Journal
IEEE TRANSACTIONS ON IMAGE PROCESSING
Volume 19, Issue 2, Pages 491-511Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2009.2035980
Keywords
Fractional difference; fractional differential operator; fractional interpolation; multiscale fractional differential analysis; texture enhancement
Funding
- China National Nature Science Foundation [60972131]
- China Postdoctoral Science Foundation [20060401016]
- Fondation Franco-Chinoise Pour La Science Et Ses Applications (FFCSA)
- Doctor Foundation of China National Education Department [20060610021]
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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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