Art pieces that 'move' in our minds - an explanation of illusory motion based on depth reversal

Certain art forms, such as Patrick Hughes's 'reverspectives', Dick Termes's 'Terme-spheres', 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.