There is a long-standing problem of repeated patterns in correspondence problems, where mismatches frequently occur because of inherent ambiguity. The unique position information associated with repeated patterns makes coordinate representations a useful supplement to appearance representations for improving feature correspondences. However, the issue of appropriate coordinate representation has remained unresolved. In this study, we demonstrate that geometric-invariant coordinate representations, such as barycentric coordinates, can significantly reduce mismatches between features. The first step is to establish a theoretical foundation for geometrically invariant coordinates. We present a seed matching and filtering network (SMFNet) that combines feature matching and consistency filtering with a coarse-to-fine matching strategy in order to acquire reliable sparse correspondences. We then introduce DEGREE, a novel anchor-to-barycentric (A2B) coordinate encoding approach, which generates multiple affine-invariant correspondence coordinates from paired images. DEGREE can be used as a plug-in with standard descriptors, feature matchers, and consistency filters to improve the matching quality. Extensive experiments in synthesized indoor and outdoor datasets demonstrate that DEGREE alleviates the problem of repeated patterns and helps achieve state-of-the-art performance. Furthermore, DEGREE also reports competitive performance in the third Image Matching Challenge at CVPR 2021. This approach offers a new perspective to alleviate the problem of repeated patterns and emphasizes the importance of choosing coordinate representations for feature correspondences.

翻译：在对应问题中，重复模式是一个长期存在的难题，由于固有的歧义性，误匹配频繁发生。与重复模式相关的唯一位置信息使得坐标表示成为外观表示的有益补充，有助于改进特征对应。然而，合适的坐标表示问题至今仍未解决。本研究表明，几何不变坐标表示（如重心坐标）能显著减少特征间的误匹配。首先，我们为几何不变坐标建立理论基础。提出一种种子匹配与滤波网络（SMFNet），该网络结合特征匹配与一致性滤波，采用从粗到精的匹配策略，以获取可靠的稀疏对应。随后，我们引入DEGREE——一种新颖的锚点至重心（A2B）坐标编码方法，该方法从成对图像生成多个仿射不变对应坐标。DEGREE可作为插件与标准描述子、特征匹配器及一致性滤波器协同使用，以提升匹配质量。在合成室内外数据集上的大量实验表明，DEGREE缓解了重复模式问题，并助力实现最先进的性能。此外，DEGREE在CVPR 2021第三届图像匹配挑战赛中也取得了具有竞争力的表现。本方法为缓解重复模式问题提供了新视角，并强调了为特征对应选择合适的坐标表示的重要性。