Hierarchical crack patterns: Identification of crack generations

Identifying crack generations from microscopic images of hierarchical crack patterns is challenging due to the lack of temporal information and sensitivity to image boundaries. Existing algorithms often fragment individual cracks or lose stability when the observed fragment is shifted. We propose a method that reduces the classification problem to topological sorting of a directed acyclic graph (descendant$\to$parent), built from T-junctions and nearly collinear edges. Sequential removal of leaf vertices assigns generation numbers starting from the youngest. On 100 computer-generated networks, our method correctly classifies $\approx 70$\% of cracks at a window size of only three mean edge lengths, whereas a conventional approach that starts from primary cracks drops nearly to zero. The classification is highly stable against reasonable shifts of image boundaries but remains limited to strictly hierarchical networks.