Vector Field Embedded Into Images, as Well as Into Gradient and Laplace Processed Images for Neural Networks Classification
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics
Date of Award
Spring 2025
Abstract
In this thesis, we developed a vector field called $\overline{\nabla}\hat{\psi}$ and investigated its features when embedded into both original and modified images. We applied two operators for modifying images: gradient and Laplacian. We then applied vector field to original and modified images to generate singular points and study the differences between the singular points of a vector field embedded into two kinds images. Convolutional Neural Networks (CNNs) were applied to classify both the original and embedded images across three public datasets: COIL-100, Fashion-MNIST, and Digit-MNIST. These datasets provided diverse testing environments: COIL-100 contains 2D images of 3D objects, Fashion-MNIST presents clothing items, and MNIST focuses on handwritten digits.The classification accuracy of the original databases and their embedded versions were evaluated with multiple statistical metrics and CNNs. The obtained results validated that the images with embedded vector field $\overline{\nabla}\hat{\psi}$ increased the machine learning statistics.
Advisor
Nikolay Sirakov
Subject Categories
Mathematics | Physical Sciences and Mathematics
Recommended Citation
Petrus-Nihi, Eluwumi Folake, "Vector Field Embedded Into Images, as Well as Into Gradient and Laplace Processed Images for Neural Networks Classification" (2025). Electronic Theses & Dissertations. 1252.
https://digitalcommons.tamuc.edu/etd/1252
