Learning Convex Decomposition via Feature Fields

Yuezhi Yang; Qixing Huang; Mikaela Angelina Uy; Nicholas Sharp

cs.CVMar 10, 2026

Learning Convex Decomposition via Feature Fields

Authors: Yuezhi Yang, Qixing Huang, Mikaela Angelina Uy, Nicholas Sharp

Organizations: NVIDIA · The University of Texas at Austin

Abstract

This work proposes a new formulation to the long-standing problem of convex decomposition through learning feature fields, enabling the first feed-forward model for open-world convex decomposition. Our method produces high-quality decompositions of 3D shapes into a union of convex bodies, which are essential to accelerate collision detection in physical simulation, amongst many other applications. The key insight is to adopt a feature learning approach and learn a continuous feature field that can later be clustered to yield a good convex decomposition via our self-supervised, purely-geometric objective derived from the classical definition of convexity. Our formulation can be used for single shape optimization, but more importantly, feature prediction unlocks scalable, self-supervised learning on large datasets resulting in the first learned open-world model for convex decomposition. Experiments show that our decompositions are higher-quality than alternatives and generalize across open-world objects as well as across representations to meshes, CAD models, and even Gaussian splats. https://research.nvidia.com/labs/sil/projects/learning-convex-decomp/

Figures & tables

Figure 1: Our method takes an input shape ( top ), infers features from an open-world model learned with our new self-supervised geometric loss ( middle ), and clusters those features to fit the shape with a collection of tight convex bounding proxies ( bottom ).

Figure 2: By adjusting the clustering threshold, our method can generate decompositions at varying granularity, all from the same feature field.

Figure 3: An overview of our convex decomposition pipeline. We train a feedforward model that takes a point-sampled 3D shape as input and predicts a feature field represented defined over the object. At training time, these features are fit with a self-supervised geometric objective derived from the definition of convexity. At inference time, the features are clustered to split the shape into components, and the convex hull of each component becomes the decomposition. Note that feature colors are visualized by running PCA on the feature field.

Figure 4: Contrastive training triplets are formed by a source point, a positive pair generated by casting a ray in a random inward direction ( left ), and a negative pair rejection-sampled from all points on the surface weighted to prefer nearby points ( right ).

Figure 5: Left: Visualization of the learned feature field during our single-shape optimization, shown at different optimization stages. Right: Feature fields produced directly by our feed-forward model.

Figure 6: A hierarchical decomposition tree from our algorithm.

Figure 7: Quantitative comparison with CoACD and VHACD on the VHACD dataset under different granularity.

Figure 8: Qualitative results against the baselines.

	VHCD Dataset			PartObjaverse-Tiny			ShapeNet
	# comp.	concavity	recon.	# comp.	concavity	recon.	# comp.	concavity	recon.
VHCD	13.39	0.1176	0.0213	21.94	0.1800	0.0318	14.73	0.1155	0.0201
COACD	14.47	0.1095	0.0321	23.63	0.1388	0.0321	13.02	0.0746	0.0172
BSP-Net (ShapeNet)	12.90	0.2249	0.1227	12.33	0.2593	0.1258	21.58	0.2107	0.0273
BSP-Net (Objaverse)	22.26	0.1857	0.0297	21.44	0.1964	0.0315	16.15	0.1592	0.0273
Cvx-Net (ShapeNet)	50.00	0.4673	0.0814	50.00	0.5079	0.0808	50.00	0.1795	0.0234

Table 1: Quantitative comparison across three datasets. #comp. denotes the number of convex components, and recon. denotes reconstruction accuracy measured using Chamfer distance. For all metrics, lower

\downarrow

means better.

	VHCD Dataset			Objaverse-Tiny
	#comp	conc.	recon.	#comp	conc.	recon.
- Hard-neg	12.88	0.0993	0.0186	21.60	0.1293	0.0268
- Hemis-Pos	13.08	0.0999	0.0219	23.27	0.1286	0.0263
- Recur. Clus.	12.25	0.1292	0.0191	25.44	0.1375	0.0288
Single opt.	12.40	0.1134	0.0198	22.35	0.1300	0.0266
Ours	11.90	0.0973	0.0180	21.18	0.1257	0.0254

Table 2: Quantitative ablation on components of our approach.

Figure 9: Convex decompositions are used to accelerate collision handling in physical simulations, shown here on rigid bodies, decomposed with our method and simulated under gravity in the Newton engine [ 38 ] .

Figure 10: Our model can take different modalities as input, including CAD models, 3D scans, and 3D Gaussian splats, and perform convex decomposition.

Figure 11: Our geometric objective produces convex-aware features for accurate decomposition (top). PartField instead yields nearly uniform features on flat regions. For example, the L-shaped surface appears almost entirely red—resulting in inferior decomposition (bottom). Feature colors are visualized by principle component analysis on the feature field.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

	VHACD	CoACD	CVX	BSP	Ours
time (s)	16.11	25.86	1.46	1.02	13.32
memory (GB)	0.5	5.5	1.78	1.38	2.61
GPU memory (GB)	-	-	2.08	1.65	3.61
model size (Mparams)	-	-	44	39	106

Appendix

Table 3: Per-shape computation cost on VHACD dataset

	VHCD Dataset			Objaverse-Tiny
	#comp	conc.	recon.	#comp	conc.	recon.
Alter. objective	15.24	0.1243	0.0260	27.36	0.1653	0.0303
Ours	11.90	0.0973	0.0180	21.18	0.1257	0.0254

Appendix

Table 4: Quantitative ablation on alternative training objectives.

I2CD: Direct Image-to-Convex Decomposition for Simulation-Ready Collision Geometry
Oct 2, 2026Qian Wang, Liam Merz Hoffmeister, Brian Scassellati +1
Department of Computer Science, Yale University
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Oct 2, 2026J/K move · Enter open · S save

I2CD: Direct Image-to-Convex Decomposition for Simulation-Ready Collision Geometry

Qian Wang, Liam Merz Hoffmeister, Brian Scassellati, Daniel Rakita

Department of Computer Science, Yale University

Open paper AskPDF arXiv

Physics simulators and motion planners require convex collision geometry, yet image-to-3D generative models output dense, frequently non-manifold visual meshes. Bridging the two today takes a slow, brittle reconstruct-then-decompose pipeline of repair, decimation, and approximate convex decomposition. We present I2CD, which predicts a convex decomposition directly from a single RGB image. Rather than train a new image-to-3D model, I2CD freezes the pretrained Hunyuan3D-2 image-conditioned diffusion transformer and shape decoder and trains only a lightweight cross-attention head (38M parameters, under ten GPU-hours) whose learned "convex-slot" tokens emit the halfplane parameters of

K

convex polytopes. The output is compact, convex by construction, and loads into physics engines without any post-processing, in

{\sim}0.5

s per image. On

227

held-out OmniObject3D and Google Scanned Objects instances, I2CD attains the highest volumetric IoU among eight reconstruct-then-decompose pipelines while running

6

37\times

faster end-to-end. In a cross-simulator study in MuJoCo, PyBullet, Genesis, and Isaac Sim, every engine uses I2CD geometry as delivered, whereas raw generated meshes "load" everywhere but are silently replaced by a different collision shape in most cases or need seconds to minutes of per-object preprocessing. On a physical xArm7, I2CD produces planner-ready geometry for a

20

-object cluttered scene in

11

s versus

328

s for the strongest baseline, at comparable pick-and-place execution success (

85

vs.

90

100

trials).

Abstract

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