Numerical analysis of pattern formation on the surface of transpiring leaves

Aaron Luttman; Emily Stone; Johnathan Bardsley

doi:10.1016/j.physd.2007.06.009

Numerical analysis of pattern formation on the surface of transpiring leaves

Mathematical Sciences

Bethany Lutheran College

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	142-155
Number of pages	14
Journal	Physica D: Nonlinear Phenomena
Volume	232
Issue number	2
DOIs	https://doi.org/10.1016/j.physd.2007.06.009
State	Published - Aug 15 2007

Funding

This work was supported by a NSF DMS-0504325 grant, and the University of Montana EPSCoR program. We would like to thank Rohn Wood and the Computational Chemistry Core Facility at UM for technical support, and James Crutchfield, Center for Computational Science and Engineering, UC Davis, for useful discussions. Data was provided by the Complexity and Stomatal Behavior Research Lab at Utah State University, and we thank David Peak (Physics, USU) and Keith Mott (Biology, USU) for making it available to us. We would also like to thank David Peak for many informative discussions and feedback on the manuscript of this paper. This work was supported by the NSF under grant DMS-0504325 and by Montana NSF EPSCoR.

Funders	Funder number
University of Montana
DMS-0504325

Keywords

Archetypes
Image segmentation
Leaf transpiration
Mutual information

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10.1016/j.physd.2007.06.009

Cite this

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title = "Numerical analysis of pattern formation on the surface of transpiring leaves",

abstract = "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.",

keywords = "Archetypes, Image segmentation, Leaf transpiration, Mutual information",

author = "Aaron Luttman and Emily Stone and Johnathan Bardsley",

note = "Funding Information: This work was supported by a NSF DMS-0504325 grant, and the University of Montana EPSCoR program. We would like to thank Rohn Wood and the Computational Chemistry Core Facility at UM for technical support, and James Crutchfield, Center for Computational Science and Engineering, UC Davis, for useful discussions. Data was provided by the Complexity and Stomatal Behavior Research Lab at Utah State University, and we thank David Peak (Physics, USU) and Keith Mott (Biology, USU) for making it available to us. We would also like to thank David Peak for many informative discussions and feedback on the manuscript of this paper. Funding Information: This work was supported by the NSF under grant DMS-0504325 and by Montana NSF EPSCoR. ",

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N2 - 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.

AB - 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.

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KW - Image segmentation

KW - Leaf transpiration

KW - Mutual information

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JO - Physica D: Nonlinear Phenomena

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IS - 2

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Numerical analysis of pattern formation on the surface of transpiring leaves

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