Statistical Assessment of Self-Affine Methods Applied to Short Profiles

Considering the small range of values that the self-affine exponent can take (0 to 1), the accuracy and precision of its determination are very important when it is used as a characteristic related to the evolution of physical phenomena or to the morphological nature of objects. In this work, a careful statistical evaluation of four common self-affine determination methods, applied to synthetic small profiles (N = 512) is reported. Accuracy, precision, confidence in the linear interval selection and computation speed are the parameters used to evaluate box counting (BC), rescaled-range analysis (Zmax), covariance analysis (Zdev) and wavelet transform (Wt) methods applied to profiles synthesized using the Weierstrass-Mandelbrot function (WMf) and the middle point displacement (Mp) methods. The results show that the log-log plot from which the self-affine exponent is computed, does not have the linear form of the BC and Zmax methods; the Wt and Zstd are the most accurate while Wt has the lowest precision. In light of these results, it is recommended to use only the Zstd or Wt methods for sample sizes of more than 100 profiles.