Certain art forms, such as Patrick Hughes's 'reverspectives', Dick Termes's 'Termespheres', intaglios, and hollow masks, appear to move vividly as viewers move in front of them, even though they are stationary. This illusory motion is accompanied by a perceived reversal of depth, where physical convex and concave surfaces are falsely seen as concave and convex, respectively. A geometric explanation is presented that considers this illusory motion as a result of the perceived depth reversal. The main argument is that the visual system constructs a three-dimensional representation of the surfaces, and that this representation is one of the sources that contribute to the illusory motion, together with vestibular signals of self-motion and signals of eye movements. This explanation is extended to stereograms that are also known to appear to move as viewers move in front of them. A quantitative model can be developed around this geometric explanation to examine the extent to which the visual system tolerates large distortions in size and shape and still maintains the illusion.