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

Date: May 15, 2007, Time 12:00, strong solar light, temperature: 34.6oC

Plant uncomfortable

Date: May 15, 2007, Time: 17:30, Sunset, temperature 23.3oC

Plant comfortable

How to understand a plant comfortable or uncomfortable

Study motivations1. 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.

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

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

Definition of drought stress index

）（1log

log

)/1log(

loglimlim r

N

r

NLWI

rrDF

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 2k (k = 0, 1, 2, …m), the cube will contain 23k 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 =2m-k (k=1, 2, ….m) is a variable with respect to the side-length of tiny cube.

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;

）（2

10

02

n

ii

DFT

AA

ALWI

Ao refers to amplitude of direct component and Ai to that of i-th alternative component of F(u, v). According to Eq.2, LWI2DFT will decrease as leaf wilting increases, and vice versa.

Based on these assumptions, we define

Using a laser scanner to obtain 3D images

Laser diode

PSD

Lens

Lens

α

y

x

）（1sin

xy

8:30, 30 ℃

Fig. 3b

11:10, 32.8 ℃15:17, 39.6 ℃

Comparison between 2D and 3D images with three wilting statues

Experiment results (1)

0

0. 2

0. 4

0. 6

0. 8

1

1. 2

7: 00 9: 00 11: 00 13: 00 15: 00 17: 00 19: 00ti me of the experi mental day

valu

es o

f in

dice

s

LWI 2DFTLWI DF

LWI2DFT

LWIDF

Recorded dynamics of LWDT and LWI2DT

y = -0.4516x + 19.649

R2 = 0.7477

0

1

2

3

4

5

6

30 32 34 36 38 40 42 44

Tair(oC)

LWI 2

DFT

(%)

Regression between air temperature (Tair) and LWI2DT

Experiment results (2)

0

0.2

0.4

0.6

0.8

1

1.2

7:00 9:00 11:00 13:00 15:00 17:00 19:00

time of the experimental day (h)

LW

I 2D

FT

2 mm

4 mm

8 mm

16 mm

32 mm

Grid:

Experiment results (3)

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25 30 35

scaning grid (mm)

dete

rmin

atio

n co

effic

ient

(R2 )

VaEC

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

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;

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.

Thanks for your attention!

China Agricultural University Beijing Forestry University