We present a method for learning discriminative filters using a shallow
Convolutional Neural Network (CNN). We encode rotation invariance directly in
the model by tying the weights of groups of filters to several rotated versions
of the canonical filter in the group. These filters can be used to extract
rotation invariant features well-suited for image classification. We test this
learning procedure on a texture classification benchmark, where the
orientations of the training images differ from those of the test images. We
obtain results comparable to the state-of-the-art. Compared to standard shallow
CNNs, the proposed method obtains higher classification performance while
reducing by an order of magnitude the number of parameters to be learned.

使用浅层卷积神经网络学习判别滤波器的一种方法，直接编码旋转不变性以提取旋转不变的特征，实现了与标准浅层卷积神经网络相比更高的分类性能并减少了一个数量级的参数量。

学习旋转不变卷积滤波器以进行纹理分类

Learning rotation invariant convolutional filters for texture  classification

This paper shows how to extract dense optical flow from videos with a
convolutional neural network (CNN). The proposed model constitutes a potential
building block for deeper architectures to allow using motion without resorting
to an external algorithm, \eg for recognition in videos. We derive our network
architecture from signal processing principles to provide desired invariances
to image contrast, phase and texture. We constrain weights within the network
to enforce strict rotation invariance and substantially reduce the number of
parameters to learn. We demonstrate end-to-end training on only 8 sequences of
the Middlebury dataset, orders of magnitude less than competing CNN-based
motion estimation methods, and obtain comparable performance to classical
methods on the Middlebury benchmark. Importantly, our method outputs a
distributed representation of motion that allows representing multiple,
transparent motions, and dynamic textures. Our contributions on network design
and rotation invariance offer insights nonspecific to motion estimation.

本文提出了一种卷积神经网络用于从视频中提取密集的光流，旨在为深度架构构建潜在的模块，以允许在视频中使用运动而无需借助外部算法，通过考虑信号处理原则构建网络结构，强制 “旋转不变性”，并提供一种分布式表示运动的方法。

从视频中学习卷积神经网络中的动作提取

Learning to Extract Motion from Videos in Convolutional Neural Networks

This paper presents a new version of Dropout called Split Dropout (sDropout)
and rotational convolution techniques to improve CNNs' performance on image
classification. The widely used standard Dropout has advantage of preventing
deep neural networks from overfitting by randomly dropping units during
training. Our sDropout randomly splits the data into two subsets and keeps both
rather than discards one subset. We also introduce two rotational convolution
techniques, i.e. rotate-pooling convolution (RPC) and flip-rotate-pooling
convolution (FRPC) to boost CNNs' performance on the robustness for rotation
transformation. These two techniques encode rotation invariance into the
network without adding extra parameters. Experimental evaluations on
ImageNet2012 classification task demonstrate that sDropout not only enhances
the performance but also converges faster. Additionally, RPC and FRPC make CNNs
more robust for rotation transformations. Overall, FRPC together with sDropout
bring $1.18\%$ (model of Zeiler and Fergus~\cite{zeiler2013visualizing},
10-view, top-1) accuracy increase in ImageNet 2012 classification task compared
to the original network.

本文介绍一种新的 Dropout 方法 ——Split Dropout (sDropout)，以及一些旋转卷积技术，用于提高卷积神经网络在图像分类中的性能和旋转不变性。sDropout 将数据随机分成两个子集，并在训练过程中同时保留这两个子集。此外，RPC 和 FRPC 旋转卷积技术编码旋转不变性到网络中，而不会增加额外的参数。经过实验验证，sDropout 不仅提高了性能，而且收敛更快。FRPC 和 sDropout 在 ImageNet2012 分类任务中带来了 1.18％的分类准确率提高。

卷积神经网络中的翻转 - 旋转 - 池化卷积和拆分丢弃用于图像分类

Flip-Rotate-Pooling Convolution and Split Dropout on Convolution Neural  Networks for Image Classification

We present an efficient and accurate algorithm for principal component
analysis (PCA) of a large set of two dimensional images, and, for each image,
the set of its uniform rotations in the plane and its reflection. The algorithm
starts by expanding each image, originally given on a Cartesian grid, in the
Fourier-Bessel basis for the disk. Because the images are bandlimited in the
Fourier domain, we use a sampling criterion to truncate the Fourier-Bessel
expansion such that the maximum amount of information is preserved without the
effect of aliasing. The constructed covariance matrix is invariant to rotation
and reflection and has a special block diagonal structure. PCA is efficiently
done for each block separately. This Fourier-Bessel based PCA detects more
meaningful eigenimages and has improved denoising capability compared to
traditional PCA for a finite number of noisy images.

该论文提出了一种基于 Fourier-Bessel 基础的主成分分析算法，具有旋转不变性和更好的去噪能力，可用于大量二维图像的处理。