Symmetry and Resonance in Visual Perception
Abstract
Whether designing animals, insects, or plants, Nature draws upon symmetry and periodicity to play a fundamental role in defining the body plan. When implemented with the proper chemical mechanisms, these principles guide our bodies from single-celled embryos to bilaterally symmetric creatures with intricate periodic structures, such as the spine and rib cage. The properties of symmetry and periodicity also appear to be fundamental to visual perception. We will show that this is no coincidence, but is a consequence of the fact that these properties are generated by the same underlying phenomenon, standing wave patterns formed from harmonic resonances. The symmetry in life forms arises from chemical harmonic resonances, whereas the symmetry in visual perception arises from harmonic resonances in the visual system. We will show that harmonic resonances have very interesting properties for the representation of geometrical form that make them eminently suitable for encoding geometric form for body plans as well as for visual perception. In particular, we will show that by being simultaneously invariant to perspective transformation and robust to deformation, such resonant representations have fundamental advantages over more traditional techniques.