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IEEE Trans Image Process. 2010 Feb;19(2):491-511. doi: 10.1109/TIP.2009.2035980. Epub 2009 Nov 24.

Fractional differential mask: a fractional differential-based approach for multiscale texture enhancement.

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  • 1School of Computer Science andTechnology, Sichuan University, 610065 Chengdu, China.


In this paper, we intend to implement a class of fractional differential masks with high-precision. Thanks to two commonly used definitions of fractional differential for what are known as GrUmwald-Letnikov and Riemann-Liouville, we propose six fractional differential masks and present the structures and parameters of each mask respectively on the direction of negative x-coordinate, positive x-coordinate, negative y-coordinate, positive y-coordinate, left downward diagonal, left upward diagonal, right downward diagonal, and right upward diagonal. Moreover, by theoretical and experimental analyzing, we demonstrate the second is the best performance fractional differential mask of the proposed six ones. Finally, we discuss further the capability of multiscale fractional differential masks for texture enhancement. Experiments show that, for rich-grained digital image, the capability of nonlinearly enhancing complex texture details in smooth area by fractional differential-based approach appears obvious better than by traditional intergral-based algorithms.

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