Luke Bagan

Date of Award

Fall 2023

Document Type

Open Access Thesis


Mechanical Engineering

First Advisor

Yi Wang


Edge determination is a challenging yet crucial step in the object detection process for images. It is the first in a multi-step process, serving as the foundation for all subsequent operations. Its accuracy directly affects the success of any future processing techniques and final detection. The challenge of edge detection is derived from a variety of factors, including noise, image sharpness, orientation, empirical parameters, and computational complexity. Many traditional kernel-based operators excel at tackling one of these problems, but trade off their ability to handle others. For example, the popular Sobel operator uses a horizontal and vertical constant high-pass kernel. The two kernels are used to tackle other operators’ challenges of directional propensity. Theoretically, the combined two kernels can estimate edge orientations with a certain degree of accuracy, however, the effectiveness of its two directional operators are not justified. This means it uses an arbitrary combination of the two kernels. Additionally, its high-pass nature amplifies noise, and the constant architecture of its kernel means it is unable to adapt to the varying light intensities in the photo. This presents large issues in localizing edges and accurately identifying them in the first place. Two new gradient detection kernels based on the two-dimensional high order Taylor Series expansion were proposed and constructed in MATLAB with the goal of tackling most of these problems. The key idea of the first kernel is to use a wide range of the pixels in view to suppress noise, hence improving the gradient intensities of edges. The second kernel builds on the first to leverage its noise suppression benefits while tackling an additional problem of degraded and low contrast edge boundaries. In principle, it can detect smooth lines in the presence of discontinuities and poor quality. The filter architecture allows for precise gradient calculation, edge detection, and orientation determination to less than one degree of the true value when faced with signal to noise ratios that exceed 0.75.


© 2024, Luke Bagan