APPLIED MATHEMATICS

Open and Shut

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Science  17 Aug 2007:
Vol. 317, Issue 5840, pp. 872
DOI: 10.1126/science.317.5840.872a

During photosynthesis, plants collect carbon dioxide through openings called stomata but also lose water vapor when these pores are open. Thus, the plant must continually optimize the aperture diameter, a process thought to be global (coordinated over large regions of the leaf surface). To better understand the optimization mechanism, researchers inject dye into a plant leaf and then use time-lapse videography to track fluorescence changes as the stomata open and close. However, processing the video sequence is mathematically tricky: Standard methods to identify the synchronized dynamics of fluorescing patches in two spatial dimensions and one time dimension can neglect important changes or overemphasize unimportant detail. Luttman and Bardsley have devised an algorithm based in variational calculus to extract the three-dimensional evolution of stomatal patch dynamics from experimental data. After preprocessing video of a fluorescing cocklebur leaf to remove noise and normalize changes in lighting, they identified the patches by looking for segmentations of the data that yielded the optimal division of light and dark regions. Processing of the spatial and temporal data as a whole proved essential; analyzing each frame independently resulted in meaningless segmentation. — DV

SIAM J. Sci. Comput. 29, 1550 (2007).

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