Robust Construction of Polycube Segmentations via Dual Loops

2024-02-01

AI Summary

To address the lack of robustness in polycube segmentation for arbitrary-genus 3D models, this paper proposes a dual-loop-structure-based iterative optimization algorithm. Starting from an initial polycube of matching genus, it jointly optimizes the polycube geometry, dual-loop topology, and segmentation mapping while rigorously preserving solution validity throughout. Key contributions include: (i) the first theoretically guaranteed validity assurance for polycube segmentation; (ii) explicit ring-space constraints via dual-loop representation to ensure topological correctness; and (iii) continuous trade-off control between segmentation quality and complexity. The method leverages dual-graph modeling, ring-space-constrained optimization, and topology-aware iterative updates. It consistently produces valid segmentations across diverse models, achieving quality on par with or surpassing state-of-the-art methods, while maintaining structural simplicity and implementation ease.

Technology Category

• Computer Vision: Segmentation
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic 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: Robustness and generalizability of Web mining methods

Abstract

Polycube segmentations for 3D models effectively support a wide variety of applications such as seamless texture mapping, spline fitting, structured multi-block grid generation, and hexahedral mesh construction. However, the automated construction of valid polycube segmentations suffers from robustness issues: state-of-the-art methods are not guaranteed to find a valid solution. In this paper we present an iterative algorithm which is guaranteed to return a valid polycube segmentation for 3D models of any genus. Our algorithm is based on a dual representation of polycubes. Starting from an initial simple polycube of the correct genus, together with the corresponding dual loop structure and polycube segmentation, we iteratively refine the polycube, loop structure, and segmentation, while maintaining the correctness of the solution. Our algorithm is robust by construction: at any point during the iterative process the current segmentation is valid. Furthermore, the iterative nature of our algorithm facilitates a seamless trade-off between quality and complexity of the solution. Our algorithm can be implemented using comparatively simple algorithmic building blocks; our experimental evaluation establishes that the quality of our polycube segmentations is on par with, or exceeding, the state-of-the-art.

Problem

• Automated construction of valid polycube segmentations lacks robustness
• Existing methods fail to guarantee valid solutions for 3D models
• Algorithm ensures valid polycube segmentation for any genus model

Innovation

• Iterative algorithm for robust polycube segmentation
• Dual loop structure ensures valid segmentation
• Simple building blocks achieve high-quality results