提出新方法生成更鲁棒的旋转不变描述子，解决真实场景中球对称数据的失效问题。
Flexible Moment-Invariant Bases from Irreducible Tensors
- 融合球谐函数与笛卡尔张量代数构建不变基
- 在球对称分布下保持不变性，避免传统方法失效
- 适合需要高鲁棒性旋转特征的应用场景
矩不变量是生成旋转不变描述子的强大工具，广泛应用于模式检测、分类和机器学习。一个最优的不变量集合应具备完备性、独立性和对抗输入退化的能力。本文指出，当前主流方法虽能抵御矩张量完全为零的情况，但在真实应用中常见的球对称函数情形下仍存在脆弱性。为此，我们提出将基于球谐函数与笛卡尔张量代数的两种主流方法相结合，有效克服该退化问题，提升不变基的稳定性与适用性。
原文摘要 · Abstract (English)
Moment invariants are a powerful tool for the generation of rotation-invariant descriptors needed for many applications in pattern detection, classification, and machine learning. A set of invariants is optimal if it is complete, independent, and robust against degeneracy in the input. In this paper, we show that the current state of the art for the generation of these bases of moment invariants, despite being robust against moment tensors being identically zero, is vulnerable to a degeneracy that is common in real-world applications, namely spherical functions. We show how to overcome this vulnerability by combining two popular moment invariant approaches: one based on spherical harmonics and one based on Cartesian tensor algebra.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。