The task of reflection symmetry detection remains challenging due to significant variations and ambiguities of symmetry patterns in the wild. Furthermore, since the local regions are required to match in reflection for detecting a symmetry pattern, it is hard for standard convolutional networks, which are not equivariant to rotation and reflection, to learn the task. To address the issue, we introduce a new convolutional technique, dubbed the polar matching convolution, which leverages a polar feature pooling, a self-similarity encoding, and a systematic kernel design for axes of different angles. The proposed high-dimensional kernel convolution network effectively learns to discover symmetry patterns from real-world images, overcoming the limitations of standard convolution. In addition, we present a new dataset and introduce a self-supervised learning strategy by augmenting the dataset with synthesizing images. Experiments demonstrate that our method outperforms state-of-the-art methods in terms of accuracy and robustness.

使用极线匹配卷积技术，通过引入极向特征汇集、自相似编码和不同角度轴的系统内核设计消除了普通卷积神经网络的旋转和对称不变的限制，并通过数据集增强的自监督学习策略，成功地从真实世界的图像中发现对称图案，证明了该方法具有更高的准确性和鲁棒性。

通过极化匹配卷积学习发现反射对称性