  Effective recognition of spatial patterns and learning their hierarchy is
crucial in modern spatial data analysis. Volumetric data applications seek
techniques ensuring invariance not only to shifts but also to pattern
rotations. While traditional methods can readily achieve translational
invariance, rotational invariance possesses multiple challenges and remains an
active area of research. Here, we present ILPO-Net (Invariant to Local Patterns
Orientation Network), a novel approach that handles arbitrarily shaped patterns
with the convolutional operation inherently invariant to local spatial pattern
orientations using the Wigner matrix expansions. Our architecture seamlessly
integrates the new convolution operator and, when benchmarked on diverse
volumetric datasets such as MedMNIST and CATH, demonstrates superior
performance over the baselines with significantly reduced parameter counts - up
to 1000 times fewer in the case of MedMNIST. Beyond these demonstrations,
ILPO-Net's rotational invariance paves the way for other applications across
multiple disciplines. Our code is publicly available at
https://gricad-gitlab.univ-grenoble-alpes.fr/GruLab/ILPO/-/tree/main/ILPONet.
