image analysis on wood fiber cross-section...

IT 11 028

Examensarbete 30 hpMaj 2011

Image Analysis on Wood Fiber Cross-Section Images

Sitao Feng

Institutionen för informationsteknologiDepartment of Information Technology

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Image Analysis on Wood Fiber Cross-Section Images

Sitao Feng

Lignification of wood fibers has a significant impact on wood properties. To measurethe distribution of lignin in compression wood fiber cross-section images, a crispsegmentation method had been developed. It segments the lumen, the normallylignified cell wall and the highly lignified cell wall of each fiber. In order to refine thisgiven segmentation the following two fuzzy segmentation methods were evaluated inthis thesis: Iterative Relative Multi Objects Fuzzy Connectedness and WeightedDistance Transform on Curved Space. The crisp segmentation is used for themulti-seed selection.

The crisp and the two fuzzy segmentations are then evaluated by comparing with themanual segmentation. It shows that Iterative Relative Multi Objects FuzzyConnectedness has the best performance on segmenting the lumen, whereasWeighted Distance Transform on Curved Space outperforms the two other methodsregarding the normally lignified cell wall and the highly lignified cell wall.

Tryckt av: Reprocentralen ITC

Sponsor: Joakim Lindblad, Filip MalmbergIT 11 028Examinator: Anders JanssonÄmnesgranskare: Cris LuengoHandledare: Bettina Selig

Acknowledgments

First of all I would like to express my gratitude to my supervisor Bettina Seligand my reviewer Cris L. Luengo Hendriks at CBA (Centre for Image Analysis,Uppsala, Sweden) for the constructive suggestions and instructions. The thesiswould have been harder without your help.

Also I would like to thank all the staff in the CBA. You are very kind. A specialthanks to Joakim Lindblad and Filip Malmberg, for your valuable suggestions onmy thesis.

Finally many thanks to my loving parents who have supported my master studiesin Sweden mentally and materially.

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Contents1 Introduction 3

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Project description . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Thesis purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Methods 52.1 Fuzzy Connectedness . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Fuzzy adjacency . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.2 Fuzzy affinity . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.3 How to calculate fuzzy connectedness . . . . . . . . . . . . . 72.1.4 Iterative Relative Multi Object Fuzzy Connectedness . . . . 8

2.2 Weighted Distance Transform on Curved Space . . . . . . . . . . . 102.2.1 Step distance . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.2 How to calculate the shortest path length . . . . . . . . . . 112.2.3 Multiple objects segmentation using the WDT method . . . 11

3 Implement details 133.1 Running environment . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Provided data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Parameter settings for the FC method . . . . . . . . . . . . . . . . 15

3.3.1 Fuzzy adjacency . . . . . . . . . . . . . . . . . . . . . . . . . 153.3.2 Fuzzy affinity . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.4 Parameter settings for the WDT method . . . . . . . . . . . . . . . 153.5 Multi-seed selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.6 Comparison methods . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.6.1 Overlapping degree of the segmented regions . . . . . . . . . 183.6.2 Deviation between the segmentation boundaries . . . . . . . 19

4 Evaluation and results 214.1 Qualitative evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 214.2 Quantitative evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2.1 Evaluation by using the overlapping degree method . . . . . 224.2.2 Evaluation by using the boundary deviation method . . . . . 234.2.3 Final evaluation result . . . . . . . . . . . . . . . . . . . . . 24

4.3 Special case analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5 Conclusion and future work 27

Bibliography 28

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1 Introduction

1.1 BackgroundWood is a biological composite material, which is formed by complex multi-celllayered structure and special phenomena of molecular mechanics [1]. The wordfiber is often used to call all wood cells. However, fibers refer to a specific cell typein the wood morphology, called tracheids [2]. These tracheids are the basic unitsof the xylem, consisting of a single elongated cell with a thick, tough cell wall andan empty space in the center, which is called lumen [3]. The space between thecells is called middle lamellae containing lignin, which holds the cells together [4].As lignin is also found in the cell walls, it confers the mechanical strength to thecells and enhances decay resistance to wood [2]. Modifications in lignin contenthave an important effect of wood properties [1]. It is particularly abundant incompression wood (see Fig. 1.1) [5].

Fig. 1.1: Compression wood cross-section. Highly lignified regions marked withwhite arrow

The production and accumulation of lignin into the wood cell walls is called lignifi-cation. Lignification of compression wood starts at the cell corners and condensesthe lignin through the cell walls to the lumen [3, 4]. It transforms the normallylignified cell wall into the highly lignified cell wall. Fig. 1.2 shows the structureof a compression wood cell, including the two regions of cell walls.

Fig. 1.2: Structure of a compression wood cell

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1.2 Project descriptionThe regions lumen (L), normally lignified cell wall (NL) and highly lignified cellwall (HL) need to be segmented, so they can be measured individually. This seg-mentation was previously done manually, but it is tedious, expensive and can bedependent on the operators [3].

Therefore an automatic method was developed to replace the manual segmenta-tion [3]. The result of this method is a crisp segmentation that divides each woodcell in L, NL and HL.

