  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.
