  We present REMM, a rotation-equivariant framework for end-to-end multimodal
image matching, which fully encodes rotational differences of descriptors in
the whole matching pipeline. Previous learning-based methods mainly focus on
extracting modal-invariant descriptors, while consistently ignoring the
rotational invariance. In this paper, we demonstrate that our REMM is very
useful for multimodal image matching, including multimodal feature learning
module and cyclic shift module. We first learn modal-invariant features through
the multimodal feature learning module. Then, we design the cyclic shift module
to rotationally encode the descriptors, greatly improving the performance of
rotation-equivariant matching, which makes them robust to any angle. To
validate our method, we establish a comprehensive rotation and scale-matching
benchmark for evaluating the anti-rotation performance of multimodal images,
which contains a combination of multi-angle and multi-scale transformations
from four publicly available datasets. Extensive experiments show that our
method outperforms existing methods in benchmarking and generalizes well to
independent datasets. Additionally, we conducted an in-depth analysis of the
key components of the REMM to validate the improvements brought about by the
cyclic shift module. Code and dataset at https://github.com/HanNieWHU/REMM.
