Equivariant and SE(2)-Invariant Neural Network Leveraging Fourier-Based Descriptors for 2D Image Classification

Emna Ghorbel, Achraf Ghorbel, Faouzi Ghorbel

Abstract: This paper introduces a novel deep learning framework for 2D shape classification that emphasizes equivariance and invariance through Generalized Finite Fourier-based Descriptors (GFID). Instead of relying on raw images, we extract contours from 2D shapes and compute equivariant, invariant, and stable descriptors, which represent shapes as column vectors in complex space. This approach achieves invariance to parameterization and rigid transformations, while reducing the number of network parameters. We evaluate the proposed lightweight neural network framework by testing it against a simple CNN and a pre-trained InceptionV3, first using the original test set and then with rotated and translated images from well-known benchmarks. Experimental results demonstrate the effectiveness of our method under rigid transformations, showcasing the benefits of Fourier-based invariants for robust classification.

External IDs:dblp:conf/icaart/GhorbelGG25