Sorted Convolutional Network for Achieving Continuous Rotational Invariance

The topic of achieving rotational invariance in convolutional neural networks (CNNs) has gained considerable attention recently, as this invariance is crucial for many computer vision tasks such as image classification and matching. In this letter, we propose a Sorting Convolution (SC) inspired by some hand-crafted features of texture images, which achieves continuous rotational invariance without requiring additional learnable parameters or data augmentation. Further, SC can directly replace the conventional convolution operations in a classic CNN model to achieve its rotational invariance. Based on MNIST-rot dataset, we first analyze the impact of convolutional kernel sizes, different sampling and sorting strategies on SC's rotational invariance, and compare our method with previous rotation-invariant CNN models. Then, we combine SC with VGG, ResNet and DenseNet, and conduct classification experiments on popular texture and remote sensing image datasets. Our results demonstrate that SC achieves the best performance in the aforementioned tasks.