Symmetry has a central role in the study of vision. The concept of symmetry has an ancient origin in considerations of visual appearance; in modern times, abstracted and formalized into Group Theory, it has found spectacular applications, far beyond the visible; but its importance for vision persists in many ways including: • As a non-accidental feature of an image that cues affordances, 3D structure or the semantic categories of object present. • As a redundant aspect of an image which many be exploited for simplicity and compactness of encoding. • As a salient feature that draws attention, and evokes distinctive brain responses. • As a constraint on priors on the distribution of structures to be found in the natural world. • As an aesthet...