# RIM-Net: Recursive Implicit Fields for Unsupervised Learning of Hierarchical Shape Structures

arXiv: https://arxiv.org/abs/2201.12763 · HTML: https://mlsanity.com/paper/2201.12763/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 30 Jan 2022.

## Builds on (most cited first, 20 of 20)

- [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)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [3D Point Capsule Networks](https://mlsanity.com/paper/1812.10775/) (2018)
- [BAE-NET: Branched Autoencoder for Shape Co-Segmentation](https://mlsanity.com/paper/1903.11228/) (2019)
- [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)
- [3D Shape Segmentation with Projective Convolutional Networks](https://mlsanity.com/paper/1612.02808/) (2016)
- [Im2Struct: Recovering 3D Shape Structure from a Single RGB Image](https://mlsanity.com/paper/1804.05469/) (2018)
- [PartNet: A Recursive Part Decomposition Network for Fine-grained and Hierarchical Shape Segmentation](https://mlsanity.com/paper/1903.00709/) (2019)
- [Unsupervised Learning for Cuboid Shape Abstraction via Joint Segmentation from Point Clouds](https://mlsanity.com/paper/2106.03437/) (2021)
- [Tags2Parts: Discovering Semantic Regions from Shape Tags](https://mlsanity.com/paper/1708.06673/) (2017)

## Built on by (most cited first, 19 of 19)

- [3D Part Segmentation via Geometric Aggregation of 2D Visual Features](https://mlsanity.com/paper/2412.04247/) (2024)
- [Iterative Superquadric Recomposition of 3D Objects from Multiple Views](https://mlsanity.com/paper/2309.02102/) (2023)
- [DPF-Net: Combining Explicit Shape Priors in Deformable Primitive Field for Unsupervised Structural Reconstruction of 3D Objects](https://mlsanity.com/paper/2308.13225/) (2023)
- [PartSDF: Part-Based Implicit Neural Representation for Composite 3D Shape Parametrization and Optimization](https://mlsanity.com/paper/2502.12985/) (2025)
- [DiViNeT: 3D Reconstruction from Disparate Views via Neural Template Regularization](https://mlsanity.com/paper/2306.04699/) (2023)
- [DAE-Net: Deforming Auto-Encoder for fine-grained shape co-segmentation](https://mlsanity.com/paper/2311.13125/) (2023)
- [ArcPro: Architectural Programs for Structured 3D Abstraction of Sparse Points](https://mlsanity.com/paper/2503.02745/) (2025)
- [DPA-Net: Structured 3D Abstraction from Sparse Views via Differentiable Primitive Assembly](https://mlsanity.com/paper/2404.00875/) (2024)
- [HAL3D: Hierarchical Active Learning for Fine-Grained 3D Part Labeling](https://mlsanity.com/paper/2301.10460/) (2023)
- [Semantic-Aware Implicit Template Learning via Part Deformation Consistency](https://mlsanity.com/paper/2308.11916/) (2023)
- [Graph Classification via Discriminative Edge Feature Learning](https://mlsanity.com/paper/2210.02060/) (2022)
- [Split, Merge, and Refine: Fitting Tight Bounding Boxes via Over-Segmentation and Iterative Search](https://mlsanity.com/paper/2304.04336/) (2023)
- [Tree-Structured Shading Decomposition](https://mlsanity.com/paper/2309.07122/) (2023)
- [Aligning Instance-Semantic Sparse Representation towards Unsupervised Object Segmentation and Shape Abstraction with Repeatable Primitives](https://mlsanity.com/paper/2503.06947/) (2025)
- [BoxSplitGen: A Generative Model for 3D Part Bounding Boxes in Varying Granularity](https://mlsanity.com/paper/2602.20666/) (2026)
- [Diverse Part Synthesis for 3D Shape Creation](https://mlsanity.com/paper/2401.09384/) (2024)
- [SAR2Struct: Extracting 3D Semantic Structural Representation of Aircraft Targets from Single-View SAR Image](https://mlsanity.com/paper/2506.06757/) (2025)
- [Hierarchical Transformers for Unsupervised 3D Shape Abstraction](https://mlsanity.com/paper/2510.27088/) (2025)
- [Organize Primitives into Semantic Parts: Reinforcement Reasoning for 3D Segmentation](https://mlsanity.com/paper/2610.04602/) (2026)

## Abstract (arXiv)

We introduce RIM-Net, a neural network which learns recursive implicit fields for unsupervised inference of hierarchical shape structures. Our network recursively decomposes an input 3D shape into two parts, resulting in a binary tree hierarchy. Each level of the tree corresponds to an assembly of shape parts, represented as implicit functions, to reconstruct the input shape. At each node of the tree, simultaneous feature decoding and shape decomposition are carried out by their respective feature and part decoders, with weight sharing across the same hierarchy level. As an implicit field decoder, the part decoder is designed to decompose a sub-shape, via a two-way branched reconstruction, where each branch predicts a set of parameters defining a Gaussian to serve as a local point distribution for shape reconstruction. With reconstruction losses accounted for at each hierarchy level and a decomposition loss at each node, our network training does not require any ground-truth segmentations, let alone hierarchies. Through extensive experiments and comparisons to state-of-the-art alternatives, we demonstrate the quality, consistency, and interpretability of hierarchical structural inference by RIM-Net.