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

Automated segmentation of cryo-electron tomograms routinely produces masks that are voxel-accurate but topologically broken: membranes fragment, organelles merge into one another, and enclosed cavities collapse. Existing topology-aware losses reduce these violations but cannot eliminate them, because topology is encouraged through gradient pressure rather than structurally enforced. We introduce TopoFuse, which reframes topology as a differentiable projection operator rather than a loss penalty. At each forward pass, the projection operator $\mathrm{Proj}_T$ (a PH-guided sparse edit) identifies the critical voxels responsible for topological violations via bottleneck matching and applies sparse edits to satisfy a specified topology target (diagram feature counts and lifetime budgets) for dimensions $d \in \{0,2\}$. If the projection converges, the output satisfies those constraints on the downsampled grid ($s=2$); when it does not, a repair certificate exposes this explicitly, enabling downstream filtering. A topology prior head predicts the correction target directly from input features, removing any dependence on ground-truth topology at inference. Across three cryo-ET benchmarks, TopoFuse reduces Betti number error by 54% over the strongest soft-loss baseline ($p < 0.001$), improves Dice by 4.6 points, and edits only 3.1% of voxels to achieve this.