PartField-generated Supervision

• PartField-generated Supervision is a method that uses dense, continuous 3D feature fields to provide unsupervised, geometry-attuned part labels without fixed semantic taxonomies.
• It employs multi-modal training with both 2D and 3D data along with contrastive loss to ensure high cross-shape consistency and robust, hierarchical segmentation.
• The approach integrates into neural pipelines for CAD models, achieving fast feedforward inference and accurate part segmentation with impressive mIoU and segmentation consistency scores.

PartField-generated Supervision refers to a methodology in which dense, continuous 3D feature fields learned by the PartField model are used to provide fine-grained, geometry-aware part labels for 3D shapes. These labels are generated without relying on fixed semantic part taxonomies or curated manual annotations, allowing for robust, open-world segmentation of 3D shapes, and serve as supervisory signals for downstream tasks such as joint neural reconstruction and semantic segmentation. The approach is distinguished by its use of large-scale, multi-modal part proposals for training, feedforward network architecture, contrastive learning objectives, and high cross-shape part consistency. PartField-generated supervision has recently been integrated into state-of-the-art implicit reconstruction pipelines for CAD models, enabling accurate, geometry-aligned segmentation without the need for explicit semantic palettes.

1. Architectural Foundations of PartField-generated Supervision

PartField is centered on a feedforward network producing a continuous 3D feature field for an input shape. For a given 3D shape $S$ and point $p$, the model outputs a feature vector $f(p; S) \in \mathbb{R}^n$ such that the proximity between feature vectors reflects part membership. Unlike prior segmentation methods tied to part templates or text labels, PartField operates in a class-agnostic, open-world regime. The design eschews per-shape optimization and instead executes a single feedforward pass, encoding local and global part structure efficiently.

The feature field is realized using a network backbone that combines a PVCNN encoder, triplane projections, convolutional blocks, and a transformer for contextualization. High-resolution feature sampling allows downstream clustering algorithms (e.g., k-means or agglomerative techniques) to segment shapes into hierarchical parts purely by exploiting feature similarity.

2. Training Methodology and Contrastive Loss

Training of PartField employs large-scale part proposal distillation from both 2D and 3D data modalities:

• 2D supervision: Multi-view images of 3D shapes are segmented with 2D foundation models such as SAM2. Resulting 2D masks are projected into 3D, generating candidate part regions.
• 3D supervision: Annotated datasets (e.g., PartNet) provide explicit 3D part proposals and hierarchies.

Within each part proposal $P \subset S$, the model samples triplets: two positives $(p_1, p_2) \in P$ and a negative $p_3 \in S \setminus P$. The triplet contrastive loss is defined as:

$$\mathcal{L} = -\frac{1}{2} \left( \log \frac{\operatorname{sim}(f(p), f(p^+))}{\operatorname{sim}(f(p), f(p^+)) + \operatorname{sim}(f(p), f(p^-))} + \log \frac{\operatorname{sim}(f(p^+), f(p))}{\operatorname{sim}(f(p^+), f(p)) + \operatorname{sim}(f(p^+), f(p^-))} \right),$$

where $\operatorname{sim}$ denotes exponential cosine similarity with a learnable temperature. Hard negative sampling strategies are used to maximize discriminative power, with negatives chosen close in Euclidean or latent space. This approach enforces compactness of part features and sharp transitions at part boundaries.

3. Feature Field Generation, Clustering, and Applications

After training, PartField generates a continuous feature field $f(p; S)$, which can be sampled at arbitrary resolution over the shape:

• Hierarchical segmentation is achieved by clustering sampled features into part groups, with hierarchies naturally emerging from the feature structure.
• Co-segmentation and correspondence exploit the cross-shape consistency of the learned field, enabling parts with analogous geometric or functional roles to be matched across shapes.
• Interactive applications include point-based selection and propagation of part correspondence across a collection, as well as enabling functional map alignment.

A tabulation of application modes is provided below:

Application	Methodology	Output
Hierarchical Segmentation	Clustering of feature vectors	Part trees
Co-segmentation	Shared feature embedding among shapes	Grouped parts
Correspondence	Nearest-neighbor in feature space	Point/part matches

4. Integration in Downstream Neural Pipelines

PartField-generated supervision has been adopted as an automated label source for semantic segmentation in recent neural implicit reconstruction methods. In the FlatCAD-based neural SDF pipeline, a lightweight segmentation head is attached to a shared SIREN trunk. The per-face part labels output by PartField provide ground-truth supervision, enabling the network to learn part predictions aligned strictly with 3D geometry, without pre-set semantic categories.

The multi-objective loss function includes the segmentation loss:

$$L_{SEG} = \frac{1}{|X_{lab}|} \sum_{x \in X_{lab}} CE(\textrm{softmax}(g(x)), y(x)),$$

where $y(x)$ is the PartField-generated label.

Results demonstrate:

• High segmentation metrics with mIoU $\geq 0.96$ and accuracy $\geq 0.97$.
• Geometry-reconstruction metrics (Chamfer distance, normal consistency) remain unaffected by the addition of semantic segmentation.
• A segmentation consistency score quantifies neighborhood label smoothness, with results consistently $\sim 0.97$.

5. Comparative Advantages and Quantitative Performance

Compared with prior class-agnostic part segmentation frameworks, PartField yields:

• Up to 20% higher mean Intersection over Union (mIoU) on benchmarks such as PartObjaverse-Tiny and PartNetE, compared to the next-best method.
• Substantially increased inference speed (seconds per shape versus minutes-hours).
• Robustness to inconsistent or noisy part proposals, due to extensive and mixed 2D/3D supervision and hard negative sampling.

A table of key advantages:

Attribute	PartField	Prior Methods
Label Requirement	Unsupervised/mixed	Supervised/fixed
Inference Speed	Feedforward (seconds)	Per-shape (minutes+)
Label Consistency	Cross-shape, hierarchy	Varies

6. Limitations and Prospects for Future Work

The reliance on per-face labels generated from meshes of varying tessellation introduces imprecision at part boundaries, occasionally resulting in discontinuities on thin features or intricate junctions. Addressing these challenges may require:

• Boundary-aware training schemes.
• Higher-resolution or smoothed label derivations.
• Further utilization of geometric cues at interfaces.

Potential research directions include extension to scene-scale segmentation, leveraging the feature field as a universal 3D prior, and improved cross-shape alignment for large, heterogeneous datasets.

7. Broader Implications in 3D Shape Understanding

PartField-generated supervision operationalizes a scalable, flexible, and label-efficient approach to 3D part decomposition. By providing high-quality, geometry-attuned part annotations without the constraints of curated taxonomies, it enables practical advances in CAD model labeling, hierarchical assembly analysis, co-segmentation, and morphable part correspondences. This aligns with broader trends in self-supervised and programmatic supervision strategies, reducing reliance on human annotation while enhancing accuracy, consistency, and scalability in 3D vision and modeling pipelines (Liu et al., 15 Apr 2025, Fan et al., 4 Oct 2025).