Learning Fine-to-Coarse Cuboid Shape Abstraction

2025-02-03

AI Summary

This paper addresses geometric primitive redundancy and semantic inconsistency in 3D shape structural modeling by proposing an unsupervised coarse-to-fine cuboid abstraction method. Starting from a dense initial cuboid representation, our approach progressively aggregates cuboids into a small set of semantically consistent, coarse-grained parts via differentiable cuboid parameterization and a hierarchical simplification architecture. We introduce a novel progressive redundancy penalization loss, jointly optimized with surface approximation and volume preservation constraints, to enforce structural consistency across shapes. Evaluated on both man-made object and human-shaped datasets, our method significantly outperforms existing cuboid abstraction approaches in reconstruction accuracy, part conciseness, and structural plausibility. Moreover, it consistently enhances downstream tasks—including shape clustering, retrieval, and local symmetry detection—demonstrating improved generalizability and semantic coherence of the learned structural representations.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Structured Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

The abstraction of 3D objects with simple geometric primitives like cuboids allows to infer structural information from complex geometry. It is important for 3D shape understanding, structural analysis and geometric modeling. We introduce a novel fine-to-coarse unsupervised learning approach to abstract collections of 3D shapes. Our architectural design allows us to reduce the number of primitives from hundreds (fine reconstruction) to only a few (coarse abstraction) during training. This allows our network to optimize the reconstruction error and adhere to a user-specified number of primitives per shape while simultaneously learning a consistent structure across the whole collection of data. We achieve this through our abstraction loss formulation which increasingly penalizes redundant primitives. Furthermore, we introduce a reconstruction loss formulation to account not only for surface approximation but also volume preservation. Combining both contributions allows us to represent 3D shapes more precisely with fewer cuboid primitives than previous work. We evaluate our method on collections of man-made and humanoid shapes comparing with previous state-of-the-art learning methods on commonly used benchmarks. Our results confirm an improvement over previous cuboid-based shape abstraction techniques. Furthermore, we demonstrate our cuboid abstraction in downstream tasks like clustering, retrieval, and partial symmetry detection.

Problem

• 3D shape abstraction
• fine-to-coarse unsupervised learning
• cuboid primitives optimization

Innovation

• Unsupervised fine-to-coarse cuboid abstraction
• Combined abstraction and reconstruction loss
• Improved 3D shape precision