The boundaries between the different regions are fuzzy by nature in the originalimage of wood cell, especially the boundary between HL and ML. Therefore theboundary is not well defined and it is difficult to set a crisp segmentation line.Naturally we would think to use a fuzzy segmentation method for the compressionwood fiber cross-section images.

1.3 Thesis purposeThe main objective of the thesis project is to use the fuzzy segmentation methodsto refine the crisp segmentation results provided by [3]. This includes the followingconcrete steps:

1. Find one or several suitable fuzzy segmentation methods.

2. Segment the regions L, NL, HL and ML individually with the fuzzy segmen-tation methods by using the given crisp results.

3. Compare the performance among these segmentation methods.

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2 MethodsSome segmentation methods based on the thresholding, like Otsu’s method [6] andFukunaga’s method [7], are used in many applications frequently. Thresholdingutilizes the significant intensity variations between regions. It does not work wellhere because the gray values of the different regions are not distinct enough. Fig.2.1 depicts a compression wood cell and its corresponding histogram. Clearly fromthe histogram that there is one obvious valley between L and other regions, whichmeans L is easy to detect. But NL and HL are not able to segment by thresholdingaccurately.

Fig. 2.1: A compression wood cell and its histogram

In recent years, fuzzy segmentation as an alternative method to traditional “crisp”segmentation methods had a big development. It is an effective way to extract ob-jects in different image types, especially microscope images [8]. In this project, wehave the results of the crisp segmentation provided. We want to refine the resultsby creating the fuzzy segmentation and use the crisp segmentation for initiation.

In what follows, first we explain the concept of fuzzy connectedness that mea-sures the hanging-togetherness of objects in a given image. We then present analgorithm based on this concept, called Iterative Relative Multi Object Fuzzy Con-nectedness (FC) [9], which segments the multiple objects in the given image. Theabove are presented in section 2.1. The second method is based on WeightedDistance Transform on Curved Space (WDT) [10], which transforms gray-levelimages to weighted distance images. Here, we apply a competition mechanismon the weighted distance images to segment multiple objects in the given image,which is presented in section 2.2.

2.1 Fuzzy ConnectednessFuzzy connectedness in images builds on two basic fuzzy relations: the fuzzyadjacency of pixels, which is decided by the properties of a plane integer space,and the fuzzy affinity between pixels, which depends on the fuzzy adjacency ofpixels and their intensity values [11]. We first present the definitions and notationsof these two fuzzy relations in section 2.1.1 and 2.1.2 respectively. We then statehow to calculate the fuzzy connectedness between pixels in section 2.1.3. At last,

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the Iterative Relative Multi Object Fuzzy Connectedness (FC), which is used todecide the memberships of pixels, is introduced in section 2.1.4.

2.1.1 Fuzzy adjacency

Fuzzy adjacency is a fuzzy relation, denoted by α, which represents the adjacentdegree of points in a plane positive integer space Z2. An image is defined asI = 〈C, f〉, where C is the set of coordinates of points in Z2 and the intensityfunction f is to calculate the intensity value of each point [12]. Fuzzy adjacencyis reflexive and symmetric, which depends on the coordinates of pixels in Z2 [12].We define a function µα(p, q) to calculate the fuzzy adjacency between any twopixels p and q in the image. It is a non-increasing function on the distance betweenpixels [13]. We use the following definition to calculate the fuzzy adjacency α:

µα(p, q) =

1

1+k1

(√∑2i=1 (pi−qi)2

) if√∑2

i=1 (pi − qi)2 ≤ 2

0 otherwise

, (1)

where p, q ∈ C, denoted as (p1, p2) and (q1, q2) respectively. k1 is the distancedecline factor. It is clear from Eq. 1 to see the closer the pixels, the larger theadjacency values.

√∑2i=1 (pi − qi)2 ≤ 2 determines the scope of fuzzy adjacency.

Fig. 2.2 shows the fuzzy adjacency scope of a pixel p. The blue grids representthe adjacent pixels to p. The scope depends on the spatial coverage function youdefined.

Fig. 2.2: Fuzzy adjacency scope of a pixel p

2.1.2 Fuzzy affinity

Fuzzy affinity, denoted by κ combines the fuzzy adjacency of pixels and theirintensity values. It describes the grades of homogeneity of the adjacent pixels. Itis also reflexive and symmetric [11, 12]. In practice, we define a function µκ(p, q)for any p, q ∈ C to calculate the affinity degrees. We use the following definitionto compute the fuzzy affinity κ:

µκ(p, q) = µα(p, q)1 + k2|f(p)− f(q)| , (2)

where k2 is the gradient weight. It is clear from Eq. 2 to find that the higher thefuzzy adjacency between p and q and the smaller the intensity difference of p andq, the greater the fuzzy affinity between p and q.

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Usually, the function of fuzzy affinity is more complex than the one that is definedin Eq. 2. Trying to find a better function to calculate the fuzzy affinity is one of themost important and difficult parts in segmentation based on fuzzy connectedness.

