Date of Award

January 2019

Degree Type

Open Access Thesis

Document Type

Master Thesis

Degree Name

Master of Science (MS)


Mathematics and Statistics

First Advisor

Atilla Sit

Department Affiliation

Mathematics and Statistics

Second Advisor

Steve Szabo

Department Affiliation

Mathematics and Statistics

Third Advisor

Eugene Styer

Department Affiliation

Mathematics and Statistics


It is known that image comparison can prove cumbersome in both computational complexity and runtime, due to factors such as the rotation, scaling, and translation of the object in question. Due to the locality of Krawtchouk polynomials, relatively few descriptors are necessary to describe a given image, and this can be achieved with minimal memory usage. Using this method, not only can images be described efficiently as a whole, but specific regions of images can be described as well without cropping. Due to this property, queries can be found within a single large image, or collection of large images, which serve as a database for search. Krawtchouk descriptors can also describe collections of patches of 3D objects, which is explored in this paper, as well as a theoretical methodology of describing nD hyperobjects. Test results for an implementation of 3D Krawtchouk descriptors in GNU Octave, as well as statistics regarding effectiveness and runtime, are included, and the code used for testing will be published open source in the near future.