Apparent motion is the perception of motion created by rapidly presenting still frames in which objects are displaced in space. Observers can reliably discriminate the direction of apparent motion when inter-frame object displacement is below a certain limit, Dmax. Earlier studies of motion perception in humans found that Dmax is lower-bounded at around 15 arcmin, and thereafter scales with the size of the spatial elements in the images. Here, we run corresponding experiments in the praying mantis Sphodromantis lineola to investigate how Dmax scales with the element size. We use random moving chequerboard patterns of varying element and displacement step sizes to elicit the optomotor response, a postural stabilization mechanism that causes mantids to lean in the direction of large-field motion. Subsequently, we calculate Dmax as the displacement step size corresponding to a 50% probability of detecting an optomotor response in the same direction as the stimulus. Our main findings are that the mantis Dmax scales roughly as a square-root of element size and that, in contrast to humans, it is not lower-bounded. We present two models to explain these observations: a simple high-level model based on motion energy in the Fourier domain and a more-detailed one based on the Reichardt Detector. The models present complementary intuitive and physiologically-realistic accounts of how Dmax scales with the element size in insects. We conclude that insect motion perception is limited by only a single stage of spatial filtering, reflecting the optics of the compound eye. In contrast, human motion perception reflects a second stage of spatial filtering, at coarser scales than imposed by human optics, likely corresponding to the magnocellular pathway. After this spatial filtering, mantis and human motion perception and Dmax are qualitatively very similar.