Automatic Extraction of Shape Features for Classification of Leukocytes

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1 00 International Conference on Artificial Intelligence and Computational Intelligence Automatic Extraction of Sape Features for Classification of Leukocytes Ermai Xie, T. M. McGinnity, QingXiang Wu Intelligent Systems Researc Centre, University of Ulster at Magee, Londonderry, BT8 7JL, N.I., UK, {xie-e, tm.mcginnity, ttp://isrc.ulster.ac.uk/ Abstract Microscope-based wite blood cell classification plays an important role in diagnosing disease. Te number of segments of nucleus and te sape of segments of nucleus are regarded as important features. Since it is difficult to automatically extract tese features from a blood smeared image, tey ave not been used in te current automatic classifiers based on smeared images. In tis paper, an approac based on te Poisson equation is proposed to extract te number of segments of nucleus in a more straigtforward manner, and inner distances are used to represent te sape features of te nucleus segments. Te experimental results sow tat te proposed approaces can extract te features efficiently. Tese important features can be added to te input feature set of neural networks or oter classifiers to improve classification results of leukocytes in a blood smeared image. Keywords- Sape feature extraction, Poisson equation, Inner distance, Leukocyte classification I. INTRODUCTION Microscope-based wite blood cell classification is still an important source of data for clinical cytology in patologies fields, even if blood cell analysis as been progressively developed using various new tecnologies. Tis process is usually performed by ematologists, and can be slow and subjective. Terefore, an automatic classifier based on blood smeared images is proposed to improve speed and accuracy of te performance. Biological evidence sows tere are five types of te wite blood cell, wic also can be divided into two categories: granulocytes and agranulocytes [-5]. Te granulocytic series include neutropilic granulocyte (N), eosinopilic granulocyte (E) and basopilic granulocyte (B). Te agranulocytic series include lympocyte (L) and monocyte (M). Some typical examples of tese types are sown in Figure, were N as small granules in cytoplasm and only one nucleus, wit a variable number of lobes; E as bilobed nucleus and coarse cytoplasmic granules; B include many cytoplasmic granules over te nucleus; L as round nucleus and is devoid of specific granules; M as a kidney-saped nucleus and sligtly basopilic in te cytoplasm. Table summarizes te caracteristic features of tese cells and teir relative size and number in normal blood. Te current approaces classify leukocytes by te color of nucleus and leukocyte cytoplasm [] [3]. Tese approaces only provide a limited accuracy. In order to gain iger performances, te size of nucleus, te sape of nucleus, te segmentation of nucleus, te presence of granules in cytoplasm and te structure are also used in most of te classifiers [7] [8] [9]. However, te definition of te sape caracteristics is not straigtforward for computer to recognize automatically. Most approaces use varieties of geometry caracteristics to describe tese sapes, i.e. circularity, concavity, convexity, principal axis ratio and so on. For classification, neural networks can also be used [7-9]. Teir results are good, but tey ave not used te number of segments and te sape of segments as inputs, terefore, it is very ard to identify te various maturity stages of te cells. Tis paper focuses on extracting tese two kinds of important sape features and te features are used as inputs for neural networks to improve te accuracy of te classification. Te proposed approac uses te notion of random walks, wic can be performed as te solution of te Poisson equation, combining wit inner distance, to obtain tose important features. Te remainder of tis paper is organized as follows. In Section, te metodology and algoritm are outlined. Te experimental results are sown in Section 3 and te conclusions are presented in Section. TABLE I. THE FEATURES OF LEUKOCYTES Features Granulocytes Agranulocytes Neutropil Eosinopil Basopil Monocyte Lympocyte Diameter -5 µm -5 µm -5 µm -0 µm 6-8 µm Nucleus U-saped, S-saped, Segmented, Poorly sown, Kidney saped Round Granules -5 segmented Azuropilic granules; specific granules bilobed Eosinopilic granules S-saped Basopilic granules of different sizes Basopilic bluis-gray Scanty, ligt blue /0 $ IEEE DOI 0.09/AICI

