Topology-Aware Differentiable Triangle-Soup Reconstruction via Persistent Homology
2026-08-17 • Graphics
Graphics
AI summaryⓘ
The authors show that traditional methods to reconstruct 3D shapes from images often miss important topological features like loops or holes because standard losses focus only on geometry or color, not topology. They introduce a new loss term that directly measures the topology by comparing the shape's evolving features to a known target, enabling the model to learn topological correctness. Their approach outperforms previous methods on synthetic datasets without needing extra tuning and works well even with noise. However, this has only been tested on simulated data with known topology, not real scans yet.
differentiable reconstructiontriangle souptopologypersistent homologypersistence diagramsChamfer distancegradient optimizationloops and voidstopology-aware loss3D shape reconstruction
Authors
Viritphon Chongpermwattanapol, Nattapat Damnernyut, Pizzanu Kanongchaiyos
Abstract
Differentiable triangle-soup reconstruction inherits a limitation from its objective: photometric and geometric losses cannot measure topology, so a reconstruction with a collapsed loop or a punctured enclosed void can score exactly as well as a correct one (on Chamfer-equal probes the diagrams differ 35-40x in bottleneck distance). The standard implicit remedy -- steer *where* the resampler spends its budget -- does not repair this: in a controlled study, a topology-informed prior is largely matched by an equally wide random one, and no prior shape repairs loops. We therefore move topology into the objective: a differentiable persistence term compares the evolving surface's diagram, measured on live surface samples, to a fixed target; gradients flow through a pair-frozen backward re-expressing matched birth/death simplices as closed-form circumradii, plus a recruitment term restoring the gradient optimal matching provably lacks when a feature is missing; one ratio knob calibrates the loss against the photometric gradient, no curriculum needed. Every claim passes a channel-controlled verdict: the loss must beat a norm-matched *non-topological* control through the identical gradient channel, at Chamfer parity. Under that rule the loss is topology-specific for enclosed voids (4.0-7.9x lower error) and -- the class every allocation prior failed -- for loops (2.3x, zero phantom handles, while the control collapses one); loss and prior compose; component counts (H0) are a null result. The verdicts replicate without per-shape tuning on eight external genus-known meshes in two pre-registered groups (group means: loops 1.52x, voids 4.87x; the one non-pass is a no-headroom null), degrading gracefully under noise. All evidence is synthetic and single-machine, with the target diagram known in advance; real scans are future work. Prescription: correct topology in the loss, allocate wide, combine.