Residual Primitive Fitting of 3D Shapes with SuperFrusta

2025-12-09

AI Summary

This paper addresses the longstanding challenge in 3D shape reconstruction of simultaneously achieving high fidelity and structural simplicity. We propose a differentiable, editable analytic primitive-based modeling framework. Our key contributions are: (1) the SuperFrustum—a novel differentiable analytic primitive parameterized by only eight scalars, capable of representing both bending and tapering deformations; and (2) ResFit—an unsupervised iterative fitting algorithm that performs joint global-local optimization in signed distance function (SDF) space via residual-driven progressive decomposition. Evaluated on multiple 3D benchmarks, our method surpasses state-of-the-art approaches by over 9 percentage points in IoU while reducing the number of primitives by nearly 50%. To our knowledge, this is the first method to achieve compact representation, high reconstruction accuracy, and strong editability simultaneously—establishing a Pareto-optimal trade-off between fidelity and conciseness.

Technology Category

• Computer Vision: 3D Computer Vision
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We introduce a framework for converting 3D shapes into compact and editable assemblies of analytic primitives, directly addressing the persistent trade-off between reconstruction fidelity and parsimony. Our approach combines two key contributions: a novel primitive, termed SuperFrustum, and an iterative fiting algorithm, Residual Primitive Fitting (ResFit). SuperFrustum is an analytical primitive that is simultaneously (1) expressive, being able to model various common solids such as cylinders, spheres, cones & their tapered and bent forms, (2) editable, being compactly parameterized with 8 parameters, and (3) optimizable, with a sign distance field differentiable w.r.t. its parameters almost everywhere. ResFit is an unsupervised procedure that interleaves global shape analysis with local optimization, iteratively fitting primitives to the unexplained residual of a shape to discover a parsimonious yet accurate decompositions for each input shape. On diverse 3D benchmarks, our method achieves state-of-the-art results, improving IoU by over 9 points while using nearly half as many primitives as prior work. The resulting assemblies bridge the gap between dense 3D data and human-controllable design, producing high-fidelity and editable shape programs.

Problem

• Converts 3D shapes into compact editable analytic primitive assemblies
• Addresses trade-off between reconstruction fidelity and parsimony
• Bridges gap between dense 3D data and human-controllable design

Innovation

• SuperFrustum primitive for expressive, editable 3D modeling
• ResFit algorithm iteratively fits primitives to shape residuals
• Combines global analysis and local optimization for parsimonious decomposition