# Adaptive Local Basis Functions for Shape Completion

arXiv: https://arxiv.org/abs/2307.08348 · HTML: https://mlsanity.com/paper/2307.08348/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 59 references that are in the map.
- First posted on arXiv 17 Jul 2023.

## Builds on (most cited first, 30 of 49)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [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)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [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)
- [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)
- [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)
- [ShapeFormer: Transformer-based Shape Completion via Sparse Representation](https://mlsanity.com/paper/2201.10326/) (2022)
- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)
- [3DILG: Irregular Latent Grids for 3D Generative Modeling](https://mlsanity.com/paper/2205.13914/) (2022)

## Built on by (most cited first, 4 of 4)

- [Explicitly Guided Information Interaction Network for Cross-modal Point Cloud Completion](https://mlsanity.com/paper/2407.02887/) (2024)
- [Neural Garment Dynamics via Manifold-Aware Transformers](https://mlsanity.com/paper/2407.06101/) (2024)
- [A Lightweight UDF Learning Framework for 3D Reconstruction Based on Local Shape Functions](https://mlsanity.com/paper/2407.01330/) (2024)
- [Fast Medical Shape Reconstruction via Meta-learned Implicit Neural Representations](https://mlsanity.com/paper/2409.07100/) (2024)

## Abstract (arXiv)

In this paper, we focus on the task of 3D shape completion from partial point clouds using deep implicit functions. Existing methods seek to use voxelized basis functions or the ones from a certain family of functions (e.g., Gaussians), which leads to high computational costs or limited shape expressivity. On the contrary, our method employs adaptive local basis functions, which are learned end-to-end and not restricted in certain forms. Based on those basis functions, a local-to-local shape completion framework is presented. Our algorithm learns sparse parameterization with a small number of basis functions while preserving local geometric details during completion. Quantitative and qualitative experiments demonstrate that our method outperforms the state-of-the-art methods in shape completion, detail preservation, generalization to unseen geometries, and computational cost. Code and data are at https://github.com/yinghdb/Adaptive-Local-Basis-Functions.