A new view of shape

A new theory that qualitatively and quantitatively describes shape is presented. Signals are treated as ordered sets and shape as a property of the order. Measures of shape are derived starting from simple two element sets. It is shown that the degree of asymmetry of relative contrast at various scales is a sufficient descriptor of shape. The shape of a signal is a composite of the shape of all possible ordered subsets. A distinction is drawn between statistical and shape measures within a unified theoretical framework which may make it possible compare diverse pattern recognition approaches in terms robustness and discrimination power.