Images and Geometry Visualized: Chandrajit Bajaj Builds Framework for Data Science

The research website of Chandrajit Bajaj is adorned with colorful renderings of biological subjects: there are ribosomal subunits, neurons, and even an entire human abdomen.

The renderings are samples of his work. But Bajaj is no biologist. His research focuses on the geometry underlying complex structures, and how computers can be used to investigate that data and map it into a range of computational models and quantifiable visual information. It turns out that Bajaj’s research is just what biomedical researchers need to bring their research subjects into view—and complex enough to drive forward his own data analysis and visualization research

“It’s a two-way street of interaction,” Bajaj said. “You’re providing the starting of a solution, but the problem is rich enough to provide you many further computational challenges.”

As the director of ICES’ Computational Visualization Center at the Institute for Computational Engineering, Bajaj is involved with a range of projects that seek to improve research in data sciences. Some of his work involves translating one form of imagery into another—for example, turning medical CT-scans into interactive 3D models. Some of it is more theoretical, and involves creating generalized algorithms that can be used by scientists to capture the complex geometry of a data set so it can be accurately manipulated in larger computational models, and thereby enhance our understanding.

Computational geometry and topology —or using computers to figure out the underlying structure of a data set, and then visualizing the inherent shape and form— is one of the foundations of Bajaj’s research. During his more than 35 years in the field, Bajaj has become a world-renown leader on the subject. He’s a fellow of the American Association for the Advancement of Science, the Association for Computing Machinery, the Institute for Electric and Electronic Engineers, and the Society for Industrial and Applied Mathematics.

“It’s hard for me to judge what his most notable accomplishments are,” said Andrew Gillette, an assistant professor at The University of Arizona who had Bajaj as a Ph.D. adviser. “To me, what’s most impressive about his research is that you could ask a dozen senior faculty this question and they would all point to different, equally impressive work.”

On September 13, Bajaj’s contributions to the field of computational data analysis and visualization are being recognized with a research symposium on Imaging and Geometric Data Sciences organized by Gillette, a professor of Mathematics at the University of Arizona and two other former Bajaj students: Tamal Dey, now a professor of Computer Science at Ohio State University, and Yongjie Jessica Zhang, now a professor of Mechanical and Biomedical Engineering at Carnegie Mellon University. The symposium is also a celebration of Bajaj’s 60th birthday.

The symposium format is an apt way to recognize Bajaj and his contributions. Bajaj said that over the years symposiums of all sorts have played an important role for fostering research collaborations, and getting ideas for new projects. He believes an essential part of his success can be attributed to ICES and relates to the Institute creating a similar type of interdisciplinary environment by encouraging computer science, mathematics and engineering disciplines to work together on shared problems.

“Being all in the same place, has led to the most invigorating of academic environments,” Bajaj said.

Gillette said that he benefited from the Bajaj’s wide range of research when he was earning his Ph.D. in mathematics from UT Austin. He contributed to work ranging from rendering the complicated geometry of viruses, molecules, and neurons to developing finite element schemes that could be applied to a variety of shapes. He said the experience built up the confidence to take on students from a variety of academic backgrounds.

“I attribute my desire and ability to manage such diverse efforts to Bajaj’s implicit influence over the years,” Gillette said.

Bajaj said that he’s currently prioritizing research that focuses on theoretical aspects of high-dimensional optimization.

A benefit of this research, he says, is that even without a specific focus in mind, computational geometry relates to problems across science. That means theoretical research today would enable our understanding and visualizations for data that people haven’t even begun acquiring yet.

“I kind of have come full circle, as my Ph.D. thesis was titled ‘The Computational Complexity of Geometric Optimization’,” Bajaj said. “Today, I’m a tad older but a lot wiser, thanks to my amazing mentors, students, colleagues, and collaborators."

--story by Monica Kortsha