Sparse2Geo: Prediction-Derived Geometry for Sparsely Supervised Segmentation and Regional Quality Assessment in Volume Electron Microscopy

Volume electron microscopy (vEM) enables nanometer-scale three-dimensional (3D) imaging of cellular ultrastructure, but semantic segmentation remains annotation-intensive. Sparse supervision reduces annotation cost, yet supervision confined to sparsely sampled locations provides limited constraints on object extent, boundaries, and 3D structure. Signed distance fields (SDFs) continuously encode object interior, exterior, and distance to the boundary, but are difficult to construct directly from sparse labels. Regional segmentation quality also remains difficult to assess without ground truth. To address both challenges, we introduce Sparse2Geo, a unified framework that exploits prediction-derived geometry for both sparsely supervised segmentation and regional quality assessment. In Stage I, Sparse2Geo constructs a teacher SDF from 3D consensus geometry aggregated from fixed full-volume predictions of an initial sparsely supervised model, providing geometric and boundary-aware supervision without additional dense semantic targets. In Stage II, local predictions are re-encoded as normalized local SDFs and combined with aligned raw volumetric patches to estimate regional segmentation quality without ground truth at inference. Our experiments use volumes from BetaSeg and UroCell, two public vEM datasets spanning mouse pancreatic $\beta$ cells and urinary bladder urothelial cells, comprising approximately 2.32 billion and 67 million voxels, respectively. Sparse2Geo achieves the highest Macro Dice among the compared segmentation methods (90.63% and 71.44%), improving over $ϵ$-Seg by 4.13 and 15.33 percentage points, respectively. For regional quality assessment, Sparse2Geo achieves the lowest Macro MAE on BetaSeg, reducing it by 12.3% relative to the best adapted external baseline, while incorporating local SDF geometry reduces Macro MAE by 35.1% relative to Raw-only on UroCell.