Most datasets encountered in computer vision and medical applications present symmetries that should be taken into account in classification tasks. A typical example is the symmetry by rotation and/or scaling in object detection. A common way to build neural networks that learn the symmetries is to use data augmentation. In order to avoid data augmentation and build more sustainable algorithms, we present an alternative method to mod out symmetries based on the notion of section of a principal fiber bundle. This framework allows the use of simple metrics on the space of objects in order to measure dissimilarities between orbits of objects under the symmetry group. Moreover, the section used can be optimized to maximize separation of classes. We illustrate this methodology on a dataset of contours of objects for the groups of translations, rotations, scalings and reparameterizations. In particular, we present a $2$-parameter family of canonical parameterizations of curves, containing the constant-speed parameterization as a special case, which we believe is interesting in its own right. We hope that this simple application will serve to convey the geometric concepts underlying this method, which have a wide range of possible applications. The code is available at the following link: $\href{https://github.com/GiLonga/Geometric-Learning}{https://github.com/GiLonga/Geometric-Learning}$. A tutorial notebook showcasing an application of the code to a specific dataset is available at the following link: $\href{https://github.com/ioanaciuclea/geometric-learning-notebook}{https://github.com/ioanaciuclea/geometric-learning-notebook}$

翻译：在计算机视觉和医学应用中遇到的大多数数据集都呈现出在分类任务中应予考虑的对称性。一个典型例子是物体检测中的旋转和/或缩放对称性。构建能够学习这些对称性的神经网络的常用方法是使用数据增强。为了避免数据增强并构建更具可持续性的算法，我们提出了一种基于主纤维丛截面概念来模掉对称性的替代方法。该框架允许在对象空间上使用简单的度量来测量对称群作用下对象轨道之间的差异。此外，所使用的截面可以被优化以最大化类别分离度。我们在平移、旋转、缩放和重参数化群作用下的物体轮廓数据集上演示了此方法。特别地，我们提出了一个包含匀速参数化作为特例的二维曲线规范参数化双参数族，我们认为其本身具有独立的研究价值。我们希望这个简单的应用能够传达该方法背后的几何概念，这些概念具有广泛的应用潜力。代码可通过以下链接获取：$\href{https://github.com/GiLonga/Geometric-Learning}{https://github.com/GiLonga/Geometric-Learning}$。展示代码在特定数据集上应用的教程笔记本可通过以下链接获取：$\href{https://github.com/ioanaciuclea/geometric-learning-notebook}{https://github.com/ioanaciuclea/geometric-learning-notebook}$