Self-supervised Shape Completion via Involution and Implicit Correspondences

TL;DR

This work tackles self-supervised 3D shape completion without complete shapes by formulating the completion function as an involution, $\\mathcal{G}\\circ\\mathcal{G}(X')=X'$, and by enforcing a canonical template space to supervise correspondences. It introduces a two-module architecture: a completion/up-sampling module $\\mathcal{G}$/$\\mathcal{U}$ and a template-based INR module $\\mathcal{T}$ that warps inputs into a common template via a deformation $D$ and predicts an unsigned distance field. Self-supervised losses, including the involution constraint, template-space consistency, and partial-shape reconstruction, are optimized via batch-wise alternation, enabling learning from partial data alone. Experiments on PartialUDF-Shapenet, PartialUDF-DFaust, and real scans (KITTI) show competitive completion quality and superior correspondences, approaching supervised performance in some cases and delivering robust performance on non-rigid shapes. The results highlight the practical impact of combining involutive completion with a deformation-based template prior for scalable, data-efficient 3D shape completion.

Abstract

3D shape completion is traditionally solved using supervised training or by distribution learning on complete shape examples. Recently self-supervised learning approaches that do not require any complete 3D shape examples have gained more interests. In this paper, we propose a non-adversarial self-supervised approach for the shape completion task. Our first finding is that completion problems can be formulated as an involutory function trivially, which implies a special constraint on the completion function G, such that G(G(X)) = X. Our second constraint on self-supervised shape completion relies on the fact that shape completion becomes easier to solve with correspondences and similarly, completion can simplify the correspondences problem. We formulate a consistency measure in the canonical space in order to supervise the completion function. We efficiently optimize the completion and correspondence modules using "freeze and alternate" strategy. The overall approach performs well for rigid shapes in a category as well as dynamic non-rigid shapes. We ablate our design choices and compare our solution against state-of-the-art methods, showing remarkable accuracy approaching supervised accuracy in some cases.

Figures (7)

• Figure 1: Architecture of our method. We show the detailed implementation of the completion module ($\mathcal{G}$ and $\mathcal{U}$), and the template-based INR module $\mathcal{T}$. The completion function $\mathcal{G}$ starts with partial input $X'$, where an encoder $\mathcal{E}$ is used to extract a shape code $c'$ and is fed to the decoder $G$ to produce $Y$. The involution is implemented by feeding $Y$ to $\mathcal{G}$ that should ideally result in the input partial points. The concatenated coarse but complete points $X_c$ go through upsampler $\mathcal{U}$ and generates detailed shape points $X$ and provides conditioning on $\mathcal{T}$. $\mathcal{L}$ denotes the losses applied on each module.
• Figure 2: Qualitative results of shape completion on Shapenet various categories, compared with SeedFormer zhou2022seedformer, cGan chen2019unpaired, ShapeInversion zhang2021unsupervised, P2C cui2023p2c, our method completes dense meshes.
• Figure 3: Qualitative results on DFaust. We show generated points (in red) from the generator (completion function) and the upsampler, and meshes compared with other methods.
• Figure 4: Qualitative results on KITTI dataset. Our method completes the partial data even when there are extremely few points available.
• Figure 5: Visualization results of ablation study on sub-modules with different settings.