Convolutional neural networks have shown great success on feature extraction
from raw input data such as images. Although convolutional neural networks are
invariant to translations on the inputs, they are not invariant to other
transformations, including rotation and flip. Recent attempts have been made to
incorporate more invariance in image recognition applications, but they are not
applicable to dense prediction tasks, such as image segmentation. In this
paper, we propose a set of methods based on kernel rotation and flip to enable
rotation and flip invariance in convolutional neural networks. The kernel
rotation can be achieved on kernels of 3 $\times$ 3, while kernel flip can be
applied on kernels of any size. By rotating in eight or four angles, the
convolutional layers could produce the corresponding number of feature maps
based on eight or four different kernels. By using flip, the convolution layer
can produce three feature maps. By combining produced feature maps using
maxout, the resource requirement could be significantly reduced while still
retain the invariance properties. Experimental results demonstrate that the
proposed methods can achieve various invariance at reasonable resource
requirements in terms of both memory and time.

本文提出了基于核旋转和翻转的一组方法，以实现对卷积神经网络中的旋转和翻转不变性，结果表明，这些方法能够在合理的资源要求下实现不同的不变性。