Construction of a novel convolution based fractional derivative mask for image edge analysis

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AUGUST, 2016
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This thesis presents a new approach in constructing a more e efficient fractional derivative mask for image edge analysis based on the ddefinition and properties of convolution. By the defi nition of convolution, the generalised Strivastiva-Owa's operator was rewritten with its order restricted to the Riemann-Liouville fractional derivative. Applying linearity, commutative and derivative properties of convolution to the resultant expression, a new mask with higher effi ciency, memory eff ect and computational equivalence to the classical edge detector is developed as per the experimental results obtained. From the experimental results, it is observed that, the new mask has the potency to find edges in details quite signifi cantly as well as hidden edges which is a deffi ciency of the classical edge detectors. It can also be used on a region growing algorithm during region segmentation acting as an edge function in its termination process. 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 signifi cant advantages over other known methods.
A thesis submitted to the Department of Mathematics,Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the Degree of Doctor of Philosophy in Applied Mathematics.