Numerical analysis of pattern formation on the surface of transpiring leaves

The process of photosynthesis is facilitated by pores on the leaf surface called stomata. When a particular stoma is open, CO2 is absorbed through its aperture, but H2O is also lost due to evaporation. Thus a plant will seek a stomatal aperture that balances its need for CO2 with its aversion to H2O loss. In order to visualize a particular leaf's stomatal aperture distribution and how it changes with time, fluorescence data is collected at regular intervals as digital images, resulting in a video sequence. It has been observed that stomatal apertures are often synchronized into spatially extended patches. In order objectively to analyze this phenomenon we have developed a technique to isolate patches via a three-dimensional PDE-based segmentation method. The resulting segmented data is then collapsed to a vector valued time series of much smaller dimension with a hybrid PCA-Archetypal Analysis approach. This allows for a unique interpretation of the data in terms of statistical measures of the motions of representative patches. The technique is illustrated with a data-set from a particularly complicated regime collected by the Complexity and Stomatal Behavior research lab at Utah State University.