Fractional directional differentiation and its application for multiscale texture enhancement
type: Item
instance of: scholarly article
title: Fractional directional differentiation and its application for multiscale texture enhancement
zbMATH Open document ID: 1264.94046
DOI: 10.1155/2012/325785
author: Ji-Liu Zhou
author: Chaobang Gao
author: Wei-Hua Zhang
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: We derive the directional derivative expression of Taylor formula for two-variable function from Taylor formula of one-variable function. Further, it proposes a new concept, fractional directional differentiation (FDD), and corresponding theories. To achieve the numerical calculation, the paper deduces power series expression of FDD. Moreover, the paper discusses the construction of FDD mask in the four quadrants, respectively, for digital image. The differential coefficients of every direction are not the same along the eight directions in the four quadrants, which is the biggest difference by contrast to general fractional differentiation and can reflect different fractional change rates along different directions, and this benefits to enlarge the differences among the image textures. Experiments show that, for texture-rich digital images, the capability of nonlinearly enhancing comprehensive texture details by FDD is better than those by the general fractional differentiation and Butterworth filter. By quantity analysis, it shows that state-of-the-art effect of texture enhancement is obtained by FDD.
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 6173189
MaRDI profile type: Publication
Wikidata QID: Q58911434
full work available at URL: https://doi.org/10.1155/2012/325785
OpenAlex ID: W2014324260
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description: scientific article; zbMATH DE number 6173189