A New Image Binarization Method Using Histogram and Spectral Clustering

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1 A Ne Image Bnarzaton Method Usng Hstogram and Spectral Clusterng Ru Wu 1 Fang Yn Janhua Huang 1 Xanglong Tang 1 1 School of Computer Scence and Technology Harbn Insttute of Technology Harbn Chna School of Computer Scence and Technology Harbn Unversty of Scence and Technology Harbn Chna Abstract We present a novel approach of bnarzaton for gray mages. The proposed algorthm uses the normalzed graph cut(ncut) as the measure for spectral clusterng and the eghted matrces used n evaluatng the graph cuts are based on the gray levels of an mage rather than the commonly used mage pxels. Thus the proposed algorthm requres much smaller spatal costs and much loer computaton complexty. Experments on text mages n natural scene sho the superor performance of the proposed method compared to the typcal thresholdng algorthms. Keyords: bnarzaton; graph cut; spectral clusterng 1. Introducton In many mage processng applcatons such as document processng cell moton estmaton and automatc target recognton the obect and background of mages need to be separated that s bnarzaton process also knon as thresholdng process. The key of thresholdng s ho to choose the best value of threshold and there are many methods of threshold choce such as the hstogram technology [1] adaptve approach [34] the gradent method [5] and all relevant edge detecton method [67] and so on. Despte the varous ays appearng n recent decades choosng the optmal threshold automatcally s stll a pendng problem n mage processng. Spectral clusterng has gradually ganed attenton from research on text classfcaton mages segmentaton and nformaton retreval [89]. In [9] the proposed algorthm uses the normalzed graph cut [8] measure as the thresholdng prncple to dstngush an obect from the background and a large number of examples are presented to sho the superor performance of the method. But t s stll a thresholdng algorthm that has lmtatons to deal th the cases hen backgrounds have the smlar color or ntensty to that of the obects. In ths paper e propose a ne mage segmentaton method based on gray hstogram and spectral clusterng. In our approach the hstogram of ntensty s used for the obect of groupng e partton the mage nto to parts usng the gray levels of an mage rather than the mage pxels. For most mages the number of gray levels s much smaller than the number of pxels. Therefore the proposed algorthm occupes much smaller storage space and requres much loer computatonal costs and mplementaton complexty than other smlar algorthms. The rest of the paper s organzed as follos. Secton ntroduces the theory of spectral graph partton brefly. Secton Proceedngs of the 11th Jont Conference on Informaton Scences (008) 1

2 3 presents the ndvdual steps of our approach. The expermental results are gven n secton 4. Fnally secton 5 concludes the paper.. Theory of Spectral Graph The basc method used by mage segmentaton s to ve an mage as a eghted undrected graph G = ( V E) here the nodes of the graph are the ponts n the feature space and an edge s formed beteen every par of nodes. The eght on each edge ( ) s a functon of the smlarty beteen nodes and. A graph G = ( V E) can be parttoned nto to dsont subsets A and B subect to A B = φ A B = V by smply removng edges connectng the to parts. The degree of dssmlarty beteen these to peces can be computed as total eght of edges that have been removed. In graph theoretc language t s called the cut[8]: cut( AB ) = uv ( ) (1) u Av B The optmal bparttonng of a graph s the one that mnmzes ths cut value. There are many crterons to measure the qualty of the fnal partton results. Then the Normalzed Cut value of a bpartton result can be defned as follos [8]: Ncut( AB ) here assoc( BV ) uv ( ) cut( AB ) cut( AB ) = + () assoc( AV ) assoc( BV ) assoc( AV ) = uv ( ) u Bv V u Av V = respectvely s the total connecton from nodes n A or B to all nodes n the graph. And no the mnmal Ncut value s ust correspondng to the optmal bpartton of the graph. In order to mnmze () e can transform the optmzaton problem nto solvng the egenvalue system 1 1 D ( D W) D z λz = (3) here D = ( ) W s a symmetrc N matrx th sze of N N λ s the egenvalue and z s the correspondng egenvector. Sh and Malk[8] have proved that the second smallest egenvector of the egensystem (3) s the real value soluton to the normalzed cut problem of (). When the sze of an mage s too bg t s dffcult to solve the above egensystem especally f the affnty matrx W s constructed by takng each pxel as a node the sze of egensystem ould be N N (N s the total number of pxels n an mage). 3. Our method Suppose V = {( ): = 01 L n 1; = 01 L n 1} h H = { H0 H1 L HL} LL= { 01 L L} here n h and n s the heght and the dth of the mage respectvely. H represents the hstogram of gray f( xy ) s the gray value of poston ( xy ).Then VH and f( xy ) satsfy the follong formulas. ( xy ) Hl l { 01 L L} ( xy ) V (4) H = {( xy ): f( xy ) = l( xy ) V} l LL (5) L l U H = V H H = LL (6) l= 0 l Usng ust the ntensty value of the pxels and ther spatal locaton e can defne the graph edge eght connectng the to nodes and as: = e F() F( ) σ I * X () X( ) (7) σ X e f X () X( ) < r 0 otherse. here F () s a feature vector based on ntensty of node and X() s the spatal locaton at that node σ and σ I X Proceedngs of the 11th Jont Conference on Informaton Scences (008)

