Elena Gribelyuk '18 to Compete in the Regeneron Science Talent Search and the Siemens Competition in Math, Science & Technology

Have you ever had an MRI? If so, you have probably been inside a very large, very loud machine wondering to yourself, "How does this thing work?" This summer, Senior Elena Gribelyuk had the opportunity to work with Dr. Baba Vemuri, Professor in the Department of Computer and Information Science and Engineering and also Director of the Center for Vision Graphics and Medical Imaging, to improve how the images from an MRI are constructed. You can find out more about Dr. Vemuri here.

Elena spent eight weeks at the University of Florida as part of a high school science enrichment program. She developed a novel computer algorithm that improves upon the conventional approaches that are used for filtering and enhancing image data. Elena's work has far-reaching implications in fields that require fast and reliable routines for processing high-resolution images of three-dimensional objects. Her algorithm has already been tested and proven to work on high quality magnetic resonance imaging (MRI) data. Perhaps Elena's contribution to the field will someday improve the accuracy with which doctors can diagnose diseases using MRI data.

Elena will be entering the results of her research in the two most elite high school Science competitions in the nation: the Regeneron Science Talent Search and the Siemens Competition in Math, Science & Technology. The Regeneron Science Talent Search competition usually has about 1700 entrants and is the oldest contest in the United States. The top 300 students are honored as Regeneron Scholars. The top 40 students compete for cash prizes with $250,000 awarded to the winner. Elena is the first King student in the history of the school to enter these contests. Next year, King hopes to have several of its Advanced Math/Science Research students enter the contests.

"It was an honor to work in Dr. Vemuri's lab, where I was exposed to the elegant applications of Mathematics and Computer Science to the field of Medical Image Analysis. It is rewarding to think that the algorithms we developed this summer may reduce the chance of medical misdiagnosis and thus improve the care of patients, " said Elena.

Elena's paper is titled: Efficient Recursive Bilateral Filters for Symmetric Positive Definite Matrix-valued Images

Kurt Schleunes, Mathematics Faculty, Co-Chair Mathematics Department provided Elena's abstract: Bilateral filtering has had great success in the field of image processing due to the feature-preserving nature of filters. However, its popularity has been stifled until recently due to the filter's high computational complexity. In 2015, Q. Yang introduced an efficient recursive implementation of the bilateral filter [1], leading to immense computational gains over traditional non-recursive algorithms. Motivated by the lack of generalization of recursively-defined filters to matrix-valued images, we propose a suite of non-recursive and recursive algorithms for de-noising. These algorithms function to noninvasively probe neural tissue microstructures. Therefore, through this paper, three non-recursive and two recursive bilateral filtering algorithms are proposed, employing disparate distance metrics in computations. Specifically, non-recursive implementations calculate output tensor fields using the Euclidean, log-Euclidean, and affine-invariant distances, and recursive algorithms employ the Euclidean and log-Euclidean distances for noise-reduction. The key contributions of this paper are: (i) To the best of our knowledge, we present the first recursive bilateral filtering implementations for SPD matrix fields utilizing Euclidean and log-Euclidean metrics. (ii) We also demonstrate the efficacy of the programs through the lower runtime, presenting the comparative timing results for calculating output diffusion tensor fields. (iii) Finally, we show the accuracy of filters using disparate distance metrics, analyzing the distance formulas for both filtering and detail preservation in the context of de-noising diffusion tensor fields. Runtimes of proposed recursive algorithms contrast significantly with the execution speeds of other novel, non-recursive implementations of bilateral filtering.