FSU mathematician earns grant to improve algorithms, develop enhanced 3D modeling structures

A Florida State University researcher will use new funding to improve the artificial intelligence and machine learning models that support 3D modeling structures used in medicine, scientific research, computer graphics and other visualization-based fields.

Associate Professor of Mathematics Martin Bauer will lead an interdisciplinary team in enhancing creation of 3D models, such as those that support medical imaging for diagnostic and monitoring purposes, enlarged cell structure models used in biology laboratories, and the computer graphics and computer-generated imagery used in film and video game production.

“We plan to analyze complex structures of data from current 3D models and improve the algorithms powering them, which will generate more accurate models in medical prosthetics, graphic design prototyping, architecture systems, manufacturing customizable parts and other areas,” Bauer said.

The joint grant from the National Science Foundation (NSF) and the French National Research Agency includes more than $650,000 in funding, with $300,000 directly awarded by NSF to Florida State.

HOW IT WORKS
The researcher will integrate techniques from shape analysis — a field within computational geometry and image processing that uses methods to represent, compare and identify geometric shapes — with infinite-dimensional differential geometry, the study of different geometric structures and properties in spaces with unlimited dimensions.

“Through this work, we strive to develop innovative algorithms for understanding and modeling the complex deformations that occur in real-world processes of 3D objects,” Bauer said. “This will in turn allow us to develop new methods to more accurately execute 3D modeling and printing projects in all variations.”

Bauer’s research combines abstract mathematics, which focuses on general concepts and theories, and applied mathematics consisting of specific problems, equations, and real-world concepts.

APPLICATIONS AND IMPACT
Bauer’s research has applications in data science, AI, shape analysis and medical imaging. He routinely works with biomedical engineers, biologists, computer scientists and other professionals to determine how to best help them in their specific fields while incorporating traditional classroom mathematic concepts, such as how algebra operations are used to digitally manipulate modifications made to 3D models.

Creating, processing and printing 3D projects utilizes mesh-extraction, a computer graphics process that digitally assembles shapes to construct a 3D object’s surface and structure. The team’s improved algorithms will strengthen models generated by mesh-extraction that are based on scans of a real-world object.

“This work is particularly timely given recent technological advances in 3D scanning and mesh-extraction,” said Ettore Aldrovandi, Department of Mathematics chair. “It has the potential for transformative impact in augmented reality, in which digital graphics are displayed to let a user see them in the real world through a phone’s camera, and virtual reality, in which computer-generated simulations immerse audiences in different realities. This impact will also assist in establishing new mathematical frameworks for shape analysis.”

Additional uses for this work include strengthening 3D modeling in applications available for use on smartphones. While AI and ML have expanded access to such applications, these programs can create inaccurate scans due to unreliable performance in running computer and graphics tasks.

“We intend to integrate the developed methodologies from this work with algorithms from large language models, such as ChatGPT, to further enhance modern software’s text-to-3D capabilities,” Bauer said. “The innovations produced in recent years in deep learning, AI, and ML are fueled by mathematics and computer science. We still have a lot to learn about what drives these innovations, and we have to keep pushing the boundaries of possibilities for applying these novel methods in 3D modeling.”

STUDENT RESEARCH AND INTERNATIONAL COLLABORATIONS
Through the collaborative grant, Bauer’s graduate students will have the opportunity to travel to Houston where they will analyze data, test models and develop further connections. Graduate students working on the research at the University of Houston will also travel to FSU to observe parts of the research.

“Dr. Bauer’s grant represents significant advancements in applying topological data analysis — looking at properties of shapes and spaces that remain unchanged when moved but not broken — and shape analysis to human body modeling,” Aldrovandi said. “The research promises to develop robust geometric deep learning models capable of handling raw 3D data regardless of data collection methods, with applications spanning from body motion generation to facial expression analysis.”

Additional contributors to this research include Bauer’s longtime collaborator Nicolas Charon, mathematics professor at the University of Houston in Texas; Mohamed Daoudi, professor of computer science at IMT Nord Europe — a graduate school of engineering partnered with the University of Lille — in Villeneuve-d’Ascq, France; and Sylvain Arguillère, a researcher at the University of Lille in Lille, France.

To learn more about research conducted in FSU’s Department of Mathematics, visit math.fsu.edu.

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