2.1.3 How to calculate fuzzy connectedness

Now we capture the global hanging-togetherness, which builds on the fuzzy adja-cency and fuzzy affinity, called fuzzy connectedness. Before presenting the defini-tion of fuzzy connectedness, we first state a definition of path. A path is defined asa sequence of pixels, which connects any two pixels in the image [12]. And eachpair of successive pixels in the path are 8-connected [11]. All the possible pathsbetween any two pixels p and q in the image are denoted by Pathpq. Fig. 2.3(left) depicts three paths in Pathpq.

Fig. 2.3: Three possible paths between pixels p and q (left) and the strength ofone path (µκ(i) denotes the affinity between the i-th pair of successive pixels)

(right)

The strength of a path is determined as the minimum affinity between every pairof successive pixels along this path, denoted by µN , that can be considered as theweakest link of the path [11, 12].

µN(path) = Minµκ(i)∈path(µκ(i)), (3)

where µκ(i) is the fuzzy affinity between i-th pair of successive pixels in the path.Fig. 2.3 (right) displays the strength of one path between p and q. For anyp, q ∈ C, the fuzzy connectedness K between p and q is defined as follows [9].

µK(p, q) = Maxpath∈Pathpq(µN(path)) (4)

The fuzzy connectedness of every pair of pixels p and q in the image is determinedas the strength of the strongest path between them [11], which is depicted in Fig.2.4.

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Fig. 2.4: Fuzzy connectedness µK between two pixels p and q (µN(i) representsthe strength of the i-th path between p and q)

2.1.4 Iterative Relative Multi Object Fuzzy Connectedness

In this subsection, we present the FC method, which segments multiple objects in agiven image and works on a set of seeds for each object [9]. An algorithm κ-fuzzyobject extraction for multiple seeds is iteratively called by the FC method [12],which outputs a fuzzy connectivity image (FCI) for a set of seeds with a specificfuzzy affinity κ. We define FCIκ,S = 〈C, fκ,S〉. For every p ∈ C, the fκ,S(p) isdefined as follow:

fκ,S(p) = Maxs∈S(µK(p, s)), (5)

where S is a set of seeds for an object. The FCI gives the strongest fuzzy con-nectedness between every pixel and the set of seeds.

The FC method is an improved version of relative fuzzy connectedness (RFC),which is devised to overcome the problem in the RFC method [14, 15]. The FCmethod outperforms the RFC method in peripheral subtle region of an object [9].Another outperformance of the FC method is to avoid “holes” exiting in the seg-mented objects except there is at least one seed of another object in that “hole” [9].A “hole” is some connected background pixels in a segmented object. It is proba-bly caused by noise.

The segmentation procedure of the FC method with a specific fuzzy affinity κ ispresented as follow: We first define a set of seeds for each object, and then wechoose a set of seeds S for the selected object to explain how the FC methodworks. For the seeds S of the selected object, we calculate its corresponding fuzzyconnectivity image FCIκ,S. Then we compute another fuzzy connectivity imageFCIκ,W by using the rest sets of seeds W . Afterwards, compare FCIκ,S withFCIκ,W , and put these pixels into the selected object if their corresponding in-tensity values in FCIκ,S are larger than them in FCIκ,W . After that, we setthe affinities of the identified pixels with all other pixels to 0 and get a modifiedfuzzy affinity κM . We then use this κM to calculate a new FCIκM ,W for the rest

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seed sets W . Then iteratively compare FCIκ,S with FCIκM ,W and put the pixels,which have larger values in FCIκ,S than in FCIκM ,W , into the selected object,until there are no affinities of pixels changed. By now the selected object has beentotally segmented. Repeat the above procedure for the rest seed sets of the objectsuntil all the objects are segmented. A pseudo-code of the FC method, which givesthe detail of data structure and program flew, is described as follows.

Input: I = 〈C, f〉, κ as defined in section 2.1.1 and 2.1.2. The sets of seeds of allobjects Seed = {S1, S2, . . . , Sn}. Any two sets are non-intersection.

Output: ISeed = 〈C, fSeed〉 containing all the segmented objects. Different objectscorrespond to different labels and the pixels have the same label to form anobject.

Auxiliary data structures: For Si ∈ Seed, the FCIκ,Si = 〈C, fκ,Si〉. The restseed sets W = ∪(Seed\{Si}) and its corresponding FCIκM ,W = 〈C, fκM ,W 〉,where κM is the modified affinity after each iteration, and the temporaryimage It = 〈C, ft〉 such that ft = 1 if the intensity value of one pixel inFCIκ,Si is greater than that in FCIκM ,W . Index i refers to the iterationnumber; that is, the number of completed while loops, in Steps 5-17, foreach fixed Si.

begin

1. for Si ∈ Seed do

2. compute FCIκ,Si ;

3. set all pixels of It to 0 ;

4. set κM = κ and flag = true;

5. while flag = true do

6. set flag = false;

7. compute FCIκM ,W ;

8. for all p ∈ C do

9. if ft(p) = 0 and fκ,Si(p) > fκM ,W (p) then

10. set ft(p) = 1;

11. set flag = true;

