(Quasi)Periodicity Quantification in Video Data, Using Topology
This provides a novel tool for analyzing repetitive patterns in videos, which could benefit fields like medical imaging or video analysis, though it is incremental in combining existing topological and time series techniques.
The authors tackled the problem of quantifying recurrent dynamics like periodicity and quasiperiodicity in video data without requiring segmentation or training, and demonstrated that their method outperforms others in human rankings and detects biphonation in vocal fold videos.
This work introduces a novel framework for quantifying the presence and strength of recurrent dynamics in video data. Specifically, we provide continuous measures of periodicity (perfect repetition) and quasiperiodicity (superposition of periodic modes with non-commensurate periods), in a way which does not require segmentation, training, object tracking or 1-dimensional surrogate signals. Our methodology operates directly on video data. The approach combines ideas from nonlinear time series analysis (delay embeddings) and computational topology (persistent homology), by translating the problem of finding recurrent dynamics in video data, into the problem of determining the circularity or toroidality of an associated geometric space. Through extensive testing, we show the robustness of our scores with respect to several noise models/levels, we show that our periodicity score is superior to other methods when compared to human-generated periodicity rankings, and furthermore, we show that our quasiperiodicity score clearly indicates the presence of biphonation in videos of vibrating vocal folds, which has never before been accomplished end to end quantitatively.