Measuring picometre-scale shifts in the positions of individual atoms in materials provides new insight into the structure of surfaces, defects and interfaces that influence a broad variety of materials' behaviour. Here we demonstrate sub-picometre precision measurements of atom positions in aberration-corrected Z-contrast scanning transmission electron microscopy images based on the non-rigid registration and averaging of an image series. Non-rigid registration achieves five to seven times better precision than previous methods. Non-rigidly registered images of a silica-supported platinum nanocatalyst show pm-scale contraction of atoms at a (111)/(111) corner towards the particle centre and expansion of a flat (111) facet. Sub-picometre precision and standardless atom counting with <1 atom uncertainty in the same scanning transmission electron microscopy image provide new insight into the three-dimensional atomic structure of catalyst nanoparticle surfaces, which contain the active sites controlling catalytic reactions.