Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently integrating topological properties of the data in the learning process in order to enhance the performance. However, there is no existing study to demonstrate all possible scenarios where introducing topological properties can boost or harm the performance. This paper performs a detailed analysis of the effectiveness of topological properties for image classification in various training scenarios, defined by: the number of training samples, the complexity of the training data and the complexity of the backbone network. We identify the scenarios that benefit the most from topological features, e.g., training simple networks on small datasets. Additionally, we discuss the problem of topological consistency of the datasets which is one of the major bottlenecks for using topological features for classification. We further demonstrate how the topological inconsistency can harm the performance for certain scenarios.

翻译：图像的持续拓扑性质作为一种额外的描述符，能够提供传统神经网络可能无法发现的洞见。现有研究主要集中于高效地将数据的拓扑性质整合到学习过程中以提升性能。然而，目前尚无研究系统阐述所有可能场景下引入拓扑性质对性能的促进或抑制效应。本文针对不同训练场景下拓扑性质对图像分类的有效性进行了详细分析，其场景定义要素包括：训练样本数量、训练数据复杂度以及骨干网络的复杂度。我们识别了最受益于拓扑特征的场景，例如在小数据集上训练简单网络。此外，本文探讨了数据集拓扑一致性问题，这是利用拓扑特征进行分类的主要瓶颈之一。我们进一步展示了拓扑不一致性在某些场景下对性能的损害机制。