12. for all q ∈ C, q 6= p, do

13. set κS(p, q) = 0;

14. endfor ;

15. endif ;

16. endfor ;

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17. endwhile;


19. if ft(p) = 1

20. fSeed = i;

21. endif ;

22. endfor ;

23. endfor ;

24. Output ISeed = 〈C, fSeed〉;end

2.2 Weighted Distance Transform on Curved SpaceThe Weighted Distance Transform on Curved Space (WDT) gives the shortestpath length between pixels in the image, and we use the weighted distance torepresent the length of a path [16]. The weighted distance of a path builds on thestep distance between every two successive pixels along the path. In section 2.2.1,we present the definition of the step distance. The weighted distance and how tocalculate the shortest path length between pixels are stated in section 2.2.2. Atlast we explain how to use the WDT method to decide the belongingness of pixelsin section 2.2.3.

2.2.1 Step distance

The step distance sd is the distance from one pixel to one of its 8-connectedneighbors, which depends on the Euclidean distance between the two pixels andtheir intensity values [17]. For any two pixels p, q ∈ C, we use the followingdefinition to compute the step distance:

sd(p, q) ={ √∑2

i=1 (pi − qi)2 + k32(f (p)− f(q))2 if

∑2i=1 |pi − qi| ≤ 2

Inf otherwise, (6)

where k3 is the scale factor between intensity and Euclidean distance. Fig. 2.5depicts the 8-connected neighbors (represented in blue) of pixel p. Eq. 6 illustratesthat the closer the intensity values of p and q and the smaller the Euclideandistance between them, the smaller the step distance from p to q.

Fig. 2.5: The 8-connected pixels of one pixel p

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2.2.2 How to calculate the shortest path length

The weighted distance of one path is the sum of all the step distances along thispath [16], which is denoted Wd. The following definition is used to calculate Wd.

Wd(path) =n∑i=1

sd(i), (7)

where sd(i) is the step distance of i-th pair of successive pixels in the path. Fig.2.6 shows the weighted distance of one path between p and q.

Fig. 2.6: The weighted distance of one path between p and q

The shortest path length between pixels is determined as the minimal weighteddistance of all possible paths between these pixels [16]. For any two pixels p, q ∈ C,the shortest path length is calculated by WDT(p, q) as follow.

WDT(p, q) = Minpath∈Pathpq(Wd(path)), (8)

where Pathpq is a set of all possible paths between p and q. Fig. 2.7 depicts theshortest path length WDT(p, q).

Fig. 2.7: The shortest path length between p and q (Wd(i) represents theweighted distance of the i-th path between p and q)

2.2.3 Multiple objects segmentation using the WDT method

The WDT algorithm is introduced in [16]. Now we state how to determine thebelongingness of pixels by using the result of the WDT algorithm. First we select

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a set of seeds for each object. Then we use the WDT method to calculate theshortest path length between each pixel and each set of seeds. Finally the pixel isassigned to the object, whose seed is closest according to the WDT [9]. A pseudo-code of this multiple objects segmentation using the WDT method is described asfollows.

Input: I = 〈C, f〉, sd as defined in section 2.1.1 and 2.2.1, the sets of seeds of allobjects Seed = {S1, S2, . . . , Sn} of pairwise disjoint sets of seed pixels.

Output: ISeed = 〈C, fSeed〉 contains all segmented objects. Different objects cor-respond to different intensity values, the pixels of the same intensity valueconstitute an object.

Auxiliary data structures: For Si ∈ Seed, the WDT imageMsd,Si = 〈C, fsd,Si〉,where fsd,Si computes the shortest path length between each pixel and Si.The rest sets of seedsW = ∪(Seed\{Si}) and its corresponding WDT imageMsd,W = 〈C, fsd,W 〉. Index i marks every set of seeds, which is between 1and n.

begin

1. set all pixels of ISeed to 0;

2. for Si ∈ Seed do

3. compute Msd,Si and Msd,W by using the WDT method;


5. if fSeed(p) = 0 and fsd,Si(p) < fsd,W (p)

6. set fSeed(p) = i;

7. endif ;

8. endfor ;

9. endfor ;

10. output ISeed = 〈C, fSeed〉;

end

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3 Implement detailsWe built on available implementations for the FC method and the WDT method.The FC method was implemented by Joakim Lindblad in MATLAB and FilipMalmberg provided a program that calculates the WDT for one single seed. Weextended this further to work on multiple objects and allow a set of seeds for eachobject. The parameter values in both methods are determined in terms of theproperties of the wood fiber cross-section images and several experiments.

In what follows, running environment is listed in section 3.1. The provided data,such as the wood fiber cross-section image and the results of the crisp segmentationand manual segmentation provided, are pooled together in section 3.2. Parametersettings for the FC method and the WDT method are presented in section 3.3 and3.4, respectively. An example is presented in section 3.5 to demonstrate the multi-seed selection for the regions L, NL, HL and ML. The overlapping degree of thesegmented regions and the deviation between the segmentation boundaries, whichare used to evaluate the performance of the FC method and the WDT method,are stated in section 3.6.

