EquivAnIA: A Spectral Method for Rotation-Equivariant Anisotropic Image Analysis

Abstract

Anisotropic image analysis is ubiquitous in medical and scientific imaging, and while the literature on the subject is extensive, the robustness to numerical rotations of numerous methods remains to be studied. Indeed, the principal directions and angular profile of a rotated image are often expected to rotate accordingly. In this work, we propose a new spectral method for the anisotropic analysis of images (EquivAnIA) using two established directional filters, namely cake wavelets, and ridge filters. We show that it is robust to numerical rotations throughout extensive experiments on synthetic and real-world images containing geometric structures or textures, and we also apply it successfully for a task of angular image registration. The code is available at https://github.com/jscanvic/Anisotropic-Analysis

Figures (6)

• Figure 1: Illustration of selected pixels using the binary line rasterization obtained with Bresenham algorithm.
• Figure 2: Filter spectra. The Fourier transform of the filters functions used in our method.
• Figure 3: Angular profiles. For each image in \ref{['fig:illustration_img']}, the predicted profiles using our method and the baselines are displayed.
• Figure 4: Example of synthetic images used in the experiments. The spectrum in logarithmic scale of each image is shown below it.
• Figure 5: Real-world images used in the experiments. (left) a CT scan from the LIDC-IDRI dataset armatoiii11Lung, (right) the bark of a tree.