LatticeRank: Spacing-Ranked Consistency for Native-Grid 3D Medical Image Segmentation

Variable voxel spacing changes more than image resolution: it alters the discrete sampling lattice, tensor geometry, and anatomical evidence available to a 3D segmentation network. While conventional pipelines restore images to a canonical grid, direct-grid deployment requires the model itself to tolerate these changes. We observe that candidate grids are not exchangeable views -- a coarse grid removes more structural information than a mildly resampled one -- yet standard consistency objectives assign them equal influence. We therefore propose LatticeRank, a training-only framework that aligns candidate posteriors in physical space and allocates consistency supervision by voxel-spacing order: among endpoint-matched candidates, the auxiliary loss concentrates on the coarsest requested grid, while inference retains a single network forward with no candidate branch or ensemble. On MSD Task04, LatticeRank improves coarse-grid Extra Dice over mean consistency by 0.03436 across five seeds while meeting the prespecified reference-grid noninferiority criterion. A controlled ladder shows that grid exposure provides the largest recovery, posterior consistency adds a second gain, and spacing-ranked allocation yields the strongest direct-grid result; requested spacing thus provides a simple, model-independent ordering signal for direct-grid consistency learning.