Systematic generation of moment invariant bases for 2D and 3D tensor fields
作者：
Highlights：
• We propose a systematic approach to find bases of moment invariants with respect to orthogonal transformations using the generator method for scalar, vector, and tensor fields in two and three dimensions.
• We show that it is always possible to construct a basis using all homo- 5 geneous invariants and simultaneous invariants with no more than two different moment tensors.
• To the best of our knowledge, this results in the first 3D generator ap- proach that produces bases that are complete, independent, and exible, i.e., working for any input pattern.
• We reveal so far unknown structural similarity between the 3D generator approach and its 2D counterpart as well as between the 3D generator approach and the 3D normalization approach.
摘要
•We propose a systematic approach to find bases of moment invariants with respect to orthogonal transformations using the generator method for scalar, vector, and tensor fields in two and three dimensions.•We show that it is always possible to construct a basis using all homo- 5 geneous invariants and simultaneous invariants with no more than two different moment tensors.•To the best of our knowledge, this results in the first 3D generator ap- proach that produces bases that are complete, independent, and exible, i.e., working for any input pattern.•We reveal so far unknown structural similarity between the 3D generator approach and its 2D counterpart as well as between the 3D generator approach and the 3D normalization approach.
论文关键词：Pattern detection,Rotation invariant,Moment invariants,Generator approach,Basis,Flexible,Vector,Tensor
论文评审过程：Received 4 November 2020, Revised 16 July 2021, Accepted 9 September 2021, Available online 8 October 2021, Version of Record 21 October 2021.
论文官网地址：https://doi.org/10.1016/j.patcog.2021.108313
