CVMar 27, 2025

Flexible Moment-Invariant Bases from Irreducible Tensors

arXiv:2503.21939v22 citationsh-index: 4
Originality Incremental advance
AI Analysis

This work addresses a specific degeneracy problem in pattern detection and machine learning applications, offering an incremental improvement over existing methods.

The paper tackled the vulnerability of current moment invariant bases to degeneracy in spherical functions, a common real-world issue, by combining spherical harmonics and Cartesian tensor algebra approaches to create more robust invariants.

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.

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