# 3DIAS: 3D Shape Reconstruction with Implicit Algebraic Surfaces

arXiv: https://arxiv.org/abs/2108.08653 · HTML: https://mlsanity.com/paper/2108.08653/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 40 references that are in the map.
- First posted on arXiv 19 Aug 2021.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (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)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [End-to-end Recovery of Human Shape and Pose](https://mlsanity.com/paper/1712.06584/) (2017)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [PartNet: A Large-scale Benchmark for Fine-grained and Hierarchical Part-level 3D Object Understanding](https://mlsanity.com/paper/1812.02713/) (2018)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Learning Category-Specific Mesh Reconstruction from Image Collections](https://mlsanity.com/paper/1803.07549/) (2018)
- [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)
- [Volumetric and Multi-View CNNs for Object Classification on 3D Data](https://mlsanity.com/paper/1604.03265/) (2016)
- [Octree Generating Networks: Efficient Convolutional Architectures for High-resolution 3D Outputs](https://mlsanity.com/paper/1703.09438/) (2017)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [Learning a Predictable and Generative Vector Representation for Objects](https://mlsanity.com/paper/1603.08637/) (2016)
- [Generative and Discriminative Voxel Modeling with Convolutional Neural Networks](https://mlsanity.com/paper/1608.04236/) (2016)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [Hierarchical Surface Prediction for 3D Object Reconstruction](https://mlsanity.com/paper/1704.00710/) (2017)
- [BAE-NET: Branched Autoencoder for Shape Co-Segmentation](https://mlsanity.com/paper/1903.11228/) (2019)
- [Image-based 3D Object Reconstruction: State-of-the-Art and Trends in the Deep Learning Era](https://mlsanity.com/paper/1906.06543/) (2019)
- [Learning 3D Shape Completion under Weak Supervision](https://mlsanity.com/paper/1805.07290/) (2018)
- [Learning Representations and Generative Models for 3D Point Clouds](https://mlsanity.com/paper/1707.02392/) (2017)

## Built on by (most cited first, 17 of 17)

- [LucidDreamer: Domain-free Generation of 3D Gaussian Splatting Scenes](https://mlsanity.com/paper/2311.13384/) (2023)
- [SceneDreamer360: Text-Driven 3D-Consistent Scene Generation with Panoramic Gaussian Splatting](https://mlsanity.com/paper/2408.13711/) (2024)
- [Few 'Zero Level Set'-Shot Learning of Shape Signed Distance Functions in Feature Space](https://mlsanity.com/paper/2207.04161/) (2022)
- [Latent Partition Implicit with Surface Codes for 3D Representation](https://mlsanity.com/paper/2207.08631/) (2022)
- [Unsupervised Occupancy Learning from Sparse Point Cloud](https://mlsanity.com/paper/2404.02759/) (2024)
- [Iterative Superquadric Recomposition of 3D Objects from Multiple Views](https://mlsanity.com/paper/2309.02102/) (2023)
- [Mixing-Denoising Generalizable Occupancy Networks](https://mlsanity.com/paper/2311.12125/) (2023)
- [Robustifying Generalizable Implicit Shape Networks with a Tunable Non-Parametric Model](https://mlsanity.com/paper/2311.12967/) (2023)
- [Primitive-based 3D Human-Object Interaction Modelling and Programming](https://mlsanity.com/paper/2312.10714/) (2023)
- [Residual Primitive Fitting of 3D Shapes with SuperFrusta](https://mlsanity.com/paper/2512.09201/) (2025)
- [Primitive3D: 3D Object Dataset Synthesis from Randomly Assembled Primitives](https://mlsanity.com/paper/2205.12627/) (2022)
- [CNC-Net: Self-Supervised Learning for CNC Machining Operations](https://mlsanity.com/paper/2312.09925/) (2023)
- [Taylor3DNet: Fast 3D Shape Inference With Landmark Points Based Taylor Series](https://mlsanity.com/paper/2201.06845/) (2022)
- [LISR: Learning Linear 3D Implicit Surface Representation Using Compactly Supported Radial Basis Functions](https://mlsanity.com/paper/2402.07301/) (2024)
- [ESCT3D: Efficient and Selectively Controllable Text-Driven 3D Content Generation with Gaussian Splatting](https://mlsanity.com/paper/2504.10316/) (2025)
- [Electrostatics-Inspired Surface Reconstruction (EISR): Recovering 3D Shapes as a Superposition of Poisson's PDE Solutions](https://mlsanity.com/paper/2602.11642/) (2026)
- [Exact Quotients of Fresnel-Kummer Surfaces and Certified Biaxial Refraction](https://mlsanity.com/paper/2609.23249/) (2026)

## Abstract (arXiv)

3D Shape representation has substantial effects on 3D shape reconstruction. Primitive-based representations approximate a 3D shape mainly by a set of simple implicit primitives, but the low geometrical complexity of the primitives limits the shape resolution. Moreover, setting a sufficient number of primitives for an arbitrary shape is challenging. To overcome these issues, we propose a constrained implicit algebraic surface as the primitive with few learnable coefficients and higher geometrical complexities and a deep neural network to produce these primitives. Our experiments demonstrate the superiorities of our method in terms of representation power compared to the state-of-the-art methods in single RGB image 3D shape reconstruction. Furthermore, we show that our method can semantically learn segments of 3D shapes in an unsupervised manner. The code is publicly available from https://myavartanoo.github.io/3dias/ .