From image formation to image representation: the human visual system preserves the hierarchy of 2-dimensional pattern regularity

Abstract

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 has been known at least since the gestalt movement of the early 20th century. Since then, symmetry has been shown to contribute to the perception of shapes[1, 2] scenes[3] and surface properties[4], as well as the social process of mate selection[5]. In the two spatial dimensions relevant for images, the four fundamental symmetries, reflection, rotation, translation and glide reflection, can be combined in 17 distinct ways, the \"wallpaper\" groups[6-8]. The 17 wallpaper obey a hierarchy of complexity, determined by mathematical group theory, where simpler groups are subgroups of more complex ones[9]. Here we use Steady-State Visual Evoked Potentials (SSVEPs) to measure responses to the complete set of wallpaper groups, and present a complete description of the neural basis of symmetry. We find that activity in human visual cortex is remarkably consistent with the hierarchical relationships between the wallpaper groups. Specifically, the amplitudes of symmetry-specific responses in individual participants (n=25) preserve these relationships at an above-chance level in 88.3% (53 out of 60) of cases. Visual cortex thus encodes all the fundamental symmetries using a representational structure that closely approximates the subgroup relationships from group theory. Given that most participants had no knowledge of group theory, the ordered structure of visual responses to wallpaper groups is likely learned implicitly from regularities in the visual environment.