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.

翻译：反射对称探测任务仍然具有挑战性,因为野外对称模式差异巨大且模糊不清。 此外,由于要求当地区域在反射中匹配检测对称模式,标准共变网络(它们并非对旋转和反射的等值性)很难学习这项任务。为了解决这个问题,我们引入了一种新的共变技术,称为极对称相配共变,它利用极地特征集合、自我相似编码和不同角度轴的系统内核设计。拟议的高维内核共振网络有效地学习从真实世界图像中发现对称模式,克服标准共变的局限性。此外,我们提出一个新的数据集,并引入一种自我监督的学习战略,通过合成图像来强化数据集。实验表明,我们的方法在准确性和稳健性方面超越了最新的方法。