TopoFuse: Topology-Aware Tri-Planar Fusion for 3D Cryo-Electron Tomography Segmentation

Automated segmentation of cryo-electron tomograms rou-tinely produces masks that are voxel-accurate but topologically broken:membranes fragment, organelles merge into one another and enclosedcavities collapse. Existing topology-aware losses reduce these violationsbut cannot eliminate them because topology is encouraged through gradi-ent pressure rather than structurally enforced. We introduce TopoFuse,which reframes topology as a differentiable projection operator rather thana loss penalty. At each forward pass, the projection operator ProjT (a PH-guided sparse edit) identifies the critical voxels responsible for topologicalviolations via bottleneck matching and applies sparse edits to satisfy aspecified topology target (diagram feature counts and lifetime budgets)for dimensions d ∈ {0, 2}. If the projection converges, the output satisfiesthose constraints on the downsampled grid (s = 2), when it does not, arepair certificate exposes this explicitly enabling downstream filtering.A topology prior head predicts the correction target directly from inputfeatures, removing any dependence on ground-truth topology at inference.Across three cryo-ET benchmarks, TopoFuse reduces Betti Number Errorby 54% over the strongest soft-loss baseline (p < 0.001), improves Diceby 4.6 pp and edits only 3.1% of voxels to achieve this. Code and SYNdataset are available at: https://github.com/rohitsalla/TopoFuse