2 Figure. Examples of 5 types of uman leukocytes. II. METHODOLOGY AND ALGORITHM Random walks are used in vision applications suc as perceptual grouping and segmentation. In tis paper, it is used to extract features from te contour of te sape of te nucleus. Sapes are considered surrounded by simple, closed contour and divided into grids. Ten a set of particles is placed at eac grid inside te sape and allowed to move by random walking until tey it te contour. During tis time, all te random walking from one grid to a contour is used to reflect te relationsip between tis grid and te global sape. For eac grid, we ave a mean time of random walking corresponding to tat a particle walks from te grid to contour via possible pats. Te mean time of random walking is able to give a ig value in te center of te sape and a low value at te contour of te sape (te value of all te grids on te contour is considered as zero ere in tis work). Unlike te distance transform, wic uses te minimum distance to te contour, te random walk can reflect more global properties of te silouette. It is beneficial to be able to analyze te sape of nucleus, and it is able to describe te cange wen te cell is growing old. Some examples are sown in Figure. Te diagrams sow te different stages of te wite blood cell growing process from left (infant stage) to rigt (mature stage). It can be seen tat te segments of te nucleus are canged from one to two. Tere is a ig computational cost to simulate te random walking algoritm in wic large number of random pats is required. Terefore te Poisson equation is employed to andle tis problem. electrostatics, mecanical engineering and teoretical pysics. Let U( x, y ) denote te mean time, is te size of grid. Ten U( x, y ) can be calculated for every grid inside te silouette by using following equation. ( x, y) U = () + ( U ( x+, y ) + U ( x, y ) + U ( x, y + ) + U ( x, y )) Here U( x, y ) is equal to te mean value of its immediate four neigbors plus a constant (Te constant means te speed of random walking is one grid per time unit). Te equation () is a discrete form approximation of te Poisson equation: ( ) U x,y U( x, y) + U( x+, y) + U( x, y ) + U( x, y+ ) U( x, y) If te sape only includes one grid wit four contour grids surrounding it and te boundary (also called Diriclet boundary conditions) conditions, ten we ave: U( x, y) = U( x+, y) = U( x, y ) = U( x, y+ ) = 0 () (3) Based on te definition of equation (), we ave: Figure. Example results of mean time distribution obtained using solution of Poisson equation. Brigt points correspond to ig value of mean time. A. Poisson Equation Te function of random walk can be formalized as te Poisson equation to be calculated. Poisson's equation is a partial differential equation, wic is commonly used in (, ) U x y = + ( U( x+, y) + U( x, y) + U( x, y+ ) + U( x, y )) () = + ( ) = Take te value to te equation (), and ten we ave:

3 (, ) U x y U( x, y) + U( x+, y) + U( x, y ) + U( x, y+ ) U( x, y) = Here (5) denotes te overall scaling and represent te speed of random walks, In order to accord wit te definition in te equation (), it is set as. = B. Solve te Poisson Equation In tis paper, eac pixel is treated as one grid. Successive over-relaxation is applied to solve tis Poisson equation. For a sape wit m pixels, it will be calculated by following m m linear system. [ A][ U] [ b] (6) =, (7) were [ U ] is te matrix wic includes all te solution of Poisson equation by using natural ordering: were [ A ] is: [ ] U = [ u, u,, u ] T, (8) D I I D I I D I 0 0 [ A] = (9) 0 0 I D I I D I 0 0 I D I is te identity matrix and D is: D = (0) m [ b] is: [ b] b b bm = [,,, ] T, () were b, b,, bm are te values decided by te Diriclet boundary condition plus te value of U( x,y). In tis paper, all te values of contour grids are defined as 0 and all U x,y =, so we ave: te ( ) b = b = = bm. () For convenience, we set b = b = = b m =. Te algoritm for te converter from an image to [A] is as follow: Algoritm : Converter.Load a binary image.count=0 3.For x= to eigt. For y= to widt 5. If tis pixel is not blank 6. count= count+ 7. A(count, count)= 8. Record te count as order number 9. If te up neigbor is not blank 0. A(count-, count)= -. A(count, count - )= -. If te left neigbor is not blank 3. A(left neigbor s order number, count)=-. A(count, left neigbor s order number)=- 5. End for 6.End for Now following algoritm is used to calculate [U]: Algoritm : Solution of Poisson equation.n equals to lengt of [b] and [U]= {0}.Repeat until te average iteration error of all pixels 5 is smaller tan 0 3. For i= to n. Temp=0 5. For j= to i- 6. Temp=Temp + A(i, j)*u(j) 7. End for 8. For j=i+ to n 9. Temp=Temp + A0(i, j)*u(j) 0. End for. U(i)=(- ω)*u0(i)+ ω *(b(i)- temp)/a(i,i). End for 3.End repeat

4 Were ω is relaxation factor, it can be set as as default, te metod will be GS metod. It also can be calculated using te spectral radius of te Jacobi transition matrix. C. Feature extraction In order to extract more straigtforward features including te number of segments and te sape of eac segment, te skeleton algoritm and inner distance are combined wit te solution of te Poisson equation. First, te U is calculated by using te central differences, and tose points wit local maximum value can be discovered by using certain tresold value. Te number of te local maximum points is used to count te number of te segments. Second, te skeleton of nucleus is also able to be extracted by using te following equations, wic are proposed in te paper []. Te skeleton can be narrowed down by using anoter tresold. U U ( ) U Ψ = U (3) Ψ represents te value for skeleton Finally, based on te skeleton, te longest inner distance of eac segment are calculated and recorded. Tis step consists of two steps: ) Build a set of all points witin one skeleton of segment. For eac pair of points, if te line segment connecting two points falls entirely witin te skeleton, ten build an edge between te two points wit te weigt equal to te Euclidean distance. ) Apply a sortest pat algoritm to te grap. For a round sape, te skeleton is sort and te inner distance is same as Euclidean distance. Figure 3. Inner distance and Euclidean distance. For a kidney sape, te inner distance is longer tan te Euclidean distance. In order to employ tem in a neural network or oter classifiers as inputs, te number of te local maximum points from step one is counted to represent te segment of nucleus. For different sape of segments, it is defined as tree numbers {0,, }. 0 represents round sape of segment, represents kidney sape, and represents U sape as sown in Figure 3. III. RESULTS OF THE EXPERIMENT Te system as been implemented using Matlab. Figure sows some samples from te test set. Figure sows te results of te process. Te sub-image A sows te nucleus of te wite blood cell after segmentation wic is based on te metod proposed in [6]. A B C D E F Neutropil Eosinopil Basopil Lympocyte Monocyte Monocyte Figure. Experimental Results. 3

