When
Tuesday, May 6, 2025 at 4:00 p.m.
John Fox
PhD Candidate
Aerospace and Mechanical Engineering
University of Arizona
"Peridynamic Enabled Fuzzy Logic for Image Analysis and Enhancement"
AME Lecture Hall, Room S212
Zoom link
Abstract: The Peridynamic Differential Operator (PDDO) allows a precise numerical approximation of derivatives. It owes its origin to Peridynamics. Which is a nonlocal theory that approximates interactions between material points located within a finite radius referred to as the ‘horizon’. The nonlocal interaction between material points can be approximated with a Gaussian weight. The PD functions for the derivatives are determined directly by making them orthogonal to every term in the Taylor Series Expansion (TSE) except for the term with the desired derivative. Many image analysis and enhancement tasks are achieved via numerical approximation of derivatives. Two of them are edge detection and noise elimination, respectively. Given the computational complexity when calculating the PD functions, they are placed in a kernel and reinterpreted as a digital filter. We named it the PDDO Kernel. The constant size and distance between pixels also enabled the creation of the PDDO Kernel. In the case of edge detection, the PDDO kernel allows us to have a better hypothesis of edge location. By using the power of Fuzzy Logic, which reinterprets uncertainty, we have created a robust edge detection methodology that allows precise edge detection in the presence of noise.
Bio: John Raphael Fox is a PhD candidate at the University of Arizona in the Department of Aerospace and Mechanical Engineering with a major focused in Solid Mechanics and a minor in Electrical Engineering. In 2006 he earned a BS degree in physics from the University of Sonora, in Hermosillo, Sonora, Mexico where he did research in particle physics. The topic of his dissertation was, "The Extension of the Higgs Mechanism with SO(2) Symmetry." From 2007 until 2017 he was a mathematics teacher where he taught from 6th to 12th grade, specializing in middle school mathematics. At the end of this time frame, he also tutored engineering and physics students. In 2017 he decided to reinvent himself as an engineer and studied for a MS in engineering degree from Arizona State University. During this time, he specialized in software engineering and machine learning and artificial intelligence. From April 29,2019 through April 29, 2025, he worked at Raytheon Technologies in the Department of Signal Processing and Algorithms where he helped multiple programs solve complex problems and meet deadlines. He has experience in algorithm development, simulation model development, radar signal processing, electronic warfare, electronic countermeasures, digital wireless communications, and tactical software testing in hardware in the loop and software integration and testing laboratories.