Research Statement

3D Shape Analysis

We study 3D objects in their full geometric form rather than through 2D projections alone. For us, 3D shape analysis means building principled methods to represent, compare, segment, and quantify complex surfaces and other non-Euclidean data. This work sits at the intersection of computer graphics, computer vision, machine learning, and applied mathematics.

These problems matter in many domains, from medical imaging and biology to robotics and design. In our team, they provide a foundation for developing rigorous algorithms for imaging data on non-regular grids. See Research Overview for our main problem areas and current directions.

Why Brain Shapes?

Many of our applications center on the brain because its anatomy is one of the richest and most challenging settings for shape analysis. Its highly folded geometry exposes the limits of standard Euclidean image processing and creates a demanding testbed for registration, segmentation, feature extraction, and quantification.

Brain applications also let us pursue questions with both methodological and clinical value. While our work supports neuroscience studies of cognition, development, and brain disorders, our primary contribution is the design of shape-processing algorithms that remain useful beyond a single application domain.

Method-Driven, Not Domain-Bound

A background in neuroscience or medicine can be helpful but is not a prerequisite for contributing to our research. The central questions our team addresses are computational: how to model, learn from, and analyze complex 3D geometry in a principled way. Students interested in computer graphics, computer vision, machine learning, geometry processing, or the mathematical foundations of shape modeling are often a strong fit for this work.

Although brain imaging is a major application area, we are also open to other domains whenever they raise compelling geometric problems. Prospective team members interested in algorithm development for 3D object processing are encouraged to explore our openings.

Commitment to Open Science

We view open-source software and reproducible methodology as part of the research contribution, not as an afterthought. To support reuse, verification, and community progress, we share code and tools through Team's repositories and Dr. Lyu's repositories.