Numerical Schemes for the Fractional Calculus and their Application to Image Feature Detection
Date
2018-06-08
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Fractional 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.
Description
Keywords
Fractional Calculus, applied mathematics, Numerical Methods, mathematical software, image processing
Citation
Adams, 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/31994