Quincy University’s visiting professor of mathematics, Congzhi Xia, Ph.D., recently co-authored an article entitled “Admissible Concentration Factors for Edge Detection from Non-uniform Fourier Data.” The article was published in the Journal of Scientific Computing, Volume 85, Article number three, in September 2020.
Edge detection from Fourier data has been emerging in many applications. The concentration factor method has been widely used in detecting edges from Fourier data. The article presents a theoretic analysis of the concentration factor method for non-uniform Fourier data in this paper. Specifically, the authors propose admissible conditions for the concentration factors such that the edge detector converges to a smoothed approximation of the jump function. Moreover, they also introduce some specific choices of admissible concentration factors and present estimates of convergence rates correspondingly.
“It is a truth universally acknowledged that mathematics not only is a beautiful subject but has remarkable applications at every level in the real world,” said Xia. “For example, detecting edges plays an important role in many applications, such as a brain tumor, or lane detection in autonomous driving.”
Xia co-authored the article with Guohui Song, Ph.D., and Gabe Tucker, both from the Department of Mathematics and Statistics, at Old Dominion University, in Norfolk, Va. Xia joined the QU faculty after earning a doctorate in mathematics from Clarkson University in 2019.
The Journal of Scientific Computing is an international interdisciplinary forum for the publication of papers on state-of-the-art developments in scientific computing and its applications in science and engineering. The journal publishes high-quality, peer-reviewed original papers, review papers and short communications on scientific computing.
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