Optimize rotation-invariant descriptors for application domains

Optimize the selection, computation, and use of rotation-invariant features based on higher-order tensors or polynomial-times-Gaussian representations for applications including molecular shape descriptors, 2D/3D image recognition, and shape comparison.

Background

The paper outlines several potential application areas—molecular shape analysis, 2D/3D object recognition, and shape comparison—where rotation-invariant features could replace costly rotation optimization. However, determining application-specific choices (e.g., normalization, invariant subsets, weighting) remains unresolved.

The authors explicitly list optimization for various applications as an open question, indicating the need for empirical and methodological work to tailor and benchmark the proposed descriptors.

References

This is initial article proposing such looking novel approach, leaving many open questions both theoretical and practical, e.g.: Optimization for various applications, like molecular shape descriptions, 2/3D image recognition, shape comparison.

— 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"