# (Quasi)Periodicity Quantification in Video Data, Using Topology

arXiv: https://arxiv.org/abs/1704.08382 · HTML: https://mlsanity.com/paper/1704.08382/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2017.

## Built on by (most cited first, 10 of 10)

- [PoseRAC: Pose Saliency Transformer for Repetitive Action Counting](https://mlsanity.com/paper/2303.08450/) (2023)
- [TopoFR: A Closer Look at Topology Alignment on Face Recognition](https://mlsanity.com/paper/2410.10587/) (2024)
- [On Logical Extrapolation for Mazes with Recurrent and Implicit Networks](https://mlsanity.com/paper/2410.03020/) (2024)
- [Toroidal Coordinates: Decorrelating Circular Coordinates With Lattice Reduction](https://mlsanity.com/paper/2212.07201/) (2022)
- [Time Series Classification via Topological Data Analysis](https://mlsanity.com/paper/2102.01956/) (2021)
- [Topology-driven identification of repetitions in multi-variate time series](https://mlsanity.com/paper/2505.10004/) (2025)
- [Topological Signal Processing using the Weighted Ordinal Partition Network](https://mlsanity.com/paper/2205.08349/) (2022)
- [Skim then Focus: Integrating Contextual and Fine-grained Views for Repetitive Action Counting](https://mlsanity.com/paper/2406.08814/) (2024)
- [Phenotyping OSA: a time series analysis using fuzzy clustering and persistent homology](https://mlsanity.com/paper/2104.13479/) (2021)
- [Topology-enhanced machine learning for speech signal processing](https://mlsanity.com/paper/2311.15210/) (2023)

## Abstract (arXiv)

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.