Descriptors of flatness and roughness

Abstract

SUMMARYThe two notions of flatness and roughness refer to local properties of the profiles and of the surfaces. They are defined in two‐ and three‐dimensional spaces. Flatness is the ratio of the measure of the surface divided by its projection, and roughness the average of the square of the mean curvature of the surface per unit area. Whatever the number of dimensions of the space is, both parameters are accessible from vertical plane sections. The problem of their digital version is discussed, and algorithms are given. The approach also applies for grey tone functions, in R2 and in R3. Finally the results are extended to the n‐dimensional case.