Non-invasive single-particle tracking techniques, such as positron emission particle tracking (PEPT), provide useful information about the behaviour of a representative particle moving in a bulk of similar particles in a rotating drum. The Lagrangian trajectories that they yield can be used to study, for example, particulate diffusion or granular interaction. However, often the Eulerian flow fields of the entire granular bed are more useful- they can be used to study segregation, for instance, or the evolution of the free surface of the bed. In this work, we present a technique for converting Lagrangian trajectories to Eulerian flow fields via a time-weighted residence time distribution (RTD) of the tracked particle. We then perform PEPT experiments on a mono-disperse bed of spherical particles in a cylindrical drum, rotated at various rates, and use the RTD procedure to obtain flow fields of the bed. We use these flow fields to investigate the effect of drum rotational speed on the shape and behaviour of a granular bed in a rotating drum, and the insights gained thereby to define a comprehensive set of surfaces- such as the bulk free surface- to divide the bed into regions of distinct granular behaviour. We further define scalar bed features- such as the centre of circulation of the bed- that can be used to quantitatively compare the behaviour of granular beds in rotating drums operated under various conditions. (C) 2016 Elsevier Ltd. All rights reserved.