Detecting small targets at range is difficult because there is not enough spatial information present in an image sub-region containing the target to use correlation-based methods to differentiate it from dynamic confusers present in the scene. Moreover, this lack of spatial information also disqualifies the use of most state-of-the-art deep learning image-based classifiers. Here, we use characteristics of target tracks extracted from video sequences as data from which to derive distinguishing topological features that help robustly differentiate targets of interest from confusers. In particular, we calculate persistent homology from time-delayed embeddings of dynamic statistics calculated from motion tracks extracted from a wide field-of-view video stream. In short, we use topological methods to extract features related to target motion dynamics that are useful for classification and disambiguation and show that small targets can be detected at range with high probability.

中文翻译：

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一种运动轨迹识别的拓扑方法

由于在包含目标的图像子区域中没有足够的空间信息，无法使用基于相关性的方法将其与场景中的动态混淆器区分开来，因此很难检测到范围内的小目标。此外，空间信息的缺乏也使大多数基于最新深度学习图像的分类器的使用不合格。在这里，我们使用从视频序列中提取的目标轨道的特征作为数据，从中得出区分拓扑特征的数据，这些特征有助于将感兴趣的目标与混淆者进行有力的区分。特别是，我们从动态统计信息的时延嵌入中计算持久性同源性，这些动态统计信息是根据从宽视场视频流中提取的运动轨迹计算得出的。简而言之，