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Author(s)

First Name Middle Name Surname Role Email

Xiwen Luo ASABE Member xwluo@scau.edu.cn

Affiliation

Organization Address Country

South China Agricultural University Guangzhou China

Author(s) – repeat Author and Affiliation boxes as needed--

First Name Middle Name Surname Role Email

Xuecheng Zhou zxcem@scau.edu.cn

Affiliation

Organization Address Country

South China Agricultural University Guangzhou China

Publication Information

Pub ID Pub Date

073051 2007 ASABE Annual Meeting Paper

The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily reflect the official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution does not constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer review process by ASABE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this work should state that it is from an ASABE meeting paper. EXAMPLE: Author's Last Name, Initials. 2007. Title of Presentation. ASABE Paper No. 07xxxx. St. Joseph, Mich.: ASABE. For information about securing permission to reprint or reproduce a technical presentation, please contact ASABE at rutter@asabe.org or 269-429-0300 (2950 Niles Road, St. Joseph, MI 49085-9659 USA).

An ASABE Meeting Presentation

Paper Number: 073051

A Fuzzy Thresholding Segmentation for Plant Root CT Images Based on Genetic Algorithm

Xiwen Luo, professorSouth China Agricultural University, Guangzhou, 510642, P R China.

Xuecheng Zhou, associate professorSouth China Agricultural University, Guangzhou, 510642, P R China.

Written for presentation at the2007 ASABE Annual International Meeting

Sponsored by ASABEMinneapolis Convention Center

Minneapolis, Minnesota17 - 20 June 2007

Abstract. The precise segmentation of roots CT images is the basis to implement the 3D

reconstruction and quantitative analysis of plant root system in situ. The problem existing in the CT

images segmentation for plant roots in situ were discussed. In order to segment plant root CT

images with the inherent indistinction, a fuzzy thresholding algorithm was implemented with the

criterion of maximum fuzzy entropy and genetic algorithm. The initial thresholds were obtained with

histogram analysis. The CT images were divided into several different regions fuzzily through

designing a simple fuzzy membership function. And according to the criterion of maximum fuzzy

entropy, a genetic algorithm was used to determine the best thresholds of CT images segmentation.

The programming test result showed that the algorithm was effective to improve the precision and

efficiency of root CT images segmentation.

Keywords. Genetic algorithm, Fuzzy Thresholding, CT images, Root in situ

The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily reflect the official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution does not constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer review process by ASABE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this work should state that it is from an ASABE meeting paper. EXAMPLE: Author's Last Name, Initials. 2007. Title of Presentation. ASABE Paper No. 07xxxx. St. Joseph, Mich.: ASABE. For information about securing permission to reprint or reproduce a technical presentation, please contact ASABE at rutter@asabe.org or 269-429-0300 (2950 Niles Road, St. Joseph, MI 49085-9659 USA).

IntroductionRoot is an important plant organ for nutrient and water uptake from the surrounding medium such as soil. Due to its special growing environment and structural complexity, it is more difficult to quantify plant root than its shoot. In fact, the lack of observation and measurement for plant root in situ has become the technical bottleneck to understand root systems. As an attempt to solve the barrier (Luo et al., 2004), plant root images in situ were obtained using multi-slice spiral computed tomography (MSCT) imaging technology, and the visualization of plant roots growing in different media was implemented after image processing and 3D reconstruction. In the methods, the precise segmentation of roots CT images is the basis to implement the 3D reconstruction and quantitative analysis of plant root system in situ. And it is a key to affect the precision of observation and quantitative analysis for root in situ.

