The content presents a new framework for rotation equivariant keypoint descriptors using "steerers" - linear maps that encode image rotations in the descriptor space. The key ideas are:
Learned keypoint descriptors, while not fully rotation invariant, are often approximately rotation equivariant. This means there exists a linear transform (a "steerer") that can be learned to align the descriptors of rotated images.
The authors investigate three settings for learning steerers: (A) optimizing a steerer for a fixed descriptor, (B) jointly optimizing a steerer and descriptor, and (C) optimizing a descriptor for a fixed steerer.
The authors show that the choice of steerer, particularly its eigenvalue structure, is crucial for performance. Steerers that spread the eigenvalues across different frequencies perform best.
Experiments on the rotation invariant matching benchmarks Roto-360 and AIMS show that the authors' best models achieve new state-of-the-art results, while also performing on par with or better than existing methods on upright images on the MegaDepth benchmark.
The authors provide theoretical insights on why steerers emerge in practice, drawing connections to representation theory and equivariance.
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