Interfacial adsorbate organization influences a variety physicochemical properties and reactivity. Surfaces that are rough, defect laden, or have large fluctuations (as in soft matter interfaces) can lead to complex adsorbate structures. This is amplified if adsorbate-adsorbate interactions lead to self-assembly. Although image analysis algorithms are somewhat common for the study of solid interfaces (from microscopy for example), images are often not readily available for adsorbates at soft matter surfaces, and the complexity of adsorbate organization necessitates the development of new characterization approaches. Here we propose the use of adsorbate "density" images from molecular dynamics simulations of liquid/vapor and liquid/liquid interfaces. Topological data analysis is employed to characterize surface active amphiphile self-assembly under nonreactive and reactive conditions. We develop a chemical interpretation of sublevelset persistent homology barcode representations of the density images, in addition to descriptors that clearly differentiate between different reactive and nonreactive organizational regimes. The complexity of amphiphile self-assembly at highly dynamic liquid/liquid interfaces represents a worst-case scenario for adsorbate characterization, and as such the methodology developed is completely generalizable to a wide variety of surface image data, whether from experiment or computer simulation.