Geometric statistical methods for curves and surfaces with applications in medical imaging

Project description

What is the average shape of a brain tumour in a cohort of patients? How might this evolve over time? Is it possible to associate the shape and its evolution with certain genetic and clinical characteristics of a patient? Advent of high-resolution imaging technologies have enabled meaningful answers to such questions based on continuous representations of tumours and organs as parametric curves and surfaces. These data objects typically reside on manifolds equipped with non-trivial geometries and symmetries (invariances). The project will focus on developing statistical methods for such data using tools from stochastic processes, differential geometry and group theory.