OneDConv: Generalized Convolution for Transform-Invariant Representation

Convolutional Neural Networks (CNNs) have ex-hibited great power in various vision tasks. However, the lack of transform-invariant property limits their further applications in complicated real-world scenarios. In this work, we pro-posed a novel generalized one-dimension convolutional operator (OneDConv), which dynamically transforms the convolution kernels based on the input features in a computationally and parametrically efficient manner. The proposed operator can extract the transform-invariant features naturally. It improves the robustness and generalization of convolution without sac-rificing the performance of common images. The proposed OneDConv operator can substitute the vanilla convolution. Thus, it can readily be incorporated into popular convolutional architectures, supporting end-to-end training. Empirical evaluations on popular benchmarks reveal OneDConv's superior performance over the standard convolution and competitive models in handling canonical and distorted images.

I. Introduction

Convolutional Neural Networks (CNNs) can extract ex-pressive learning representations from high-dimensional data, achieving impressive performance on current visual benchmarks [1]–[3]. The weight sharing mechanism, in which the convolution filter parameters are shared across all spatial positions, helps to extract the common features re-gardless of how the input images are translated. Nevertheless, current convolutional models are still ineffective in tackling other transformations like rotation and reflection [4], [5]. With the lack of an internal mechanism to deal with affine transformations, CNNs demonstrate limited generalization capability across various poses of real-world objects. An enormous number of replicated feature detectors or labeled training images are required exponentially as the dimensions of affine transformations increase [6], [7].