A new construction of a fractional derivative mask for image edge analysis based on Riemann-Liouville fractional derivative

Advances in Difference Equations

Peter Amoako-Yirenkyi¹  Isaac Kwame Dontwi¹  Justice Kwame Appati² 

[1] Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana;Scientific and Technical Computing Centre, National Institute for Mathematical Sciences, Kumasi, Ghana

关键词: convolution;    fractional integral;    fractional derivative;    edge detection;    Riemann-Liouville;   

DOI  :  10.1186/s13662-016-0946-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY