Symmetropy,an entropy-like measure of visual symmetry

A new objective measure of symmetry for single patterns, called symmetropy, is developed on two bases, the two-dimensional discrete Walsh transform of a pattern and the entropy concept in information theory. It is extended to a more general measure, called the symmetropy vector. In order to test the predictive power of the symmetropy vector, multiple regression analyses of judged pattern goodness and of judged pattern complexity were carried out. The analyses show that the symmetropy vector predicts pattern goodness and pattern complexity, as well as the amount of symmetry in a pattern. They also suggest that pattern goodness is a concept based on the holistic properties of a pattern, while pattern complexity (or simplicity) is a concept based on both holistic and partial properties of a pattern.