3.1 Running environmentThe following inventory shows the operating system and the application softwares,which are used in this thesis.

1. Operating System: Red Hat Enterprise Linux Client release 5.6 (Tikanga)

2. Intel(R) Xeon(TM) CPU 3.60GHz

3. Cache size: 2048KB

4. MATLAB 7.11.0 (2010b)

3.2 Provided dataThere are three kinds of provided image data in this project.

1. The cross-section image: Pinus sylvestris L., a sample (2 ×1 ×1 cm3) ofScots pine is used to generate the wood fiber cross-section image. Then a 20µm thick cross-section was cut using a sledge microtome. The section wasmounted on glass slides with some drops of distilled water and viewed withan epifluorescence microscope (Leica DM RE) and a HCX PLFLUOTAR 40xobjective. 16-bit intensity image was obtained from the microscope with aLeica DFC490 CCD camera attachment and a blue filter (470 µm). The sizeof the image is 3264 ×2448 and the resolution is 0.1072 µm/pixel [3]. Theacquired image, which is shown in Fig. 3.1(a), is divided into sub-images.Each sub-image includes a whole compression wood cell. Fig. 3.1(b) showsone sub-image.

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a bFig. 3.1: (a) The acquired wood fiber cross-section image. (b) One

sub-image of a compression wood cell

2. Automatic segmentation results of 29 sub-images: For each cell there arethree crisp segmentation results, which are corresponding to L, NL and HLrespectively. These segmentations were achieved with the method describedby Selig et al. [3]. Fig. 3.2 (a-c) depict the crisp segmentation results of Fig.3.1(b).

3. Manual segmentation results of 29 sub-images (same as for automatic seg-mentation): For each cell there are three manual segmentation results, whichare corresponding to L, NL and HL respectively. The cells were delineatedmanually by an expert. Fig. 3.2 (d-f) depict the manual segmentation resultsof Fig. 3.1(b).

a b c

d e fFig. 3.2: (a-c) Crisp segmentation of a sub-image in L, NL and HL in sequence.

(d-f) Manual segmentation of a sub-image in L, NL and HL in sequence

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3.3 Parameter settings for the FC methodThe FC method is based on fuzzy connectedness. And fuzzy connectedness buildson fuzzy adjacency and fuzzy affinity. We present how to choose the values for eachparameter in fuzzy adjacency and affinity in section 3.3.1 and 3.3.2, respectively.

3.3.1 Fuzzy adjacency

The function of calculating the adjacency contains three input parameters: theoriginal image I, the adjacent scope and the distance decline factor k1. In thisthesis, I is the sub-image of each compression wood cell. The adjacent scopeof one pixel p is shown in Fig. 2.2 in section 2.1.1. Eq. 1 in section 2.1.1 isused to calculate the adjacency of a given image. k1 was chosen experimentally.Therefore, we tested the values between 0.1 and 1.0, and 0.5 was the best choice.As mentioned in section 2.1.1, the adjacency value is in [0 1], which just depends onthe Euclidean distance between any two adjacent pixels. The maximum Euclideandistance is 2 in the defined adjacent scope. So k1 = 0.5 makes the adjacency valuesdistribute in [0.5 1].

The output of the function is a square matrix, whose row length is the numberof pixels in a given image. Each row of the matrix contains the adjacency valuesbetween one pixel and all the pixels in the image.

3.3.2 Fuzzy affinity

Three input parameters need to be specified in the affinity function, see Eq. 2 insection 2.1.2. They are the image I, the adjacency matrix and the gradient weightk2. The image I and the adjacency matrix were used as described in section 3.3.1.But here, we converted the intensity values of I to the range [0 1]. k2 was chosenexperimentally, we tried 10, 20, . . . , 100 and 20 was the best choice. The differenceof intensity values of two adjacent pixels was too small due to range of the intensityvalues. Therefore, we set k2 = 20 to increase the impact of the intensity values ofpixels.

The result of this affinity function is also a square matrix, same as the fuzzyadjacency matrix. But here, the values in each row are the fuzzy affinity valuesbetween one pixel and all the pixels in the image.

3.4 Parameter settings for the WDT methodWe state how to choose values for each parameter in the WDT method in thissection. There are three parameters in this method: the original image I, thepositions of the seeds and the scale factor k3 in Eq. 6 in section 2.2.1. In thisthesis, image I is the sub-image of each cell as described in section 3.2. Theposition of the seed is the linear index of seed in image I. We set k3 = 1.0. It keepsthe original effect of the intensity values of pixels.

The result of the WDT method is a matrix, whose size is same with the imageI. The value of each element in the matrix is corresponding to the shortest pathlength from the pixel to the closest seed.

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3.5 Multi-seed selectionSeeds selection is one of the most important parts in these two fuzzy segmentationmethods. Seeds are pixels, which are chosen to represent an object. It needs agood strategy to choose the seed pixels, and we also should consider which seedsare better for an object to be segmented from the others in a given image. In thissection we introduce three multi-seed selection methods, which utilize the crispsegmentation results of the objects L, NL, HL and ML and convert them to theirown seeds. We use the crisp segmentation results of one compression wood cell toexplain how to select the set of seeds for each object. At last we present how tocombine the sets of seeds of the four objects into a seed image.

