DMS-EPSRC Stochastic Shape Processes and Inference

A shape that changes over time—a dividing cell, a bending spine, a growing tumour—has no standard statistical language to describe it. This project will build one. Biologists and engineers have long known that form and function are linked, but they lack mathematical tools to model how shapes evolve across a population. A cell’s shape during division might predict whether the process will fail, but current methods treat each snapshot in isolation. The researchers will develop stochastic shape processes—formal statistical frameworks that capture not just how a single shape changes, but how those changes vary between individuals. This fills a gap: existing shape analysis is static; this project makes it dynamic. If successful, the methods will let scientists ask questions that are currently out of reach. For example, why does cell division sometimes fail? How can factory workers’ postures be adjusted to reduce strain? The project will test these ideas on cell motility and human posture as proofs of concept. The core mathematics, however, is fundamental science. It will not directly change a manufacturing line or a clinic tomorrow. But it will give practitioners in biology, medicine, and ergonomics a general toolkit for linking form to function over time—a capability that, like earlier advances in statistical shape analysis, could eventually underpin diagnostics, prosthetic design, or automated quality control in manufacturing.