# Probabilistic Shape Completion by Estimating Canonical Factors with Hierarchical VAE

arXiv: https://arxiv.org/abs/2212.03370 · HTML: https://mlsanity.com/paper/2212.03370/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 57 references that are in the map.
- First posted on arXiv 6 Dec 2022.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [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)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [PoinTr: Diverse Point Cloud Completion with Geometry-Aware Transformers](https://mlsanity.com/paper/2108.08839/) (2021)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [AutoSDF: Shape Priors for 3D Completion, Reconstruction and Generation](https://mlsanity.com/paper/2203.09516/) (2022)
- [High-Fidelity Pluralistic Image Completion with Transformers](https://mlsanity.com/paper/2103.14031/) (2021)
- [ShapeFormer: Transformer-based Shape Completion via Sparse Representation](https://mlsanity.com/paper/2201.10326/) (2022)
- [PointGrow: Autoregressively Learned Point Cloud Generation with Self-Attention](https://mlsanity.com/paper/1810.05591/) (2018)
- [3DILG: Irregular Latent Grids for 3D Generative Modeling](https://mlsanity.com/paper/2205.13914/) (2022)
- [Unsupervised 3D Shape Completion through GAN Inversion](https://mlsanity.com/paper/2104.13366/) (2021)
- [Variational Autoencoder with Arbitrary Conditioning](https://mlsanity.com/paper/1806.02382/) (2018)
- [Unpaired Point Cloud Completion on Real Scans using Adversarial Training](https://mlsanity.com/paper/1904.00069/) (2019)
- [BLOCK: Bilinear Superdiagonal Fusion for Visual Question Answering and Visual Relationship Detection](https://mlsanity.com/paper/1902.00038/) (2019)

## Built on by (most cited first, 1 of 1)

- [Point Cloud Part Editing: Segmentation, Generation, Assembly, and Selection](https://mlsanity.com/paper/2312.11867/) (2023)

## Abstract (arXiv)

We propose a novel method for 3D shape completion from a partial observation of a point cloud. Existing methods either operate on a global latent code, which limits the expressiveness of their model, or autoregressively estimate the local features, which is highly computationally extensive. Instead, our method estimates the entire local feature field by a single feedforward network by formulating this problem as a tensor completion problem on the feature volume of the object. Due to the redundancy of local feature volumes, this tensor completion problem can be further reduced to estimating the canonical factors of the feature volume. A hierarchical variational autoencoder (VAE) with tiny MLPs is used to probabilistically estimate the canonical factors of the complete feature volume. The effectiveness of the proposed method is validated by comparing it with the state-of-the-art method quantitatively and qualitatively. Further ablation studies also show the need to adopt a hierarchical architecture to capture the multimodal distribution of possible shapes.