Symmetry as a fundamental feature dimension in mid-level vision
Peter J. Kohler
Stanford, Psychology Department
Symmetries are present at many scales in images of natural scenes, due to a complex interplay of physical forces that govern pattern formation in nature. The importance of symmetry for visual perception was first understood by the gestalt movement in the early 20th century, and has since been explored by a substantial literature, mostly focused on reflection. I have taken a broader approach, and studied symmetry in the context of “wallpaper” groups – a class of regular 2-D textures that comprise 17 distinct combinations of the four fundamental symmetries: reflection, rotation, translation and glide reflection. Among the 17 wallpaper groups, there is a well-defined hierarchy of complexity, where simpler groups are sub-groups of more complex ones. Here I present a series of experiments in which algorithmically generated exemplar textures from the 17 wallpaper groups were used as stimuli. I apply a multi-modal imaging approach to show that human visual cortex carriers highly ordered representations of the fundamental symmetries, that closely approximate the subgroup relationships from group theory. These representations arise in a feedforward manner, beginning as early as area V3, and are most robust in LOC and ventral areas V4 and VO1, with the latter being the primary driver of perceptual decisions about symmetry. These results suggest that symmetry is a fundamental feature dimension in mid-level vision, and part of an encoding strategy that has likely been learned implicitly from regularities in the environment.