In computer vision, models must be able to adapt to changes in image
resolution to effectively carry out tasks such as image segmentation; This is
known as scale-equivariance. Recent works have made progress in developing
scale-equivariant convolutional neural networks, e.g., through weight-sharing
and kernel resizing. However, these networks are not truly scale-equivariant in
practice. Specifically, they do not consider anti-aliasing as they formulate
the down-scaling operation in the continuous domain. To address this
shortcoming, we directly formulate down-scaling in the discrete domain with
consideration of anti-aliasing. We then propose a novel architecture based on
Fourier layers to achieve truly scale-equivariant deep nets, i.e., absolute
zero equivariance-error. Following prior works, we test this model on
MNIST-scale and STL-10 datasets. Our proposed model achieves competitive
classification performance while maintaining zero equivariance-error.

在计算机视觉中，为了有效地执行图像分割等任务，模型必须能够适应图像分辨率的变化，这被称为尺度等变性。最近的研究通过权重共享和内核调整等方式，取得了在发展尺度等变性卷积神经网络方面的进展。然而，在实践中，这些网络并不是真正的尺度等变性的。为了解决这个问题，我们直接在离散域中考虑了抗锯齿，并提出了一种基于傅里叶层的新型架构，以实现真正的尺度等变深度网络，即绝对零等变误差。在先前的研究基础上，我们对 MNIST-scale 和 STL-10 数据集上测试了这个模型。我们提出的模型在保持零等变误差的同时，实现了有竞争力的分类性能。

具有傅立叶层的真正尺度相等深度神经网络

Truly Scale-Equivariant Deep Nets with Fourier Layers

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。