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.

Which processes underly our ability to quickly recognize familiar objects within a complex visual input scene? In this paper an imple(cid:173) mented neural network model is described that attempts to specify how selective visual attention, perceptual organisation, and invari(cid:173) ance transformations might work together in order to segment, select, and recognize objects out of complex input scenes containing multi(cid:173) ple, possibly overlapping objects. Retinotopically organized feature maps serve as input for two main processing routes: pathway' dealing with location information and the'what-pathway' computing the shape and attributes of objects. A location-based at(cid:173) tention mechanism operates on an early stage of visual processing selecting a contigous region of the visual field for preferential proces(cid:173) sing. Additionally, location-based attention plays an important role for invariant object recognition controling appropriate normalization processes within the what-pathway.

A large number of deep learning architectures use spatial transformations of CNN feature maps or filters to better deal with variability in object appearance caused by natural image transformations. In this paper, we prove that spatial transformations of CNN feature maps cannot align the feature maps of a transformed image to match those of its original, for general affine transformations, unless the extracted features are themselves invariant. Our proof is based on elementary analysis for both the single-and multi-layer network case. The results imply that methods based on spatial transformations of CNN feature maps or filters cannot replace image alignment of the input and cannot enable invariant recognition for general affine transformations, specifically not for scaling transformations or shear transformations. For rotations and reflections, spatially transforming feature maps or filters can enable invariance but only for networks with learnt or hardcoded rotation-or reflection-invariant features.