Supplementary Figure 1: Principles of persistence clustering with watershed
From: Fast, accurate reconstruction of cell lineages from large-scale fluorescence microscopy data
(a) One-dimensional example of a watershed. The function profile is segmented into three basins (red, blue, orange) by grouping convex segments associated with the same local minima.
(b) Graphical representation using a dendrogram of how persistence-based clustering (PBC) can establish a hierarchical order for merging the different regions generated by the watershed in (a). In order to merge two regions, the parameter τ needs to be set to a value higher than the difference between the function value at the contact point between the two regions and the higher of the two local minima. Every time two regions in the dendrogram are merged, the τ value for the next merge can change. Thus, the dendrogram needs to be calculated sequentially. For example, the merging of region 1 (red) and region {2,3} (blue plus orange) is associated with a τ equal to f1,{2,3} instead of f1,2, since region 3 has a lower local minimum than region 1.
