Curve-like sets, normal complexity, and representation

Abstract

Proposes a theory of the complexity of curves that is sufficient to separate those which extend along their length (e,g., in one dimension) from those that cover an area (e.g., 2-D). The theory is based on original results in geometric measure theory, and is applied to the problems of (i) perceptual grouping and (ii) physiological interpretation, of axonal arbors in developing neurons.