Learning Convex Decomposition via Feature Fields

2026-03-10

AI Summary

This work proposes the first open-world, feedforward model for convex decomposition of 3D shapes—a long-standing challenge in geometry processing. By learning a continuous feature field and integrating self-supervised geometric optimization objectives, the method decomposes arbitrary 3D shapes—represented as meshes, CAD models, or Gaussian splats—into unions of convex parts without requiring manual annotations or assumptions about closed-category objects. The core innovations lie in geometric constraints derived directly from the definition of convexity, a feature-field clustering mechanism, and strong generalization across diverse shape representations. Experiments demonstrate that the approach consistently produces high-quality convex decompositions across multiple 3D representations and exhibits exceptional generalization capability on open-world objects.

Technology Category

• Computer Vision: 3D Computer Vision
• Search and Optimization: Non-convex Optimization
• Machine Learning: Unsupervised & Self-Supervised Learning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Large pretrained models with web data

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/

Problem

• convex decomposition
• 3D shapes
• collision detection
• feature fields
• open-world

Innovation

• convex decomposition
• feature fields
• self-supervised learning
• 3D shape representation
• open-world generalization