Prof Alain Goriely (University of Oxford)

Seeing is deceiving: The mathematics of visual illusions

Illusions have been a constant source of amusement but they are also a unique gateway into understanding the way we perceive the world and how the brain processes information. The simplest visual illusions often involve a primary element—be it a line or a circle—that undergoes deformation or displacement due to the influence of surrounding elements, such as additional lines or dots. Mathematically, these deformations can be modelled as transformations in the plane. I will show that that these perceptual interactions between different elements can indeed be modelled through universal visual laws inducing small deformations and explaining a wide range of illusions. Moreover, these laws find their foundations in models of our visual processing system that exhibits a rich geometric structure, thereby forging a direct connection between the processing of geometric information in our brain and the emergence of illusions.