Thresholding is a common method for image segmentation. It is based on the assumption that the objects can be distinguished by their gray levels. Many thresholding methods have been developed, which may be classified into two groups (Sahoo et al., 1988): global and local. Global thresholding method selects one threshold value for the entire image. Points that have the gray level above the threshold are classified as background; alternatively, the other points are classified as objects. A local thresholding method selects some different threshold values for different regions, or even for each pixel (Yang et al., 2000). It is an important issue for selecting one or more correct gray level threshold to separate different objects or separate objects from background. Based on the different criteria, various methods to select threshold have been developed (Milan, et al., 2002), such as minimum error thresholding, Otsu’s method and maximum entropy thresholding. Many methods of thresholding based on entropy criterion are developed in recent years (Zhang, 2001). In these methods, however, there are few algorithms for segmenting multi-dimensional and multi-thresholds images. In order to improve the precision and efficiency of CT images segmentation for plant root in situ, a multilevel thresholding method is required and is necessary to deal with the ambiguity in CT images thresholding. According to the analysis of histogram for the CT images of plant root in situ (Zhou, 2004), a simple fuzzy membership function was designed, the criterion of maximum fuzzy entropy was introduced; and a genetic algorithm was used to determine the best thresholds of root CT images in this paper.

Algorithm Descriptions

General Ideas

The object to be segmented is the CT serial images of plant root in situ, which is a kind of space-series images produced by MSCT, with each slice consisting of an matrix with the size of 512×512 pixels and gray levels of 12 bits. According to the earlier research (Zhou, 2004), the whole histogram of CT images can be divided into 3 regions, the gray level of the first region is between 0 and 360, where the main materials are air and the mattress of CT bed with minimum density; the second region is mainly composed of organic soil, plastic container and light impurity with smaller density and maximum volume, of which the gray level is between 360 and 800; and the root system and weighty impurity belong to the third region with the gray level from 800 to 4096. However, the root CT images are the same gray-level images with higher resolution and lower contrast as other CT images, of which the edges between any two different regions within these images are ambiguous in nature and the gray-level of pixels within some region is uneven, with caused by the negative factors of imaging technology such as local effect, false imaging and noise. Therefore, some suitable methods must be selected to eliminate

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or weaken this ambiguity in image segmentation. However, it is not easy to determine a fuzzy region and select the appropriate membership function in the fuzzy region for a given image. Based on information theory, the entropy is select as the criteria to judge if the information of an image is mostly retained after thresholding.

The detail line of algorithm is, the initial thresholds are obtained with histogram analysis, the CT images are divided into several different regions fuzzily through designing a simple fuzzy membership function. And according to the criterion of maximum fuzzy entropy, a genetic algorithm is used to determined the best thresholds of CT images segmentation.

The Criterion of Fuzzy Entropy

CT Images’ Fuzzy Partition A digital image (CT slice) is given with the size of M × N pixels and L gray levels. Let D={（i，j）: i=0,1,…,M-1; j=0,1,…,N-1}, G={0,1,…,L-1}. Then each CT slice image with gray L levels is considered to be a two-variable function I(x,y) with the domain D and the range G.

Where, 0≤I(x,y)≤L-1 is the gray level value of the image at the pixel (x,y), L=4096.

Let Dk={（x,y）: I(x,y)=k, (x,y)∈D}, hk=nk/(M×N), k=0,1,…,L-1; where nk denotes the number of pixels in Dk. Obviously,

, and Dj∩Dk=φ（j≠k）,

Where, φ represents an empty set.

Thus, 0≤hk≤1, and ∑hk=1，k=0,1,…,L-1. And H={h0, h1, …, hL-1} is just the histogram of the image I, of which probabilistic distribution is,

pk=P(Dk)=hk, k=0,1,…,L-1.According to fuzzy set theory, of the image domain D, the fuzzy set R can be characterized by its membership function (also called as membership function) μR(k). The value of μR(k) is the degree of k belonging to R, and 0 ≤μR(k) ≤1. The domain D in the paper is defined as the set of the local gray-level k belonging to the region of interest (ROI) in an image, and Lmin≤k≤ Lmax, where Lmin=800, Lmax=4095. On the basis of the earlier research (Zhou, 2004), it needs to select two thresholds for segmentation of root ROI, here calling them as T1 and T2 respectively. Then the domain D of the original image is divided into the three regions of R1, R2 and R3 by the two thresholds. Let μ1(k), μ2(k) and μ3(k) to denote respectively the membership function of R1, R2 and R3, then {R1, R2, R3} is just a fuzzy Partition of ROI, and μ1(k)+μ2(k)+μ3(k)=1. And their probabilistic distributions are defined as p1=P(R1), p2=P(R2), p3=P(R3).

