# Primitive-based Shape Abstraction via Nonparametric Bayesian Inference arXiv: https://arxiv.org/abs/2203.14714 ยท HTML: https://mlsanity.com/paper/2203.14714/ ## Key facts - Cited by 15 papers in the map (data through 14 Oct 2026). - Builds on 27 of its 50 references that are in the map. - First posted on arXiv 28 Mar 2022. ## Builds on (most cited first, 27 of 27) - [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) - [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016) - [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) - [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019) - [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020) - [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016) - [Learning Category-Specific Mesh Reconstruction from Image Collections](https://mlsanity.com/paper/1803.07549/) (2018) - [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019) - [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) - [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019) - [Deep Mesh Reconstruction from Single RGB Images via Topology Modification Networks](https://mlsanity.com/paper/1909.00321/) (2019) - [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021) - [Hierarchical Surface Prediction for 3D Object Reconstruction](https://mlsanity.com/paper/1704.00710/) (2017) - [DualSDF: Semantic Shape Manipulation using a Two-Level Representation](https://mlsanity.com/paper/2004.02869/) (2020) - [3D-PRNN: Generating Shape Primitives with Recurrent Neural Networks](https://mlsanity.com/paper/1708.01648/) (2017) - [Learning Unsupervised Hierarchical Part Decomposition of 3D Objects from a Single RGB Image](https://mlsanity.com/paper/2004.01176/) (2020) - [Unsupervised Learning of 3D Structure from Images](https://mlsanity.com/paper/1607.00662/) (2016) - [Im2Struct: Recovering 3D Shape Structure from a Single RGB Image](https://mlsanity.com/paper/1804.05469/) (2018) - [Unsupervised Learning for Cuboid Shape Abstraction via Joint Segmentation from Point Clouds](https://mlsanity.com/paper/2106.03437/) (2021) - [Robust and Accurate Superquadric Recovery: a Probabilistic Approach](https://mlsanity.com/paper/2111.14517/) (2021) - [Closed-Form Minkowski Sums of Convex Bodies with Smooth Positively Curved Boundaries](https://mlsanity.com/paper/2012.15461/) (2020) ## Built on by (most cited first, 15 of 15) - [Differentiable Blocks World: Qualitative 3D Decomposition by Rendering Primitives](https://mlsanity.com/paper/2307.05473/) (2023) - [Marching-Primitives: Shape Abstraction from Signed Distance Function](https://mlsanity.com/paper/2303.13190/) (2023) - [Iterative Superquadric Recomposition of 3D Objects from Multiple Views](https://mlsanity.com/paper/2309.02102/) (2023) - [Self-supervised Learning of Hybrid Part-aware 3D Representations of 2D Gaussians and Superquadrics](https://mlsanity.com/paper/2408.10789/) (2024) - [Light-SQ: Structure-aware Shape Abstraction with Superquadrics for Generated Meshes](https://mlsanity.com/paper/2509.24986/) (2025) - [Learnable Earth Parser: Discovering 3D Prototypes in Aerial Scans](https://mlsanity.com/paper/2304.09704/) (2023) - [SweepNet: Unsupervised Learning Shape Abstraction via Neural Sweepers](https://mlsanity.com/paper/2407.06305/) (2024) - [WIR3D: Visually-Informed and Geometry-Aware 3D Shape Abstraction](https://mlsanity.com/paper/2505.04813/) (2025) - [Aligning Instance-Semantic Sparse Representation towards Unsupervised Object Segmentation and Shape Abstraction with Repeatable Primitives](https://mlsanity.com/paper/2503.06947/) (2025) - [A Bayesian Approach Toward Robust Multidimensional Ellipsoid-Specific Fitting](https://mlsanity.com/paper/2407.19269/) (2024) - [Deep Polycuboid Fitting for Compact 3D Representation of Indoor Scenes](https://mlsanity.com/paper/2503.14912/) (2025) - [DualPrim: Compact 3D Reconstruction with Positive and Negative Primitives](https://mlsanity.com/paper/2603.16133/) (2026) - [D-Prism: Differentiable Primitives for Structured Dynamic Modeling](https://mlsanity.com/paper/2604.17082/) (2026) - [A Holistic Method for Superquadric Fitting Using Unsupervised Clustering Analysis](https://mlsanity.com/paper/2605.16779/) (2026) - [Organize Primitives into Semantic Parts: Reinforcement Reasoning for 3D Segmentation](https://mlsanity.com/paper/2610.04602/) (2026) ## Abstract (arXiv) 3D shape abstraction has drawn great interest over the years. Apart from low-level representations such as meshes and voxels, researchers also seek to semantically abstract complex objects with basic geometric primitives. Recent deep learning methods rely heavily on datasets, with limited generality to unseen categories. Furthermore, abstracting an object accurately yet with a small number of primitives still remains a challenge. In this paper, we propose a novel non-parametric Bayesian statistical method to infer an abstraction, consisting of an unknown number of geometric primitives, from a point cloud. We model the generation of points as observations sampled from an infinite mixture of Gaussian Superquadric Taper Models (GSTM). Our approach formulates the abstraction as a clustering problem, in which: 1) each point is assigned to a cluster via the Chinese Restaurant Process (CRP); 2) a primitive representation is optimized for each cluster, and 3) a merging post-process is incorporated to provide a concise representation. We conduct extensive experiments on two datasets. The results indicate that our method outperforms the state-of-the-art in terms of accuracy and is generalizable to various types of objects.