A descriptive model for perception of optical illusions

The apparent curves of stable geometrical illusions of angle are modeled by a first-order differential equation depending on a single parameter, called the strength of the illusion. The model is based on Brentano's theory that the human visual system tends to overestimate acute angles. It is mathematically equivalent to Hoffman's Lie-theoretic model (SIAM Review, 13 (1971), pp. 169–184) except for some deficiencies of detail in Hoffman's approach which are noted and corrected. By reversing the sign of the strength parameter, “correction” curves may be plotted which cause the illusion to “disappear,” thereby demonstrating the effectiveness and accuracy of the model. The method is illustrated with the classical illusions of Poggendorff, Zöllner, Hering, Orbison, Ponzo, and Müller-Lyer.