Rotation-equivariance is an essential yet challenging property in oriented
object detection. While general object detectors naturally leverage robustness
to spatial shifts due to the translation-equivariance of the conventional CNNs,
achieving rotation-equivariance remains an elusive goal. Current detectors
deploy various alignment techniques to derive rotation-invariant features, but
still rely on high capacity models and heavy data augmentation with all
possible rotations. In this paper, we introduce a Fully Rotation-Equivariant
Oriented Object Detector (FRED), whose entire process from the image to the
bounding box prediction is strictly equivariant. Specifically, we decouple the
invariant task (object classification) and the equivariant task (object
localization) to achieve end-to-end equivariance. We represent the bounding box
as a set of rotation-equivariant vectors to implement rotation-equivariant
localization. Moreover, we utilized these rotation-equivariant vectors as
offsets in the deformable convolution, thereby enhancing the existing
advantages of spatial adaptation. Leveraging full rotation-equivariance, our
FRED demonstrates higher robustness to image-level rotation compared to
existing methods. Furthermore, we show that FRED is one step closer to non-axis
aligned learning through our experiments. Compared to state-of-the-art methods,
our proposed method delivers comparable performance on DOTA-v1.0 and
outperforms by 1.5 mAP on DOTA-v1.5, all while significantly reducing the model
parameters to 16%.

全旋转等变定向物体检测器 (FRED) 严格等变地实现了从图像到边界框预测的整个过程，利用旋转等变向量表示边界框实现旋转等变定位，并通过修正卷积操作进一步增强对图像层级旋转的鲁棒性，相比现有方法，FRED 在 DOTA-v1.0 上达到可比性能，而在 DOTA-v1.5 上提升了 1.5 mAP，同时模型参数显著减少至 16%。

FRED：实现航拍图像目标检测的完全旋转等变性

FRED: Towards a Full Rotation-Equivariance in Aerial Image Object  Detection

Correspondence matching is a fundamental problem in computer vision and
robotics applications. Solving correspondence matching problems using neural
networks has been on the rise recently. Rotation-equivariance and
scale-equivariance are both critical in correspondence matching applications.
Classical correspondence matching approaches are designed to withstand scaling
and rotation transformations. However, the features extracted using
convolutional neural networks (CNNs) are only translation-equivariant to a
certain extent. Recently, researchers have strived to improve the
rotation-equivariance of CNNs based on group theories. Sim(2) is the group of
similarity transformations in the 2D plane. This paper presents a specialized
dataset dedicated to evaluating sim(2)-equivariant correspondence matching
algorithms. We compare the performance of 16 state-of-the-art (SoTA)
correspondence matching approaches. The experimental results demonstrate the
importance of group equivariant algorithms for correspondence matching on
various sim(2) transformation conditions. Since the subpixel accuracy achieved
by CNN-based correspondence matching approaches is unsatisfactory, this
specific area requires more attention in future works. Our dataset is publicly
available at: mias.group/SIM2E.

论文提出了基于 group theories 针对 sim (2)-equivariant correspondence matching 的专门数据集，并对 16 种最新的相关算法进行了实验比对，结果表明了算法的对应模糊度和精度，同时也提高了对该领域的重视程度。

基于 SIM2E 的对应匹配算法群等变性能基准测试

SIM2E: Benchmarking the Group Equivariant Capability of Correspondence Matching Algorithms

This paper proposes a set of rules to revise various neural networks for 3D
point cloud processing to rotation-equivariant quaternion neural networks
(REQNNs). We find that when a neural network uses quaternion features under
certain conditions, the network feature naturally has the rotation-equivariance
property. Rotation equivariance means that applying a specific rotation
transformation to the input point cloud is equivalent to applying the same
rotation transformation to all intermediate-layer quaternion features. Besides,
the REQNN also ensures that the intermediate-layer features are invariant to
the permutation of input points. Compared with the original neural network, the
REQNN exhibits higher rotation robustness.

本文提出了一组规则，将各种神经网络修改为旋转等变四元数神经网络（REQNN），以处理 3D 点云。 REQNN 确保中间层特征对输入点的排列具有不变性，并表现出更高的旋转鲁棒性。