GenHarris-ResNet: A Rotation Invariant Neural Network Based on Elementary Symmetric Polynomials

Abstract

In this paper, we propose a rotation invariant neural network based on Gaussian derivatives. The proposed network covers the main steps of the Harris corner detector in a generalized manner. More precisely, the Harris corner response function is a combination of the elementary symmetric polynomials of the integrated dyadic (outer) product of the gradient with itself. In the same way, we define matrices to be the self dyadic product of vectors composed with higher order partial derivatives and combine the elementary symmetric polynomials. A specific global pooling layer is used to mimic the local pooling used by Harris in his method. The proposed network is evaluated through three experiments. It first shows a quasi perfect invariance to rotations on Fashion-MNIST, it obtains competitive results compared to other rotation invariant networks on MNIST-Rot, and it obtains better performances classifying galaxies (EFIGI Dataset) than networks using up to a thousand times more trainable parameters.