Liao, WenyuanBoyd, Jeffrey EdwinAdams, Matthew Paul2018-06-202018-06-202018-06-08Adams, M. P. (2018). Numerical Schemes for the Fractional Calculus and their Application in Image Feature Detection (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/31994http://hdl.handle.net/1880/106768Fractional calculus is an extension of integer-order differentiation and integration which explains many natural physical processes. New applications of the fractional calculus are in constant development. The current thesis introduces fractional differentiation to feature detection in digital images. The Harris-Laplace feature detector is adapted to use the non-local properties of the fractional derivative to include more information about image pixel perturbations when quantifying features. Numerical schemes for the computation of fractional derivatives and integrals are also presented, and methods for increasing their computational efficiency are discussed. An implementation of some numerical algorithms is introduced in this thesis as the Python software package differint. The geometric and physical interpretations of fractional derivatives are also included. The work in this thesis shows that the use of fractional derivatives in the Harris-Laplace detector leads to higher repeatability when detecting features in grayscale images. Applications of this development are suggested.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.Fractional Calculusapplied mathematicsNumerical Methodsmathematical softwareimage processingMathematicsApplied Sciencesmaster thesis10.11575/PRISM/31994