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A new construction of a fractional derivative mask for image edge analysis based on Riemann-Liouville fractional derivative. (English) Zbl 1419.34009

Summary: We present a new way of constructing a fractional-based convolution mask with an application to image edge analysis. The mask was constructed based on the Riemann-Liouville fractional derivative which is a special form of the Srivastava-Owa operator. This operator is generally known to be robust in solving a range of differential equations due to its inherent property of memory effect. However, its application in constructing a convolution mask can be devastating if not carefully constructed. In this paper, we show another effective way of constructing a fractional-based convolution mask that is able to find edges in detail quite significantly. The resulting mask can trap both local discontinuities in intensity and its derivatives as well as locating Dirac edges. The experiments conducted on the mask were done using some selected well known synthetic and Medical images with realistic geometry. Using visual perception and performing both mean square error and peak signal-to-noise ratios analysis, the method demonstrated significant advantages over other known methods.

MSC:

34A08 Fractional ordinary differential equations
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
92C55 Biomedical imaging and signal processing
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