Estimation of the fractal dimension of surface roughness in 2D and 3D modes by means of a new estimator taking into account the sampling problems

J.F. QUINIOU, G. REMOND, G.MONTEIL*, C. ROQUES-CARMES
LMS-ENSMM 25030 Besançon

Abstract : The methods of determining the fractal dimension -all approximately equivalent in theory- when they are applied to the study of digitized data, present different forms of convergence. The problem therefore exists in determining the measurement of the fractal dimension through estimators whose bias and variance will be first qualified on fractal functions of known dimensions. In this approach, a new estimator, adapted to the variation method, has been proposed for the sampled data z(x) with extrapolation to z(x, y) data.

*PSA – Centre Technique de Belchamp, 25420 Voujeaucourt