The University of Montana
Department of Mathematical Sciences

Technical report #3/2006


A Variational Approach to Video Segmentation for Botanical Data

Aaron Luttman
University of Montana

and

John Bardsley
University of Montana

Abstract

In order to engage in photosynthesis, plant leaves absorb CO2 via the opening of pores in their surfaces called stomata. Water evaporates through open stomata, however, which is a detriment to plant function. 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, an experimentalist injects the leaf with dye so that it fluoresces. The regions with a higher relative intensity then correspond to areas in which the stomata are closed and the darker regions where the stomata are open. A camera is used to collect the emitted light, and a fluorescence pattern is measured. Images are continually recorded as these patterns change with time, resulting in a video sequence. Our task in this paper is to segment one such video sequence into fluorescing and non-fluorescing regions. After preprocessing the video, we take a variational approach to the segmentation problem. The associated three-dimensional evolution equation is solved using a semi-implicit numerical scheme. Results of the segmentation for actual leaf data are presented.

Keywords: Image Segmentation, Shape Reconstruction, Variational Methods

AMS Subject Classification: 68U10

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