1. Seeds of L: We use the morphological thinning, which is implemented inMATLAB in the bwmorph function with the “thin” parameter [18], toget the seeds of L. The crisp segmentation result of L will be shrunk intoa minimally connected stroke. We use this stroke as the seeds of L. Fig.3.3(a) shows the crisp segmentation result of L and Fig. 3.3(b) depicts theminimally connected stroke of L.

a bFig. 3.3: (a) The crisp segmentation result of L. (b) Seed image of L,

which is the minimally connected stroke of (a).

2. Seeds of NL and HL: The seeds of NL and HL are selected experimentally.We choose the pixels on the following three places as the seeds of NL and HLrespectively: (1) The ring halfway between the outer and inner boundariesof NL and HL. (2) The ring halfway between (1) and the outer boundaries ofNL and HL. (3) The ring halfway between (1) and the inner boundaries of NLand HL. Make the three options (1), (2) and (3) as a list. The experimentsshow that choosing (2) as seeds is the best choice.

We still use the morphological thinning operation to get the seeds of NLand HL. Fig. 3.4(a) shows the crisp segmentation result of NL. We call thebwmorph function with “thin” to shrink NL, so that the outer boundaryof the object after the shrinkage is positioned at (2), which is shown in Fig.3.4(b). We then extract the pixels of this outer boundary and use them asseeds for NL (see Fig. 3.4(c)). We apply the same operation for HL. Fig.3.5(a-c) display the seeds selection of HL.

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a b cFig. 3.4: (a) Crisp segmentation result of NL. (b) After shrinking NL theouter boundary of the object is positioned at (2). (c) Seed image of NL,

which is the outer boundary of (b).

a b cFig. 3.5: (a) Crisp segmentation result of HL. (b) After shrinking HL theouter boundary of the object is positioned at (2). (c) Seed image of HL,

which is the outer boundary of (b).

3. Seeds of the ML: For this step we use the image including the crisp results ofthe segmented cells (see Fig. 3.6(a)). First we invert this binary image to getthe crisp result of ML, which is shown in Fig. 3.6(b). Then we shrink it intoa minimally stroke, the skeleton, by calling the bwmorph with the “thin”parameter. The stroke as the seeds of ML of the whole image is shown inFig. 3.6(c). Divide it into sub-images for corresponding compression woodcells. The seeds of ML of the example cell are depicted in Fig. 3.6(d).

a b

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c dFig. 3.6: (a) Image including the crisp result of the segmented cells. (b)

The complement image of (a). (c) Seed image of ML, which is the skeletonof (b). (d) Seed image of ML for the example cell.

The seeds of the fours objects (L, NL, HL and ML) are notated SL, SnL, ShL andSmL, respectively. The intensity values of the seeds are 1. We combine them intoa seed image S by using the following equation.

S = SL+ SnL ∗ 2 + ShL ∗ 3 + SmL ∗ 4, (9)

Hence, the pixels in the seed image S, whose intensity values are 1 are seeds ofL, the pixels with the intensity value 2, 3 and 4 correspond to seeds of NL, HLand ML, respectively. The FC method and the WDT method use the same seedimage for the same cell. Fig. 3.7 shows the seed image of the example cell.

Fig. 3.7: The seed image of the example cell

3.6 Comparison methodsThe overlapping degree of the segmented regions (overlapping degree) and the devi-ation between the segmentation boundaries (boundary deviation). These methodsare used to measure the similarity of two segmented regions of the same wood cell.

3.6.1 Overlapping degree of the segmented regions

The overlapping degree method utilizes the relation between the overlapping areaand the total area of the two regions, which is depicted in Fig. 3.8.

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Fig. 3.8: The two regions A, B and the overlapping part of A and B

We define the following equation to calculate the overlapping degree η of A andB:

η(A,B) = 2 ∗ |A ∩B||A|+ |B| (10)

It is clearly from Eq. 10 that the range of η is between 0 and 1. When the valueof η is large, the two regions have a great overlap. 1 means the two regions totallyoverlap and 0 means the two regions do not intersect.

3.6.2 Deviation between the segmentation boundaries

In the boundary deviation method, the deviation between segmentation bound-aries of the same region are used to evaluate the distance between the segmentationlines. Fig. 3.9 shows the diagram of two segmentation boundaries.

Fig. 3.9: The diagram of two segmentation boundaries.

The deviation D is calculated as follow:

D = 12(DL1L2 +DL2L1), (11)

where

DLjLk =

√√√√∑i ωid2i∑

i ωi, (12)

where di is the minimal distance, which is from the pixel i on Lj to Lk. ωi is theweight, which is related to the position of pixel i and based on the curvature of Lj.

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It ensures a better evaluation of the distances between Lj and Lk. The followinggives the weights, which were suggested by Dorst and Smeulders [19].

