Topology-Aware Differentiable Triangle-Soup Reconstruction via Persistent Homology

Differentiable triangle-soup reconstruction has a familiar blind spot: if the surface looks right under photometric and geometric metrics, it can still be topologically wrong. Collapsed loops, phantom handles, and punctured voids can all slip through with the same score as a correct mesh, which is a serious problem for any pipeline that needs structural fidelity rather than just visual similarity.

The new approach moves topology into the objective itself. It adds a differentiable persistence term that compares the evolving surface’s persistence diagram against a known target, with gradients flowing through a pair-frozen backward pass and a recruitment term to recover signal when a feature is missing. A single ratio parameter balances the topology term against the photometric gradient, so the method does not rely on a curriculum or per-shape hand tuning.

The practical result is a topology-specific loss that beats a norm-matched non-topological control at the same Chamfer distance. Reported gains are strongest for enclosed voids, where error drops by 4.0-7.9x, and for loops, where the method is about 2.3x better and avoids phantom handles entirely. The loss also composes with allocation priors, which means budget steering and topology correction can be used together instead of treated as competing fixes.

The evaluation is still synthetic and single-machine, with the target diagram known in advance, and real scans remain future work. Even so, the broader takeaway is useful for anyone building reconstruction or asset-processing tools: if topology matters, it likely needs to...