Let, Dk1={(x,y): Lmin≤I(x,y) ≤T1, (x,y) ∈Dk},

Dk2={(x,y): T1＜I(x,y) ≤T2, (x,y) ∈Dk},

Dk3={(x,y): T2＜I(x,y) ≤Lmax, (x,y) ∈Dk}。 Then, pk1=P(Dk1)=pk·p1|k, pk2=P(Dk2)=pk·p2|k, pk3=P(Dk3)=pk·p3|k

Where, p1|k, p2|k and p3|k are the conditional probabilities of a pixel with the gray-level k to be classified into the region R1, R2, and R3, respectively. And then,

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，

，.

According to fuzzy set theory, the conditional probabilities can be denoted by relevant membership functions. Thus,

，

，.

Based on Probability Partition, under comprehensive consideration of boundary condition and symmetry condition (Murphy, 1990), a kind of simple membership functions is used to characterize those fuzzy subsets. These functions are respectively given as the following:

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Where, nb,nd and nk are respectively the number of pixels with gray-level b, d and k in histogram; and Lmin<a<b<c<d<Lmax.

Maximum Fuzzy EntropyAfter finishing fuzzy partition, the effect of segmentation may be scaled by a fuzzy measurement. Based on information theory, an entropy function can be used to measure how much information is contained in a data set (i.e., an image). And a fuzzy entropy function can be used to measure the information amount of a fuzzy set. Generally, for different fuzzy partitions, the amounts of information are also different. The criterion of maximum fuzzy entropy is to search for a group of parameters in the gray level domain of an image, by which the fuzzy partition determined can make image information retaining a maximum value after thresholding. For these fuzzy sets of R1, R2 and R3, their fuzzy entropy function are given as,

，

，.

The total fuzzy entropy of an image is

H (a,b,c,d)=H1+H2+H3

Obviously, the total fuzzy entropy is determined by the four parameters of a, b, c and d. According to the criterion of maximum fuzzy entropy, the best combination of a, b, c and d can be found out when H(a,b,c,d) arrives at a maximum value. Then the best value of T1 and T2 can be determined by the best combination of four parameters. The best T1 and T2 should meet the following condition:

μ1(T1)=μ2(T1) =0.5, μ2(T2)=μ3(T2) =0.5.

i.e., T1 is at the cross-point of the two curves μ1(k) and μ2(k), T2 is at the cross-point of the two curves μ2(k) and μ3(k). Combining with histogram analysis of image, T1 and T2 can be given as the following:

， .

Where, na, nb, nc and nd are respectively the number of pixels with gray-level a, b, c and d in histogram; and Lmin<a<b<c<d<Lmax.

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Genetic AlgorithmAccording to the above analysis, if the best combination of four parameters a, b, c and d which make H(a,b,c,d) arrive at a maximum value could be found out, the best thresholds of T1 and T2

should be determined by them. In fact, that is an optimization method to seek in the domain of image for a set of parameters (a, b, c, d) that make the total fuzzy entropy H maximize. Exhaustive search is the simplest method of optimization and easy to understand, but it is also equivalent to spending the time, effort, and resources. In order to reduce seeking-up time and improve running speed, the genetic algorithm (GA) is selected to seek up the best solution.

The genetic algorithm (GA) is an optimization and search technique based on the principles of genetics and natural selection. The method was developed by John Holland (1975) over the course of the 1960s and 1970s and finally popularized by one of his students, David Goldberg, who was able to solve the difficult problem involving the control of gas-pipeline transmission for his dissertation (Goldberg, 1989). As it can be seen in literally, Genetic Algorithm is inspired by Darwins theory about evolution. GAs are inherently parallel optimization procedures, which utilize a "survival of the fittest" approach. A basic GA employs selection, crossover and mutation operators. The whole process can be referred to as "reproduction". Algorithm is started with a set of solution (represented by chromosomes) called sub-population. Solutions from one sub-populations are taken and used to form a new sub-population by a hope that the new population will be better, at least not worse than the old one. Solutions are selected according to their fitness. The more suitable they are the more chances they have to reproduce. The main characteristic of the GA is that it is simple, universal and robust. After about 20 year’s development, GA has been successfully used in a lot of fields such as Scheduling, Function Optimization, Machine Learning etc. Generally, the problems which need to deal with in applications of GA include Chromosome encoding, Initial population selection, Fitness function definition, Genetic operators and Stopping criteria.Chromosome Encoding. Four genes need encoding, which are a, b, c and d with the level value from 800 to 4095. Each gene (parameter) is encoded into a 12-bit binary number. The length of a chromosome code is 48 bits.

