Metal additive manufacturing surface topographies are complex and challenging to characterise due to e.g. steep local slopes, re-entrant features, varying reflectivity and features of interest in vastly different scale ranges. Nevertheless, average height parameters such as Ra or Sa are commonly used as sole parameters for characterisation. In this paper, a novel method for selecting relevant parameters for evaluation is proposed and demonstrated using a case study where the smoothing effects after three processing steps of the electro chemical post-process Hirtisation of a metal AM surface are quantified. The method uses a combination of conventional areal texture parameters, multiscale analysis and statistics and can be used to efficiently achieve a detailed and more relevant surface topography characterisation. It was found that the three process steps have different effects on the surface topography regarding the types and sizes of features that were affected. In total, Sdq was reduced by 97 %, S5v was reduced by 81 % and Sa was reduced by 78 %. A surface texture with much lower average roughness, less deep pits and less steep slopes was produced, which is expected to be beneficial for improved fatigue properties.