# Marching-Primitives: Shape Abstraction from Signed Distance Function

arXiv: https://arxiv.org/abs/2303.13190 · HTML: https://mlsanity.com/paper/2303.13190/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 51 references that are in the map.
- First posted on arXiv 23 Mar 2023.

## Builds on (most cited first, 26 of 26)

- [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)
- [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)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [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)
- [ScanComplete: Large-Scale Scene Completion and Semantic Segmentation for 3D Scans](https://mlsanity.com/paper/1712.10215/) (2017)
- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)
- [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)
- [Im2Struct: Recovering 3D Shape Structure from a Single RGB Image](https://mlsanity.com/paper/1804.05469/) (2018)
- [RoutedFusion: Learning Real-time Depth Map Fusion](https://mlsanity.com/paper/2001.04388/) (2020)
- [Unsupervised Learning for Cuboid Shape Abstraction via Joint Segmentation from Point Clouds](https://mlsanity.com/paper/2106.03437/) (2021)
- [Deep Parametric Shape Predictions using Distance Fields](https://mlsanity.com/paper/1904.08921/) (2019)
- [GenSDF: Two-Stage Learning of Generalizable Signed Distance Functions](https://mlsanity.com/paper/2206.02780/) (2022)
- [Robust and Accurate Superquadric Recovery: a Probabilistic Approach](https://mlsanity.com/paper/2111.14517/) (2021)
- [PatchComplete: Learning Multi-Resolution Patch Priors for 3D Shape Completion on Unseen Categories](https://mlsanity.com/paper/2206.04916/) (2022)
- [Neural Star Domain as Primitive Representation](https://mlsanity.com/paper/2010.11248/) (2020)
- [Primitive-based Shape Abstraction via Nonparametric Bayesian Inference](https://mlsanity.com/paper/2203.14714/) (2022)
- [PSDF Fusion: Probabilistic Signed Distance Function for On-the-fly 3D Data Fusion and Scene Reconstruction](https://mlsanity.com/paper/1807.11034/) (2018)
- [Efficient Path Planning in Narrow Passages for Robots with Ellipsoidal Components](https://mlsanity.com/paper/2104.04658/) (2021)
- [PriFit: Learning to Fit Primitives Improves Few Shot Point Cloud Segmentation](https://mlsanity.com/paper/2112.13942/) (2021)
- [HybridSDF: Combining Deep Implicit Shapes and Geometric Primitives for 3D Shape Representation and Manipulation](https://mlsanity.com/paper/2109.10767/) (2021)

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

- [SuperDec: 3D Scene Decomposition with Superquadric Primitives](https://mlsanity.com/paper/2504.00992/) (2025)
- [CADTalk: An Algorithm and Benchmark for Semantic Commenting of CAD Programs](https://mlsanity.com/paper/2311.16703/) (2023)
- [PrimitiveAnything: Human-Crafted 3D Primitive Assembly Generation with Auto-Regressive Transformer](https://mlsanity.com/paper/2505.04622/) (2025)
- [Light-SQ: Structure-aware Shape Abstraction with Superquadrics for Generated Meshes](https://mlsanity.com/paper/2509.24986/) (2025)
- [Implicit-ARAP: Efficient Handle-Guided Neural Field Deformation via Local Patch Meshing](https://mlsanity.com/paper/2405.12895/) (2024)
- [SweepNet: Unsupervised Learning Shape Abstraction via Neural Sweepers](https://mlsanity.com/paper/2407.06305/) (2024)
- [Residual Primitive Fitting of 3D Shapes with SuperFrusta](https://mlsanity.com/paper/2512.09201/) (2025)
- [WIR3D: Visually-Informed and Geometry-Aware 3D Shape Abstraction](https://mlsanity.com/paper/2505.04813/) (2025)
- [SuperFlex: Deformable Superquadrics for Point Cloud Decomposition](https://mlsanity.com/paper/2607.01015/) (2026)
- [Learning Convex Decomposition via Feature Fields](https://mlsanity.com/paper/2603.09285/) (2026)
- [Articulation in Prime: Primitive-Based Articulated Object Understanding from a Single Casual Video](https://mlsanity.com/paper/2605.18645/) (2026)
- [SAR2Struct: Extracting 3D Semantic Structural Representation of Aircraft Targets from Single-View SAR Image](https://mlsanity.com/paper/2506.06757/) (2025)
- [A 3D Generation Framework from Cross Modality to Parameterized Primitive](https://mlsanity.com/paper/2510.08656/) (2025)
- [DualPrim: Compact 3D Reconstruction with Positive and Negative Primitives](https://mlsanity.com/paper/2603.16133/) (2026)
- [Rethinking 3D Shape Generation: Diffusion over Superquadrics](https://mlsanity.com/paper/2606.08957/) (2026)
- [Prompting Image Generators for Training-free Primitive Shape Abstraction](https://mlsanity.com/paper/2607.05568/) (2026)
- [Hi-TOPS: Hierarchical Topology-aware Scoring Prior for 3D Part Decomposition](https://mlsanity.com/paper/2608.00767/) (2026)
- [PART: Learning 3D Part Assembly and Retrieval with Transformers](https://mlsanity.com/paper/2609.19872/) (2026)
- [Organize Primitives into Semantic Parts: Reinforcement Reasoning for 3D Segmentation](https://mlsanity.com/paper/2610.04602/) (2026)

## Abstract (arXiv)

Representing complex objects with basic geometric primitives has long been a topic in computer vision. Primitive-based representations have the merits of compactness and computational efficiency in higher-level tasks such as physics simulation, collision checking, and robotic manipulation. Unlike previous works which extract polygonal meshes from a signed distance function (SDF), in this paper, we present a novel method, named Marching-Primitives, to obtain a primitive-based abstraction directly from an SDF. Our method grows geometric primitives (such as superquadrics) iteratively by analyzing the connectivity of voxels while marching at different levels of signed distance. For each valid connected volume of interest, we march on the scope of voxels from which a primitive is able to be extracted in a probabilistic sense and simultaneously solve for the parameters of the primitive to capture the underlying local geometry. We evaluate the performance of our method on both synthetic and real-world datasets. The results show that the proposed method outperforms the state-of-the-art in terms of accuracy, and is directly generalizable among different categories and scales. The code is open-sourced at https://github.com/ChirikjianLab/Marching-Primitives.git.