Flexible Moment-Invariant Bases from Irreducible Tensors

• URL: http://arxiv.org/abs/2503.21939v2
• Date: Thu, 03 Apr 2025 16:25:35 GMT
• Title: Flexible Moment-Invariant Bases from Irreducible Tensors
• Authors: Roxana Bujack, Emily Shinkle, Alice Allen, Tomas Suk, Nicholas Lubbers,
• Abstract summary: A set of invariants is optimal if it is complete, independent, and robust against degeneracy in the input.<n>We show how to overcome this vulnerability by combining two popular moment invariant approaches.
• Score: 0.8248781893273871
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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