Design shape similarity metrics based on rotation invariants

Develop rotation-invariant shape similarity metrics derived from the proposed tensor/polynomial invariants in R^d, such as distances between vectors consisting of selected invariants, to efficiently quantify differences between two shapes modulo rotation.

Background

To avoid costly optimization over rotations, the paper advocates using vectors of rotation-invariant features computed from higher-order tensors or polynomial representations. A distance between such vectors can serve as a shape similarity measure that is zero when shapes differ only by rotation.

The authors leave as an open question the concrete design of such metrics, including which invariants to select and how to weight them to achieve robust, efficient comparison across practical tasks.

References

This is initial article proposing such looking novel approach, leaving many open questions both theoretical and practical, e.g.: Designing shape similarity metrics based on such invariants, e.g. as distance between vectors of chosen subset of invariants - allowing to inexpensively evaluate difference between two shapes modulo rotation.

— Higher order PCA-like rotation-invariant features for detailed shape descriptors modulo rotation  (2601.03326 - Duda, 6 Jan 2026) in Section "Conclusion and further work"