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G-FARS: Gradient-Field-based Auto-Regressive Sampling for 3D Part Grouping
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Introduces the 3D part grouping task and G-FARS, a score-based (gradient-field) auto-regressive sampler with an edge-convolution GNN that iteratively selects groups of parts from a mixed PartNet part set.
Problem
Given a mixed set of scattered 3D parts from an unknown number of shapes, find every possible grouping of parts that belongs to a shape, without knowing the number of groups in advance.
Approach
Learn the gradient of a conditional log-probability over part selection vectors with a fully connected edge-convolution GNN on PointNet part features (score-based SDE training), then auto-regressively sample groups with a predictor-corrector sampler, removing selected parts and repeating until none remain.
Key results
- G-FARS achieves chair F1 of 0.781 (single set average) and 0.768 (overall average), vs. 0.651 for GRU-Mask and 0.678 for Comp-Net.
- On Table, G-FARS F1 is 0.814 / 0.797 versus 0.712 / 0.685 for the best baseline Comp-Net; on Lamp, 0.73 / 0.711 versus 0.666 / 0.647.
- Ablation on Chair: removing the score-matching loss (w/o GF) drops F1 to 0.386 / 0.406; the predictor-corrector sampler outperforms Euler-Maruyama (0.781 vs 0.76 F1 at 500 steps).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use G-FARS instead of the strongest baseline | 3D part grouping · Chair | F1 Score: 0.678 / 0.651 -> 0.781 / 0.768 | Helped |
| use G-FARS instead of the strongest baseline | 3D part grouping · Table | F1 Score: 0.712 / 0.685 -> 0.814 / 0.797 | Helped |
| use G-FARS instead of the strongest baseline | 3D part grouping · Lamp | F1 Score: 0.666 / 0.647 -> 0.73 / 0.711 | Helped |
| add score-matching loss instead of Binary Cross Entropy (ablation) | G-FARS on Chair · Chair | F1 Score: 0.386 / 0.406 -> 0.781 / 0.768 | Helped |
| add graph neural network instead of MLP (ablation) | G-FARS on Chair · Chair | F1 Score: 0.512 / 0.495 -> 0.781 / 0.768 | Helped |
| use PC sampler instead of EM sampler (ablation) | G-FARS on Chair · Chair | F1 Score: 0.76 / 0.749 -> 0.781 / 0.768 | Helped |
| use PC sampler with 500 steps rather than 100 steps (ablation) | G-FARS on Chair · Chair | F1 Score: 0.6 / 0.582 -> 0.781 / 0.768 | Helped |
| increase PC sampler steps from 500 to 600 (ablation) | G-FARS on Chair · Chair | F1 Score: 0.781 / 0.768 -> 0.779 / 0.767 | Hurt |
Surprising findings
- Replacing the score-matching objective with binary cross-entropy causes a large drop in F1 (0.386), indicating the gradient-field formulation is critical.
- Model is reported to remove noisy parts from a chair set in a zero-shot manner.
Limitations
- Evaluation confined to virtual, synthetic PartNet mixtures; no real-world validation.
- No existing baselines for the new task, so comparisons use self-proposed alternatives.
- Absolute F1 remains moderate (around 0.78 on chairs).
Experimental setup
Datasets: PartNet
Benchmarks: PartNet mixed part sets (Chair, Table, Lamp)
Metrics: precision recall F1 score Jaccard similarity matching
Baselines: GRU-Mask Comp-Net G-FARS-CG G-FARS-R G-FARS-T
Builds on: score-based SDE modeling PointNet EdgeConv predictor-corrector sampler
Closest papers by meaning
- AutoGPart: Intermediate Supervision Search for Generalizable 3D Part Segmentation (CVPR 2022 · similarity 0.85)
- Learning to Group: A Bottom-Up Framework for 3D Part Discovery in Unseen Categories (ICLR 2020 · similarity 0.85)
- 3D Student Splatting and Scooping (CVPR 2025 · similarity 0.83)
- DiffAssemble: A Unified Graph-Diffusion Model for 2D and 3D Reassembly (CVPR 2024 · similarity 0.83)
- AutoPartGen: Autoregressive 3D Part Generation and Discovery (NeurIPS 2025 · similarity 0.82)
- Learning Partonomic 3D Reconstruction from Image Collections (CVPR 2025 · similarity 0.82)
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