1. Yurui Sun, China Agricultural University Yandong Zhao, Beijing Forestry University Rapid identification of plant drought stress by 3D-image process Supercomputer technologies of mathematical modeling, Yakutsk, Nov.28-30, 2011

2. Date: May 15, 2007, Time 12:00, strong solar light, temperature: 34.6 o C Plant uncomfortable Date: May 15, 2007, Time: 17:30, Sunset, temperature 23.3 o C Plant comfortable How to understand a plant comfortable or uncomfortable

3. Study motivations 1.This is an interesting and a disciplinary study which is basically associated with differential geometry, artificial intelligence, pattern identification, and on-line computation. 2. For developing sensor technology, one wants to seek a plant sensor that can speak, rather than a complete electronic sensor. 3. Wilting identification can be significantly beneficial for precision irrigation.

4. Question: Is it possible with 2D-based image processing to reliably identify the early response of the plant to drought stress? If the answer is yes, which mathematical tool can be used for this purpose? We think that 3D-based image processing can meet the requirement of this study Our viewpoint: it is thorny to do with 2D-based image because a 2D image is regarded as a mapping from 3D space to that of 2D. Consequently, part of necessary data lost. Research methodology

5. How to view a leaf ● A leaf is just an organ of a plant. ● From sensor technology, a leaf is a sensing component due to its function of photosynthesis ● From mathematical window, a leaf can be considered a surface in 3D space. Thus, the wilting process of the leaf can be viewed as a cluster/set of mathematical surface with different geometric characterizations

6. Definition of drought stress index 1: Fractal dimension index A leaf is enclosed in a cube within a 3D coordinate system. Suppose each side length is divided into a number of segments increasing with 2 k (k = 0, 1, 2, …m), the cube will contain 2 3k sub-cubes. For each sub-cube, if one of its vertexes is lower the height of the leaf, the sub-cube is regarded as a part of the leaf in space. Based on box counting method of fractal analysis, the dimension of leaf wilting index by fractal analysis can be defined as Where N is the number of tiny cubes enclosed by the leaf space and r =2 m-k (k=1, 2, ….m) is a variable with respect to the side-length of tiny cube.

7. 2: 2DFT index 1.A leaf wilting dynamics can be described as a stochastic event ( f (x(t), y (t), t) ) in 4D space; 2. A leaf appears a flat surface without wilting, whereas leaves with more or less bending/crimpling shapes refer to severely or slightly wilting status, that is, the curvature at each point of f (x, y) will be altered as the leaf wilting progresses; 3. The spectrum of 2DFT can reflect the variations of the curvatures with different wilting status;

8. A o refers to amplitude of direct component and A i to that of i-th alternative component of F(u, v). According to Eq.2, LWI 2DFT will decrease as leaf wilting increases, and vice versa. Based on these assumptions, we define

9. Using a laser scanner to obtain 3D images

10. 8:30, 30 ℃ Fig. 3b 11:10, 32.8 ℃ 15:17, 39.6 ℃ Comparison between 2D and 3D images with three wilting statues

11. Experiment results (1)  LWI 2DFT  LWI DF Recorded dynamics of LW DT and LWI 2DT

12. Regression between air temperature (T air ) and LWI 2DT Experiment results (2)

13. Grid: Experiment results (3)

14. Experiment results (4) A: Grid=2 mm, duration 300 s C: Grid=8 mm, duration 75 s B: Grid=4 mm, duration 150 s D: Grid=16 mm, duration 38 s

15. Remarks 1.Although this is only a preliminary research for a specific plant (Zucchini), one can understand that leaf wilting process refers to an interesting mathematical approach in 3D space ; 2. Because different species have various behaviors responding to drought stress and have different forms of leave, we must consider more mathematical methods to define drought stress indices based on 3D morphology of plants;

16. 3. This is a leaf-based example. Indeed, when a plant is scanned, the data sets will be drastically increased and it takes much longer in data processing. For some plants, their response times to drought stress can be quicker than the times of image capturing and data processing. 4. Advanced 3D scanning technique leads us into a 3D image world. Meanwhile, a new challenge should pay more attention. That is, large extended data and on-line processing in 3D space need more powerful computers and smarter computing strategy.

17. Thanks for your attention! China Agricultural University Beijing Forestry University