Initial Population. If four genes may be allowed to produce in random within the range from 800 to 4095, it will be impossible to let them meet the condition: Lmin<a<b<c<d<Lmax. Thus it will bring a lots of invalid chromosomes. In order to avoid the situation, the following rule was design to make a new chromosome to meet the above constraint condition:

a=a0，b=a+(4096-a)*(b0/4096)，c=b+(4096-b)*(c0/4096)，d=c+(4096-c)*(d0/4096).

Where, (a0, b0, c0, d0) is a initial chromosome given in random by computer under the constraint condition.

Fitness Function. The total fuzzy entropy function H (a,b,c,d) is just defined as the fitness function in the paper.

Genetic Operators. Three kinds of operators including selection, crossover and mutation operators are used which are respectively rank selection and single bit mutation. Rank selection operator means that chromosomes are assigned to the probability of selection based on the rank in the population. Two-point crossover is a crossover scheme that selects two points in the chromosome and exchanges bits between those two points. And single bit mutation (Point mutation ) alters a single feature to some random value.

Stopping Criteria. It is the condition to judge if GA should end. In the paper, program running will not stop until the number in generation counter arrives at maximum or the highest fitness value becomes stable. And the best solution will be got after the chromosome of individual with the highest fitness value is decoded.

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Algorithm Flow and Programming Implementation Fig.1 shows the flowchart of the algorithm proposed in the paper. After testing, the parameters of GA are selected as the following: Population Size, PoPs=100 ; Maximum Generations, MaxGen=200; Probability of crossover, Pc=0.8; Probability of mutation, Pm=0.01. The algorithm are implemented by programming in C++ and GA toolbox in Matlab. Image preprocessing in Fig.1 mostly indicates pre-segmentation to image based on histogram analysis. If I(x,y) is an original image, then its pre-segmented image can be denoted as

Fig.1 Flowchart of algorithm

Experimental Results and AnalysisThe experiment of segmentation was carried out by the algorithm proposed in the paper for the CT images of plant root in situ used in the earlier research (Zhou, 2004). As a result, the fitness of population became stable when the number of genetic generations was increased to 128.

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Generate initial population

Selection

Crossover

Mutation

New population

Output the best solution

Begin

End

The best and average fitness

Stopping criteria?

Find fitness for each chromosome

Get the best thresholds

Image Thresholding

Image Preprocessing

Define fitness function, Select GA parameters

And at the moment the best combination of four parameters a, b, c and d was 812，863 ，1326 and 1375. The best threshold T1=846, T2=1354. Fig. 2a and Fig. 2b showed respectively the effect of segmentation (labeled by reticulate hatching) with the algorithm proposed in this paper (a) and the one described in the earlier paper (b) (Zhou, 2004) for the slice 160 of root CT images. While Fig. 3a and Fig. 3b showed respectively the effect of 3D reconstruction from the CT images segmented with the algorithm proposed in this paper (a) and the one described in the earlier paper (b) (Zhou, 2004) (from the same viewpoint).

It was clear in Fig. 2 that each of three regions segmented in Fig. 2a was larger than the corresponding one of those three regions segmented in fig.2b. And comparison of the region 2 in Fig. 2a and Fig. 2b was more obvious. According to Tab. 1, the number of pixels in three

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（ a ） （ b ）Fig.2 Comparison of segmentation (labeled by reticulate hatching) with the

algorithm proposed in this paper (a) and the one described in the earlier paper (b) (Zhou, 2004) for the slice 160 of root CT images

①②③

②③

③ ③②③ ①

②③

（ a ） （ b ）Fig.3 Comparison of 3D reconstruction effect of CT images segmented with the

algorithm proposed in this paper (a) and the one described in the earlier paper (b) (Zhou, 2004) (from the same viewpoint)

① ①② ②

regions segmented in Fig. 2a was increased of 10.78% than those in Fig. 2b, and the area increased of 9.60%.

