The periodicity test we use is based on how well the peaks in A fit a planar lattice. The similarity plot S encodes the dynamics of the periodic motion. Different types of periodic motion yield qualitatively different types of features in S and A . We exploit this to classify periodic motion. Below we show both synthetic and real image sequences for various types of periodic motion.
Pendulums Below are four simple planar pendulum systems.
While each system is periodic, each has qualitatively different types of periodicities, which is shown in their respective similarity plots an autocorrelations. Similarity plot for pendulum. Darker pixels are more similar. Autocorrelation of similarity plot. Similarity plot for pendulum.