A Topological Approach for Motion Track Discrimination

TL;DR

This paper introduces a topological method using persistent homology on motion tracks to improve the detection and discrimination of small targets in video sequences, especially when spatial information is limited.

Contribution

The paper presents a novel application of topological data analysis to extract features from motion tracks for target discrimination in challenging visual conditions.

Findings

High probability detection of small targets at range

Effective differentiation of targets from confusers using topological features

Robust classification based on motion dynamics

Abstract

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.