CAREER: Advancing Shape Learning for Biosciences

Understanding the healthy and pathological shapes of biological structures (proteins, cells, organs) directly from image data is critical to understand their roles in living organisms. The impact for human health and society range from our understanding of cancers to the diagnosis of neurodegenerative diseases. This CAREER proposal will evaluate and develop reliable shape analysis methods that can harness the recent bio-imaging data explosion, advance our understanding of the fundamental rules of life, and enable breakthroughs in data-driven biomedicine. Tightly integrated with the research activities, the education and outreach objective is to engage diverse audiences in shape analysis and bioscience through novel art-science performances for high-school students, pioneering courses on geometric machine learning for shape analysis, training of graduate students, and free community outreach lectures for the wide audience. Despite impressive advances in the field of shape analysis, its deployment to biosciences is prohibited by computational and statistical hurdles. This yields challenges related to the interpretation of results, where inconsistent analyses bear the danger of driving scientific conclusions in the wrong direction —a serious drawback for a discipline that ultimately researches human health. In mathematics, (biological) shapes can be represented as shapes of key points, shapes of curves, or shapes of surfaces. The associated shape data spaces present common abstract geometric structures of non-Euclidean manifolds. This project will utilize these commonalities to establish a consistent numerical framework to systematically and exhaustively evaluate the possible inconsistencies of machine learning algorithms on shape spaces. In particular, it will provide a deep dive into the geodesic and polynomial regression models on non-Euclidean manifolds. The findings will be leveraged into a pilot study that will reliably extract biologically relevant parameters on the morphodynamics of cells migrating in vivo. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.