Structure---whether inorganic matter, the morphology of living things, or objects crafted by culture---is data rich. If the information contained within a single material, organism, or cultural artifact is immense, the collective information contained in the universe of things is fathomless.
X-Ray Computed Tomography (CT) creates reconstructions of objects down to micron resolution, but a method to quantify and summarize the shape and structure of these exquisite objects is lacking. The emerging field of Topological Data Analysis (TDA) is a collection of tools from pure mathematics that quantifies the shape of data. These tools include persistent homology, which gives an algebraic descriptor summarizing changes in structure over a changing parameter, and the mapper graph, which provides a skeletonization of structure through the lens of a chosen filtration function. Different filtration functions highlight varying features in data.
We will be using X-ray CT and TDA to quantify shapes in nature, not least of which, plants. Evolution, domestication, and environment sculpt the morphology of living organisms. Embedded in organismal morphology is information, about the genes that increase yield in crops, have been modulated by evolution to create the spectacular diversity in plants, or features that can be used as a proxy to measure the effects of environment and climate change on plants. There is also the chance to change our perspective of the plant phenotype: rather than a series of shapes that develop through time, it is also possible to describe the plant form as a single, 4D shape. We will be using X-ray CT and analysis using TDA to explore plant morphology, development, plasticity, and to innovate new ways of thinking about, describing, quantifying, and using shape information in the plant sciences and beyond.
Research Website: https://dhchitwood.