# Self-supervised Shape Completion via Involution and Implicit Correspondences

arXiv: https://arxiv.org/abs/2409.15939 · HTML: https://mlsanity.com/paper/2409.15939/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 52 references that are in the map.
- First posted on arXiv 24 Sep 2024.

## Builds on (most cited first, 30 of 37)

- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [PartNet: A Large-scale Benchmark for Fine-grained and Hierarchical Part-level 3D Object Understanding](https://mlsanity.com/paper/1812.02713/) (2018)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [PoinTr: Diverse Point Cloud Completion with Geometry-Aware Transformers](https://mlsanity.com/paper/2108.08839/) (2021)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [GRNet: Gridding Residual Network for Dense Point Cloud Completion](https://mlsanity.com/paper/2006.03761/) (2020)
- [SnowflakeNet: Point Cloud Completion by Snowflake Point Deconvolution with Skip-Transformer](https://mlsanity.com/paper/2108.04444/) (2021)
- [PF-Net: Point Fractal Network for 3D Point Cloud Completion](https://mlsanity.com/paper/2003.00410/) (2020)
- [Morphing and Sampling Network for Dense Point Cloud Completion](https://mlsanity.com/paper/1912.00280/) (2019)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [Point Cloud Completion by Skip-attention Network with Hierarchical Folding](https://mlsanity.com/paper/2005.03871/) (2020)
- [Variational Relational Point Completion Network](https://mlsanity.com/paper/2104.10154/) (2021)
- [PMP-Net: Point Cloud Completion by Learning Multi-step Point Moving Paths](https://mlsanity.com/paper/2012.03408/) (2020)
- [Deep Implicit Templates for 3D Shape Representation](https://mlsanity.com/paper/2011.14565/) (2020)
- [SeedFormer: Patch Seeds based Point Cloud Completion with Upsample Transformer](https://mlsanity.com/paper/2207.10315/) (2022)
- [MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks](https://mlsanity.com/paper/2111.14549/) (2021)
- [Detail Preserved Point Cloud Completion via Separated Feature Aggregation](https://mlsanity.com/paper/2007.02374/) (2020)
- [Unsupervised 3D Shape Completion through GAN Inversion](https://mlsanity.com/paper/2104.13366/) (2021)
- [Unpaired Point Cloud Completion on Real Scans using Adversarial Training](https://mlsanity.com/paper/1904.00069/) (2019)
- [Multimodal Shape Completion via Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2003.07717/) (2020)
- [CaDeX: Learning Canonical Deformation Coordinate Space for Dynamic Surface Representation via Neural Homeomorphism](https://mlsanity.com/paper/2203.16529/) (2022)
- [Cycle4Completion: Unpaired Point Cloud Completion using Cycle Transformation with Missing Region Coding](https://mlsanity.com/paper/2103.07838/) (2021)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)

## Built on by (most cited first, 2 of 2)

- [LaS-Comp: Zero-shot 3D Completion with Latent-Spatial Consistency](https://mlsanity.com/paper/2602.18735/) (2026)
- [SGSoft: Learning Fused Semantic-Geometric Features for 3D Shape Correspondence via Template-Guided Soft Signals](https://mlsanity.com/paper/2605.18039/) (2026)

## Abstract (arXiv)

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.