  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.