Tab.1 Quantitative comparison with segmenting effect of the two algorithms

AlgorithmRegions segmented of the slice 160 3D root constructed

No. Area (mm2) Pixels (unit) Vol. (mm3) Surface (mm2)

proposed in this paper

1 128.24 673

33449.41 26179.832 117.55 6103 32.89 187

subtotal 278.68 1470

described in the earlier paper

(Zhou, 2004)

1 121.58 631

29526.03 23769.312 102.21 5223 30.47 174

subtotal 254.26 1327Contrast (%) * 9.60 10.78 13.29 10.14

In order to observe distinctly the effect of segmentation with the algorithm, by means of 3D marching construction (MC) methods based on segmentation (Tian, 2003), 3D reconstruction from these images segmented with the above two algorithms was carried out, and the effect of their reconstruction was shown in Fig. 3. It was easy to see that, the detail shown in Fig.3a was more abundant than Fig. 3b, and there were more fine roots (at the locations labeled by ① and ②). Even if at the same place of these two figures, the diameter of root was larger in Fig.3a than Fig.3b. And these contrasts can be quantified in Tab.1, in comparison with the earlier research results, the volume and surface area of 3D root system reconstructed from CT images segmented with the algorithm proposed in the paper were respectively increased of 13.29% and 10.14%.

According to the above result of observation and quantitative analysis, the algorithm proposed in the paper was effective to improve the precision of segmentation for CT images of plant root.

ConclusionIn order to eliminate or weaken the negative effects caused by the inherent indistinction of CT images to segment plant root regions, a fuzzy thresholding algorithm was developed with the criterion of maximum fuzzy entropy and genetic algorithm.

The initial thresholds were obtained with histogram analysis. The CT images were divided into several different regions fuzzily through designing a simple fuzzy membership function. And according to the criterion of maximum fuzzy entropy, the best thresholds of CT images were determined by a genetic algorithm. And the algorithm was implemented with programming by using C++ and GA toolbox in Matlab.

According to the observation and quantitative analysis of root CT images segmented and 3D reconstruction image, it was proved that the algorithm was effective to improve the precision and efficiency of segmentation for CT images of plant root in situ.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China under Grant No. 60375005.

.

ReferencesGoldberg,D. E. 1989. Genetic Algorithms in Search, Optimization, and Machine Learning.

Reading, MA: Addison-Wesley.Luo Xiwen, Zhou Xuecheng, Yan Xiaolong. 2004. Visualization of Plant Root Morphology in Site

Based on X-ray CT Imaging Technology. 2004 ASAE/CSAE Annual International Meeting, No.043078

Milan Sonka, Vaclav Hlavac, et al. 2002. Image processing, analysis and machine vision (2nd edition). Beijing: People’s Posts and Telecommunications Publishing House.

Murphy C A, Pal S K. Fuzzy thresholding. Mathematical Framework, Bound Functions and Weighted Moving Average Technique. Pattern Recognition Letter, 1990, 11:197-206.

Sahoo P. K., Soltani S., Wong A. K. C., and Chan, Y.C. 1988. A survey of thresholding techniques. Computer Vision, Graphics, Image Process. 41:233–260

Tian jie, Bao shanglian and Zhou mingquan. 2003. Medical image processing and analysis. Beijing: Publishing House of Electronics Industry.

Yang Y., Yan H. 2000. An adaptive logical method for binarization of degraded document images. Pattern Recognit., 33(5):787–807

Zhang Minjin. 2001. Image segmentation．Beijing：Beijing Science Press.Zhou Xuecheng, Luo Xiwen, Yan Xiaolong. 2004. Research on segmenting algorithm for MSCT

images of plant root system based on its morphological feature. 2004 ASAE/CSAE Annual International Meeting, No.043079

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