A researcher from Florida State University will utilize new funding to enhance the artificial intelligence and machine learning frameworks that facilitate 3D modeling systems applied in medicine, scientific inquiry, computer graphics, and various visualization-oriented domains.
Martin Bauer, Associate Professor of Mathematics, will spearhead a multidisciplinary group focused on advancing the development of 3D models, including those that underpin medical imaging for diagnostic and observational uses, enlarged cellular architecture utilized in biological laboratories, and the digital graphics and CGI employed in film and video game industries.
“Our objective is to examine intricate data structures from existing 3D models and refine the algorithms that drive them, thereby producing more precise models in medical prosthetics, graphic design prototyping, architectural frameworks, manufacturing of tailored components, and beyond,” Bauer stated.
A collaborative grant from the National Science Foundation (NSF) and the French National Research Agency encompasses over $650,000 in funding, with $300,000 directly granted by the NSF to Florida State.
HOW IT FUNCTIONS
The researcher will merge techniques from shape analysis — a domain within computational geometry and image processing that employs methodologies to depict, compare, and recognize geometric forms — with infinite-dimensional differential geometry, which investigates diverse geometric structures and characteristics in limitless dimensional spaces.
“With this research, we aim to devise groundbreaking algorithms for comprehending and modeling the intricate distortions occurring in the real-world dynamics of 3D objects,” Bauer commented. “This will consequently enable us to develop new techniques for more accurately executing 3D modeling and printing endeavors across various applications.”
Bauer’s inquiry amalgamates abstract mathematics, emphasizing overarching concepts and theories, with applied mathematics that focuses on specific challenges, equations, and real-life constructs.
APPLICATIONS AND INFLUENCE
Bauer’s work has implications in data science, AI, shape analysis, and medical imaging. He frequently collaborates with biomedical engineers, biologists, computer scientists, and other specialists to assess how best to assist them within their unique disciplines while integrating foundational mathematical concepts, such as how algebra techniques are utilized for digitally manipulating alterations made to 3D models.
The creation, processing, and printing of 3D projects rely on mesh extraction, a computer graphics technique that digitally compiles shapes to construct the surface and structure of a 3D object. The team’s optimized algorithms will enhance models produced via mesh extraction based on scans of real-world entities.
“This endeavor is particularly timely due to recent advancements in 3D scanning and mesh extraction technologies,” noted Ettore Aldrovandi, chair of the Department of Mathematics. “It holds the promise for transformative effects in augmented reality, where digital graphics are displayed so users can view them in the actual world through a phone camera, and virtual reality, where computer-generated simulations immerse users in alternate realities. This influence will also aid in establishing new mathematical frameworks for shape analysis.”
Further applications of this research include bolstering 3D modeling in platforms accessible on smartphones. While AI and ML have broadened access to such software, these applications can produce flawed scans due to inconsistent performance in executing computational and graphical tasks.
“We aim to merge the methodologies developed in this project with algorithms from large language models, such as ChatGPT, to further augment contemporary software’s text-to-3D functionalities,” Bauer remarked. “The advancements witnessed in recent times in deep learning, AI, and ML are driven by mathematics and computer science. We still have much to explore regarding the forces behind these innovations and must continue to expand the limits of feasibility for applying these novel approaches in 3D modeling.”
STUDENT RESEARCH AND GLOBAL COLLABORATIONS
Through this collaborative funding, Bauer’s graduate students will have the chance to travel to Houston to analyze data, test models, and foster additional connections. Graduate students engaged in the research at the University of Houston will also visit FSU to observe segments of the research.
“Dr. Bauer’s grant signifies important progress in the application of topological data analysis — examining properties of shapes and spaces that remain invariant when transformed but not disrupted — and shape analysis to human body modeling,” Aldrovandi stated. “This research intends to create solid geometric deep learning models capable of managing raw 3D data regardless of the methods used for data collection, with applications ranging from body motion generation to facial expression assessment.”
Other contributors to this research include Bauer’s long-time collaborator Nicolas Charon, a mathematics professor at the University of Houston in Texas; Mohamed Daoudi, a computer science professor at IMT Nord Europe — a graduate engineering institution affiliated with the University of Lille — located in Villeneuve-d’Ascq, France; and Sylvain Arguillère, a researcher at the University of Lille in France.
For more information regarding the research conducted in FSU’s Department of Mathematics, please visit math.fsu.edu.
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