ωi ={

0.948 if step i is vertical or horizontal1.343 if step i is diagonal (13)

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4 Evaluation and resultsWe applied the FC method and the WDT method on 29 sub-images of woodcells to get the results of the two fuzzy segmentation methods. These results andadditionally the results of the crisp segmentation were compared with the manualdelineation. Here, we checked if the fuzzy segmentation methods refine the resultsof the crisp segmentation. A qualitative evaluation is described in section 4.1.A quantitative analysis, which is using the overlapping degree of the segmentedregions and the deviation between the segmentation boundaries, is presented insection 4.2.

4.1 Qualitative evaluationThis evaluation aims to get an intuitive comparison between the results of thefour segmentation methods for the regions L, NL and HL. Fig. 4.1 displays foursub-images of wood cells and their corresponding segmentation results.

Fig. 4.1: Four sub-images of wood cells are listed in the first row and theirsegmentation results are shown from the second row to the fifth row, which

correspond to the manual segmentation, the crisp segmentation, the FC methodand the WDT method.

The first thing to note is that the boundaries of each region in the manual andcrisp segmentation results are smooth lines, which is derived from the nature of the

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two segmentation methods. The segmentation boundaries of the WDT methodare a bit jagged, whereas the boundaries of the FC method are very jagged. Thisis because the definition of the fuzzy affinity is not suitable for this problem, es-pecially for the outer boundaries of NL and HL. This might be a reason for thelower accuracy of the FC method compared to the WDT method.

The second thing we observed is about the similarity of the automatic segmenta-tion results to the manual one. For the first two example cells in Fig. 4.1 (firstand second columns) the manual and automatic segmentation results look verysimilar, whereas for the last two example cells (third and fourth column in Fig.4.1) the WDT and FC results are mostly related to the crisp segmentation. Thisis because the seed images for the two fuzzy segmentation methods are based onthe crisp segmentation results.

4.2 Quantitative evaluationIn this subsection we evaluate the results of the four segmentation methods ina quantitative way. For this we used the overlapping degree of the segmentedregions and the deviation between the segmentation boundaries as described insection 3.6. There are six combinations of the four segmentation methods: Manualvs Crisp, Manual vs FC, Manual vs WDT, Crisp vs FC, Crisp vs WDT and FC vsWDT. We use the manual segmentation results as the ground truth. The closer tothe manual segmentation results the better. So in the following two evaluations weemphatically analyze the relationship between the three automatic segmentationmethods and the manual segmentation.

4.2.1 Evaluation by using the overlapping degree method

In the first evaluation, the overlapping degree of the segmented regions is used tocalculate the similarity of each combination. For each cell we calculate the meanand standard deviation of the overlapping degree of the regions L, NL and HLseparately for all before mentioned combinations. Tables 4.1-4.3 list the mean withthe standard deviation of the overlapping degrees of L, NL and HL, respectively.The closer the overlapping degree is to 1, the more similar the segmentation resultsare.

Crisp WDT FCManual 0.91 (0.04) 0.91 (0.03) 0.93 (0.03)FC 0.97 (0.02) 0.97 (0.02) -

WDT 0.98 (0.02) - -Table 4.1: Mean (and standard deviation) of the overlapping degree of L.


WDT 0.97 (0.01) - -Table 4.2: Mean (and standard deviation) of the overlapping degree of NL.

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WDT 0.90 (0.02) - -Table 4.3: Mean (and standard deviation) of the overlapping degree of HL.

The first rows of Table 4.1-4.3 show the mean (with the standard deviation) ofoverlapping degrees of the three automatic segmentation methods compared withthe manual segmentation in L, NL and HL respectively. It is clear from the firstrow of Table 4.1 that the FC method has the best performance in L. The WDTmethod and the crisp segmentation have the same mean, but the WDT method isbetter because it has the smaller standard deviation. We note from the first row inTable 4.2 that the means of the three automatic segmentation methods are samein NL. So according to their standard deviations, the FC and the WDT methodsperform similar, but better than the crisp segmentation method. The first row ofTable 4.3 shows that the WDT method outperforms both the FC method and thecrisp segmentation in HL.

By observing the rest of the overlapping degree results it became obvious that theperformance of the crisp segmentation and the WDT method are most similar inL, NL and HL. So the WDT method works more similar to the crisp segmentationmethod than the FC method.

4.2.2 Evaluation by using the boundary deviation method

In the second evaluation, we use the deviation between the segmentation bound-aries to calculate the deviation of the segmentation boundaries of regions L, NLand HL. The means and the standard deviations of the three regions are calculatedto measure the similarity of each combination, which are listed in Table 4.4-4.6.The smaller the boundary deviation is, the more similar the segmentation resultsare.


WDT 1.55 (0.47) - -Table 4.4: Mean (and standard deviation) of the boundary deviation of L


WDT 1.78 (0.46) - -Table 4.5: Mean (and standard deviation) of the boundary deviation of NL


WDT 2.51 (0.46) - -Table 4.6: Mean (and standard deviation) of the boundary deviation of HL

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By comparing the manual result with the automatic results, it is clear that theFC method also performs best in L. The WDT method has the best performancein NL and HL.

