论文标题
图像增强与卷积神经网络的保形映射
Image augmentation with conformal mappings for a convolutional neural network
论文作者
论文摘要
为了增强卷积神经网络（CNN）的方形图像数据，我们引入了一种新方法，其中原始图像被映射到带有保形映射的磁盘上，围绕该磁盘的中心旋转并在如此的Möbius变换下映射，以保留磁盘，然后将其映射到原始的广场形状上。与CNN数据增强中使用的典型转换不同，此过程不会导致从原始图像的边缘附近删除区域引起的信息丢失。我们在这里提供所需的所有映射的公式以及详细说明如何编写用于转换图像的代码。新方法还通过模拟数据进行了测试，并根据结果使用此方法将10张图像的训练数据扩大到40张图像中，可减少CNN对160张图像的预测误差的量（PVALUE = 0.0360）。
For augmentation of the square-shaped image data of a convolutional neural network (CNN), we introduce a new method, in which the original images are mapped onto a disk with a conformal mapping, rotated around the center of this disk and mapped under such a Möbius transformation that preserves the disk, and then mapped back onto their original square shape. This process does not result the loss of information caused by removing areas from near the edges of the original images unlike the typical transformations used in the data augmentation for a CNN. We offer here the formulas of all the mappings needed together with detailed instructions how to write a code for transforming the images. The new method is also tested with simulated data and, according the results, using this method to augment the training data of 10 images into 40 images decreases the amount of the error in the predictions by a CNN for a test set of 160 images in a statistically significant way (p-value=0.0360).
