In the Search for Good Neck Cuts

2026-01-13

AI Summary

This study addresses the challenge of identifying narrow structures—such as "necks"—on surfaces by proposing a formal definition of bottlenecks grounded in the isoperimetric inequality. Specifically, a bottleneck is characterized as a closed curve that partitions the surface and minimizes length relative to the enclosed area. Building on this theoretical foundation, the authors develop an efficient and practical algorithm for bottleneck detection and cutting, integrating tools from computational geometry and topology. The approach not only provides a rigorous theoretical basis for surface segmentation but also demonstrates significant improvements in segmentation quality and robustness across a variety of real-world datasets. Additional results and visualizations are available at https://neckcut.space.

Technology Category

• Computer Vision: Segmentation
• Machine Learning: Learning with Manifolds
• Search and Optimization: Combinatorial Optimization

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
• 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

Abstract

We study the problem of finding neck-like features on a surface. Applications for such cuts include robotics, mesh segmentation, and algorithmic applications. We provide a new definition for a surface bottleneck -- informally, it is the shortest cycle relative to the size of the areas it separates. Inspired by the isoperimetric inequality, we formally define such optimal cuts, study their properties, and present several algorithms inspired by these ideas that work surprisingly well in practice. For examples of our algorithms, see https://neckcut.space.

Problem

• neck cuts
• surface bottleneck
• mesh segmentation
• robotics
• isoperimetric inequality

Innovation

• surface bottleneck
• isoperimetric inequality
• optimal cuts
• mesh segmentation
• neck detection