5 Te result of te Poisson equation, wic uses te algoritm, is sown in te sub-image B. Te value is sown by te color map, and te brigt colour zone represents a ig value zone, wic normally is located in te centre of te sape, and blue represents a low value. Te sub-image C sows U wic is te cange rate of te result of te Poisson equation, and is calculated by te central differences metod. Te sub-image D sows te local maximum value of te result of te Poisson equation. In tis experiment, te tresold of U is set as 0.5 to extract te local maximum points. Te result of equation (3) is sown in te sub-image E and ere is used to extract te skeleton of te sape. Te sub-image F is te skeleton diagram wic is segmented by using te tresold 0.. To classify different sapes of segments, te lengt of longest inner-distance and te ratio between longest inner-distance and Euclidean distance are used. If te longest inner-distance is smaller tan 3 pixels and te ratio is, te sape is defined as a circle. If te longest inner-distance is bigger tan 3 pixels and te ratio is bigger tan but smaller tan.57, ten te sape is defined as a kidney. If te ratio is bigger tan.57, te sape is defined as U sape. Tese parameters can be used as efficient features for inputs of classifiers. Te test applied tese new sape features is carried out and te results are sown in te Table. Compared wit current approaces, it successfully improves te accuracy of te recognition of Eosinopil and Neutropil. It also provides straigtforward sape features for doctors to confirm te classification of te cells. TABLE II. THE CONFUSION MATRIX N E B M L Correct (%) N E B M L IV. CONCLUSION Tis paper presents a Poisson equation based approac for leukocyte classification from a blood smeared image. Te results provided a set of efficient sape features for leukocyte classifiers suc as neural networks or oter classifiers. Te advantage is tat te features can be automatically extracted important sape features from a blood smeared image. It is also able to reduce te input number and complexity of leukocyte classifiers using suc features. Tese features are able to distinguis different ages of leucocytes in a smear image efficiently so tat te performance of leukocyte classifiers can be improved. REFERENCES [] L. Gorelick, M. Galun, E. Saron, R. Basri,A. Brandt, "Sape representation and classification usingte poisson equation," In CVPR (),00. [] L. C. Junqueira,J. Carneiro, R. O. Kelley, "Basic Histology Appleton & Lange," Norwalk, Conn,99. [3] S. Zang, "In An atlas of istology," New York: Springer-verlag, 998, pp [] I. Berman, Color Atlas of Basic Histology. ed, Stawford, Connecticut, EUA: Appleton and Lange,998. [5] W. Sandritter, C. Tomas, W. B. Wartman, "Color atlas & textbook of istopatology," Year Book Medical Publisers, 979. [6] Q. X. Wu, X. Huang, J. Cai, Y. Wu, M. Lin, "Segmentation of Leukocytes in Blood Smeare Images Using Color Processing Mecanism Inspired by Te Visual System," BMEI'09, IEEE, 009, pp [7] S. Mircic, N. Jorgovanovic, "Application of neural network for automatic classification of leukocytes", Proceedings of te 8t IEEE seminar on neural network applications in electrical engineering, 006, pp.. [8] D.M.U. Sabino, L.F. Costa, E.G. Rizzatti, M.A. Zago, "Toward leukocyte recognition using morpometry, tex-ture and color," IEEE Intl Symp Biom Imag, 00. [9] H. Ramoser,V. Laurain, H. Biscof, R. Ecker, "Leukocyte segmentation and classification in blood-smear images," EMBS 005 IEEE, 005, pp [0] M. Ferri, S. Lombardini, C. Pallotti, "Leukocyte classification by size functions," Proceedings of te second IEEE Worksop on Applications of Computer Vision. IEEE Computer Society Press, Los Alamitos, CA, 99, pp.3-9. [] D.M.U. Sabino, L.F. Costa, E.G. Rizzatti, M.A. Zago, "A texture approac to leukocyte recognition," Real-Time Imaging, vol. 0, 00, pp [] D. H. Tycko, S. Anbalagan, H.C. Liu, L. Ornstein, "Automatic leukocyte classification using cytocemically stained smears," J Histocem Cytocem. (), 976, pp [3] P.E. Pavlova, K.P. Cyrrilov, I. N. Moumdjiev, "Application of HSV colour system in te identification by colour of biological objects on te basis of microscopic images," Computerized Medical Imaging and Grapics. 0(5), 996, pp