Abstract
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 \(\rho _a(y)\) which conform to Weber’s model, (b) complete description of the dominant asymptotic behaviour of the density functions \(\rho _a(y)\) for \(y \rightarrow \infty \) and \(y \rightarrow 0^+\) for the cases (i) \(0< a < 1\) and (ii) \(a > 1\), (c) a method of computing the asymptotic expansion of \(\rho _a(y)\) for \(y \rightarrow \infty \) to any number of terms for the case \(0< a < 1\).
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Acknowledgements
We gratefully acknowledge that this research has been supported in part by the Natural Sciences and Engineering Research Council of Canada (ERV) in the form of a Discovery Grant as well as Assistantships from the Department of Applied Mathematics and the Faculty of Mathematics, University of Waterloo (DL).
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Li, D., La Torre, D., Vrscay, E.R. (2019). Existence, Uniqueness and Asymptotic Behaviour of Intensity-Based Measures Which Conform to a Generalized Weber’s Model of Perception. In: Karray, F., Campilho, A., Yu, A. (eds) Image Analysis and Recognition. ICIAR 2019. Lecture Notes in Computer Science(), vol 11662. Springer, Cham. https://doi.org/10.1007/978-3-030-27202-9_27
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DOI: https://doi.org/10.1007/978-3-030-27202-9_27
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