Illustration of the persistence parameter of the DisPerSE algorithm. It shows a 1D function, with red dots as maxima and blue dots as minima. The left column is the actual function to which the persistence threshold is applied, and the right column shows the result after this threshold is applied. The length between the dashed purple lines represents the persistence threshold in that case. The green arrows represent the smoothing of the curve when the corresponding critical points are removed. This illustration is inspired by Sousbie (2011).