Include shape variability in rotation-invariant descriptors

Develop methods to incorporate shape variability into rotation-invariant descriptors by modeling distributions or sets of invariants over dynamic shape ensembles, and devise approaches to compare such variability-aware descriptors, potentially against protein binding sites.

Background

Shapes of interest, particularly molecules, often vary dynamically. The paper suggests replacing single invariant vectors with sets or probability distributions over invariants, estimated from snapshots (e.g., molecular dynamics) and compared to targets such as binding sites.

The authors identify inclusion of shape variability as an open question, calling for methodologies to capture and compare such distributions within the rotation-invariant framework.

References

This is initial article proposing such looking novel approach, leaving many open questions both theoretical and practical, e.g.: Including shape variability, crucial for various 2/3D objects e.g. molecules, maybe comparing with binding sites.

— 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"