Plant leaves take on a remarkable variety of forms and their shape has consequences for their mechanical, thermal, and light-intercepting properties.
Currently, leaf shape is characterized by qualitative descriptors such as “entire”, “lobed”, or “serrated”, and by simple geometric measures such as the ratio of area to perimeter or the radius of the maximal inscribed sphere.
The goal of this project is to develop more refined quantitative measures of leaf shape using a new mathematical tool called persistent homology.
These new measures will enable biologists to perform more accurate analyses of how genetic variations affect leaf shape, and the resulting changes in leaf function.
On completion of this project, the student will be skilled in topological data analysis, a widely-applicable approach to discovering structure in many types of data from digital images to medical clinical studies and financial markets.