Localizing Periodicity in Time Series and Videos

Periodicity detection is a problem that has received a lot of attention, thus several important tools exist to analyse purely periodic signals. However, in many real world scenarios (time series, videos of human activities, etc) periodic signals appear in the context of non-periodic ones. In this work we propose a method that, given a time series representing a periodic signal that has a non-periodic prefix and tail, estimates the start, the end and the period of the periodic part of the signal. We formulate this as an optimization problem that is solved based on evolutionary optimization techniques. Quantitative experiments on synthetic data demonstrate that the proposed method is successful in localizing the periodic part of a signal and exhibits robustness in the presence of noisy measurements. Also, it does so even when the periodic part of the signal is too short compared to its non-periodic prefix and tail. We also provide quantitative and qualitative results obtained from the application of the proposed method to the problem of unsupervised localization and segmentation of periodic activities in real world videos.