The values of the boundary deviation show that the results of the crisp segmenta-tion and the WDT method are most similar regarding the regions L and NL. Butfor HL the FC and the WDT methods performed most similar.

4.2.3 Final evaluation result

In the evaluation results of the two comparison methods, the best segmentationmethods in regions L, NL and HL are shown in the first two rows of Table 4.7. Forthe regions L and HL the results are clear. The FC method performed best forL and the WDT method performed best for HL. For NL we have to take a closerlook, because according to the overlapping degree the WDT and FC methods had asimilar performance. But since the boundary deviation votes for the WDT methodand as mentioned in the qualitative evaluation, the segmentation boundaries of NLby using the FC method are most ragged among the three automatic segmentationmethods, we regard the WDT method as more accurate concerning NL. The finalevaluation results are shown in the last row of Table 4.7.

L NL HLoverlapping degree FC WDT, FC WDTboundary deviation FC WDT WDT

Final results FC WDT WDTTable 4.7: The best segmentation methods in L, NL and HL

4.3 Special case analysisWe noticed that for some cells the overlapping degree and the boundary deviationwere quite large when comparing manual and automatic segmentations. Especiallythe region HL was affected by this.

We chose one example wood cell, see Fig. 4.2(a), to visualize this phenomena. Fig.4.2(b-e) show the results of the manual segmentation, the crisp segmentation, theFC method and the WDT method, respectively.

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a b

c d

e fFig. 4.2: (a) Sub-image of wood cell. (b) Manual segmentation result. (c) Crisp

segmentation result. (d) Result of the FC method. (e) Result of the WDTmethod. (f) Seed points for HL.

In the first column of Table 4.8 and 4.9 we listed the overlapping degrees and theboundary deviations of the three automatic segmentation results compared withthe manual result on HL of the selected cell. For comparison the second and thirdcolumns contain the corresponding means (compare Table 4.3 and 4.6) and thedifferences between these means and the calculated values of the selected cell.

overlapping degree Mean DifferenceCrisp 0.62 0.83 -0.21FC 0.64 0.81 -0.17

WDT 0.67 0.85 -0.18Table 4.8: The first column contains the overlapping degree of HL of the selected

cell. Here, the manual segmentation was compared with the three listedautomatic segmentations. The second column contains the mean of the

overlapping degree for all 29 cells and the third column contains the differencebetween the values in the first and the second column.

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Deviation Mean DifferenceCrisp 6.07 3.65 2.42FC 6.93 3.52 3.41

WDT 6.69 3.17 3.52Table 4.9: The first column contains the boundary deviation of HL of the

selected cell. Here, the manual segmentation was compared with the three listedautomatic segmentations. The second column contains the mean of the

boundary deviation for all 29 cells and the third column contains the differencebetween the values in the first and the second column.

Tables 4.8-4.9 show that there are large difference between the three automaticsegmentation results and the manual result. As we mentioned before, the multi-seed selection is based on the crisp segmentation results. If the seed points arebadly chosen, the quality of the performance of FC and WDT is directly affected.Comparing the seed points of HL, in Fig. 4.2 (f), and the manual segmentation,in Fig. 4.2 (b), it is clear that a part of the seeds lie outside the manually selectedregion HL. This means that the results of FC and WDT will always contain pixelsthat are wrongly classified as HL. With the here described methods this is notavoidable.

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5 Conclusion and future workThe original intention was to replace the manual segmentation of compressionwood cells by an automatic method. A crisp segmentation method [3] has beendeveloped for this purpose. This thesis aimed to refine the results of the crisp seg-mentation provided by using fuzzy segmentation methods. We applied two fuzzysegmentation methods: Iterative Relative Multi Object Fuzzy Connectedness andWeighted Distance Transform on Curved Space, the FC method performs best forthe region L compared to the other automatic segmentation methods. For the re-gions NL and HL the WDT method outperforms the others. Here, we see that wewere able to refine the crisp segmentation results by using the fuzzy segmentationmethods.

We note that there are still some drawbacks with the two fuzzy segmentationmethods. The problem with the FC method is that the fuzzy affinity functiondoes not work well on the regions NL and HL. It causes jagged segmentationboundaries, which differed a lot in appearance compared with the manual seg-mentation. In future work we could consider using different functions to calculatethe fuzzy affinity according to the properties of different regions. The other prob-lem is related to the multi-seeds selection. Since it is based on the given crispsegmentation result, a bad crisp segmentation leads to bad fuzzy segmentationresults. Since it is difficult to select the seeds from the original image directly, infuture work we could weigh the seed points based on how probable it is that thepixels are actually lying in the corresponding region.

According to the evaluation results, the FC method performs best for region L andthe WDT method has the best performance for the regions NL and HL. Since thesealgorithms use the same seed images, it is possible to develop a hybrid algorithm.This hybrid algorithm could perform better than one of the fuzzy segmentationmethods alone.

It is also relevant to consider the time performance of the segmentation algorithms.Until now most of the algorithms of this thesis are implemented in MATLAB,which is an interpreted language. An implementation using a compiler language,like C, would probably be more time efficient.

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