A wide range of techniques can be considered for segmentation of images of nanostructured surfaces. Manually segmenting these images is time-consuming and results in a user-dependent segmentation bias, while there is currently no consensus on the best automated segmentation methods for particular techniques, image classes, and samples. Any image segmentation approach must minimise the noise in the images to ensure accurate and meaningful statistical analysis can be carried out. Here we develop protocols for the segmentation of images of 2D assemblies of gold nanoparticles formed on silicon surfaces via deposition from an organic solvent. The evaporation of the solvent drives far-from-equilibrium self-organisation of the particles, producing a wide variety of nano- and micro-structured patterns. We show that a segmentation strategy using the U-Net convolutional neural network outperforms traditional automated approaches and has particular potential in the processing of images of nanostructured systems.