Visual Illusions of Angle as an Application of Lie Transformation Groups
William C. Hoffman · SIAM Review · 1971
Visual illusions of angle are explained in terms of a calculus of visual constancies laid down earlier as misapplication of constancy. The rule is as follows : Identify the curves appearing in the visual illusion as orbits of the appropriate visual constancy (or constancies). Keep the Lie derivative that corresponds to the constancy whose orbit(s) appear distorted in the illusion, but replace the other by the Lie derivative orthogonal to it. Form a linear combination of the resulting two Lie derivatives, weighting the one that is kept the more strongly. This linear combination will generate the distorted portion of the illusion.