible AMOS22-CT cases, metric RoPE maintained higher absolute Surface Dice than index-based RoPE, although its advantage decreased from 0.0512 at the original spacing to 0.0216 at 5 mm. The change in Surface Dice from the original-spacing condition was less favorable for metric RoPE (contrast: −0.0241; 95% CI: −0.0296 to −0.0186). For the evaluated models, metric coordinates did not demonstrate a more favorable response to retrospective resampling, despite sensitivity to supplied spacing and higher absolute Surface Dice in AMOS22-CT. The 95% confidence intervals quantify uncertainty due to patient sampling conditional on the trained models; they do not capture variability across training runs.