Learning to Discover Reflection Symmetry via Polar Matching Convolution

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 selfsimilarity 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-ofthe-art methods in terms of accuracy and robustness.