Numerical Schemes for the Fractional Calculus and their Application to Image Feature Detection

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dc.contributor.advisorLiao, Wenyuan
dc.contributor.advisorBoyd, Jeffrey Edwin
dc.contributor.authorAdams, Matthew Paul
dc.contributor.committeememberAiffa, Mohammed
dc.contributor.committeememberRios, Cristian
dc.date2018-11
dc.date.accessioned2018-06-20T21:16:46Z
dc.date.available2018-06-20T21:16:46Z
dc.date.issued2018-06-08
dc.description.abstractFractional 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.en_US
dc.identifier.citationAdams, 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/31994en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/31994
dc.identifier.urihttp://hdl.handle.net/1880/106768
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.facultyScience
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity 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.
dc.subjectFractional Calculus
dc.subjectapplied mathematics
dc.subjectNumerical Methods
dc.subjectmathematical software
dc.subjectimage processing
dc.subject.classificationMathematicsen_US
dc.subject.classificationApplied Sciencesen_US
dc.titleNumerical Schemes for the Fractional Calculus and their Application to Image Feature Detection
dc.typemaster thesis
thesis.degree.disciplineMathematics and Statistics
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameMaster of Science (MSc)
ucalgary.item.requestcopytrue
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