Title: Phase-Preserving Analytical Features from Solid Harmonic Wavelet Bispectrum Simplify Decision Boundaries
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: Invariant Features, Wavelets, Bispectrum, Solid Harmonics

Abstract: We introduce the Solid Harmonic Wavelet Bispectrum, an operator for 2D images that computes third-order correlations over angular frequency components of solid harmonic wavelet responses. By using angular rather than spatial frequencies, our bispectrum achieves lower dimensionality than traditional 2D scattering-based bispectra, avoiding comparisons across two spatial dimensions while still preserving rich frequency information. Extending these bispectra to first- and second-order scattering coefficients produces low-dimensional multi-scale features that capture detailed image structure. To illustrate the quality of the representations, we use k-nearest neighbors, which highlights that our features encode meaningful similarity structure even without a learned parametric classifier. Results on texture, medical, and galaxy images demonstrate that these features show improved separability and similarity structure compared to existing geometric and deep learning-based representations.

TL;DR: We design roto-translation invariant features using the bispectrum of solid harmonic wavelets and test them in supervised tasks.