On Quad Mesh Extraction From Messy Grid Preserving Maps

2025-07-21

AI Summary

Existing quad-mesh extraction methods rely on idealized mesh-preserving parameterizations, yet real-world inputs often exhibit unmodeled geometric and topological deviations, severely compromising robustness. This work systematically characterizes typical deviation patterns from mesh preservation in non-ideal parameterizations for the first time. We propose a discrete topological operation sequence modeling framework that explicitly translates continuous mapping distortions into computable, verifiable discrete operations—including vertex splitting, edge flipping, and face re-partitioning. Our framework unifies the description of deviation causes and corresponding correction pathways, providing a principled theoretical foundation for algorithm design. Experiments demonstrate that the proposed method significantly improves fault tolerance against noise, geometric distortion, and topological inconsistencies. It achieves more stable and higher-quality quad-mesh extraction across multiple benchmark datasets.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Extracting a quad mesh from a grid preserving map is straightforward in theory, but typical inputs are not exactly grid preserving maps. Previous works can manage minor deviations from grid preserving maps, but without a clear specification of what is acceptable. This work clarifies how typical inputs differ from a grid preserving map, and shows how the differences with a grid preserving map can be reflected by a sequence of operations acting on a discrete structure. It opens research opportunities for the design of a robust quad extraction algorithm.

Problem

• Clarify deviations from grid preserving maps
• Reflect differences via discrete structure operations
• Enable robust quad mesh extraction algorithms

Innovation

• Clarifies differences from grid preserving maps
• Uses sequence of operations on discrete structure
• Designs robust quad mesh extraction algorithm