Natural Numbers, Natural Shapes

Abstract

We explain the general significance of integer-based descriptors for natural shapes and show that the evolution of two such descriptors, called mechanical descriptors (the number N(t) of static balance points and the Morse–Smale graph associated with the scalar distance function measured from the center of mass) appear to capture (unlike classical geophysical shape descriptors) one of our most fundamental intuitions about natural abrasion: shapes get monotonically simplified in this process. Thus mechanical descriptors help to establish a correlation between subjective and objective descriptors of perceived objects.