Achieving rotation invariance in deep neural networks without relying on data
has always been a hot research topic. Intrinsic rotation invariance can enhance
the model's feature representation capability, enabling better performance in
tasks such as multi-orientation object recognition and detection. Based on
various types of non-learnable operators, including gradient, sort, local
binary pattern, maximum, etc., this paper designs a set of new convolution
operations that are natually invariant to arbitrary rotations. Unlike most
previous studies, these rotation-invariant convolutions (RIConvs) have the same
number of learnable parameters and a similar computational process as
conventional convolution operations, allowing them to be interchangeable. Using
the MNIST-Rot dataset, we first verify the invariance of these RIConvs under
various rotation angles and compare their performance with previous
rotation-invariant convolutional neural networks (RI-CNNs). Two types of
RIConvs based on gradient operators achieve state-of-the-art results.
Subsequently, we combine RIConvs with different types and depths of classic CNN
backbones. Using the OuTex_00012, MTARSI, and NWPU-RESISC-45 datasets, we test
their performance on texture recognition, aircraft type recognition, and remote
sensing image classification tasks. The results show that RIConvs significantly
improve the accuracy of these CNN backbones, especially when the training data
is limited. Furthermore, we find that even with data augmentation, RIConvs can
further enhance model performance.

基于不可学习算子（梯度、排序、局部二值模式、最大值等），本研究设计了一套旋转不变卷积操作（RIConvs），与传统卷积操作具有相同数量的可学习参数和类似的计算过程，可相互替换。在不同数据集上的实验证明，RIConvs 明显提高了卷积神经网络的准确性，尤其是在训练数据有限的情况下，RIConvs 能进一步提升模型性能。