Testing the reliability of bonded joints in material assemblies is one of the major subjects in the aeronautical industry. One of the methods for characterizing adhesion is based on the study of the roughness of the fracture surfaces of assemblies. In this study, the interest is focused on the quantication of the adhesion of the bonded structure by the corner cleavage test, allowing the study of crack propagation within bonded assemblies. Optical prolometry measurements, obtained by scanning the surface of the fractured surfaces of monoadhesives: ABT M52, copolymer-doped and non-nanostructured AHT are used. The aim of the prolometric study is to quantify surface roughness. To go further than traditional methods of characterizing roughness, we analyze the proles using mathematical methods to conrm the ex- perimental studies and extract more geometric information. We apply various techniques of topological data analysis (TDA) to extract the topological features of the proles. These techniques recover experi- mental elements in a quantitative manner. Persistence diagrams give us a multi-scale characterization of the rupture facies, attesting the voids, micro-cracks at nano-level, quantifying the maximum amplitude of the peaks at micro level. We extract features vectors using persis- tent images for each prole and we look for similarities in persistence diagrams using Bottleneck and Wasserstein distances in perspective of a machine learning application in a future study. Then the proles were studied by Takens embedding which will produce a point cloud analyzed by homological persistence in order to produce indications of periodicity or quasi-periodicity. This computational topological ap- proach makes it possible to extract the essential characteristics of the 2 surface and roughness of the prole of the adhesives in order to con- clude on their toughness and fracture resistance.