Existence, Uniqueness and Asymptotic Behaviour of Intensity-Based Measures Which Conform to a Generalized Weber's Model of Perception

摘要

In this paper, we report on further progress on our study of "Weberized" metrics for image functions presented at ICIAR 2018. These metrics allow greater deviations at higher intensity values and lower deviations at lower intensity values in accordance with Weber's model of perception. The purpose of this paper is to address some important mathematical details that were not considered in the ICIAR 2018 paper, e.g., (a) proving the existence and uniqueness of greyscale density functions pa{y) which conform to Weber's model, (b) complete description of the dominant asymptotic behaviour of the density functions pa(y) for y —> oo and y —* 0+ for the cases (i) 0 < o < 1 and (ii) a > 1, (c) a method of computing the asymptotic expansion of pa{y) for y —► oo to any number of terms for the case 0 < a < 1.