3 are scale factors used to adust the varaton of gray or spatal locaton beteen nodes r s used to decde the number of nodes from node to. And then e can get a bpartton V = AB correspondng to the graph { } G = ( V E) here A= U H B = U H and k LA k k LB L L = L L = LL. Let A B A B cut( H H ) = uv ( ) be the total u H v H connecton eghts from nodes n H th gray level to all nodes n H th gray level e can rerte the above formulas as: cut( AB ) = cut( H H ) (8) LA LB asso( AA ) = cut( H H ) (9) LA LA asso( BB ) = cut( H H ) (10) LB LB Snce asso( AV ) = asso( AA ) + cut( AB ) asso( BV ) = asso( BB ) + cut( AB ) e can rerte () as: cut( AB ) Ncut( AB ) = asso( AA ) + cut( AB ) (11) cut( AB ) + asso( BB ) + cut( AB ) Gven an mage e can construct a hstogram-based matrx M that s smlar to [9] by computng the all eghts of nodes n the correspondng graph. = s an L L symmetrcal M m matrx th m = cut( H H ) and m k = m here L s the number of gray level of hstogram. No let M be the affnty matrx e can get a complete approach of mage segmentaton usng spectral clusterng [8]. Note that the sze of the affnty matrx M depends on the number of graylevel L rather than the number of all pxels N n an mage. Meanhle the sze of egensystem to solve s L L rather than N N and usually L th a fxed sze s much smaller than N. Hence the complexty of computaton and spatal cost reduce greatly. 4. Expermental Results We perform a seres of experments to test the performance of ths method. Our method s compared th to other methods: the Otsu thresholdng method [10] and the Ncut-based thresholdng method [9]. We choose them because the Otsu method s a smple but classc soluton employed by many mage segmentaton schemes hle the latter s an Ncut-based but thresholdng soluton proposed recently. Frstly e can see our segmentaton result s almost same to the Otsu s from Fg.1 and the parameter settngs n formula (7) are σ I = 50 σ X = 5 r = 5 L = 100 hch dran from the experments. (a)orgnal Image (c)ncut-based result (b) Ostu result (d) Our result Fg.1. Comparson of three bnarzaton results for the cell mage Secondly e use the gray mages th the text of characters for testng and hch are the real mages from the Proceedngs of the 11th Jont Conference on Informaton Scences (008) 3

4 natural envronment. From Fg. e can see the latter to methods both based on Ncut crteron are superor to the Otsu method from the expermental results. In Fg.3 The proposed method can be the rght segmentaton at a reflectve hte spots thn the part of black spots on the letter 'B' hch s dffcult to acheve for the conventonal thresholdng methods. (a) Orgnal mage (b) Ostu result (c) Ncut-based result (d)our result Fg.. Comparson of three segmentaton methods for the text mage (a) (b) (c) (d) Fg.3. Comparson of three text segmentaton methods for an llumnated mage ((a)orgnal mage (b) Ostu result (c) Ncut-based result (d) Our result) Fnally e choose 150 mages th clear dfferences and 50 mages th blur text respectvely to test the three methods. The am of the three algorthms s to separate the foreground (texts) from the background (non-texts). The precson p and recall r are used to evaluate the methods hch are defned as follos. base_im p = (1) age o base_im r = (13) base_im here age O s a ponts set of obects ncludng texts; base_im s the ground-truth text regon. And then the comprehensve assessment ndcator f s defned as follos [11]: 1 f = (14) a/ p+ (1 a)/ r here a s a relatve rate beteen precson and recall lettng a = 0.5. The result of 150 mages shos n table I and the result of 50 mages shos n table II. From the results e can see the proposed method has a good performance for both the to knds of mages. And our method s superor to other to methods from the pont of comprehensve ndcator f. Table I The segmentaton result of three methods for normal mages Method p r f Ostu method Ncut-based thresholdng method Our method Table II The segmentaton result of three methods for abnormal mages Method p r f Ostu method Ncut-based thresholdng method Our method Concluson Image segmentaton s a long-standng problem n mage processng. Due to ts smplcty and effcency thresholdng s a dely used method for solvng ths problem. But t could not handle the cases hen backgrounds have the smlar Proceedngs of the 11th Jont Conference on Informaton Scences (008) 4

5 color or ntensty to that of the obects. In ths paper the proposed spectral clusterng can do th the ssue by usng spectral graph theory. And ths method controls the complexty of algorthm effectvely by changng the clusterng obects from pxels to gray levels. The experment results from text mages have proved ts superorty to the tradtonal thresholdng method. 6. References [1] Kapur N. Sahoop K. ; Wong A. K. C. A Ne Method for Gray-level Pcture Thresholdng Usng the Entropy of the Hstogram Computer vson graphcs and mage processng vol. 9 no.3pp [] C.A.Glasbey An analyss of Hstogram-based Thresholdng Algorthms CVGIP:Graphcal Models and ImageProcessng55(6) pp [3] Felx Abramovch Yoav Benamn Adaptve Thresholdng of Wavelet Coeffcents Computatonal Statstcs&Data Analyss : [4] B. Gatos I. Pratkaks S. J. Perantons Adaptve Degraded Document Image Bnarzaton Pattern Recognton Vol.39 No.3 pp [5] D Wang A Multscale Gradent Algorthm for Image Segmentaton Usng Watershelds Pattern Recognton 30(1) pp [6] Mo Da Perre Baylou Lous Humbert Mohamed Nam Image Segmentaton by a Dynamc Thresholdng Usng Edge Detecton Based on Cascaded Unform Flters Sgnal Processng 5(1) pp [7] Qang Chen Quan-sen Sun Pheng Ann Heng De-shen Xa A Doublethreshold Image Bnarzaton Method Based on Edge Detector Pattern Recognton 41(4) pp [8] Janbo Sh Jtendra Malk Normalzed Cuts and Image Segmentaton IEEE Transactons Pattern Analyss and Machne Intellence (8): [9] Tao Wen-Bng Jn Ha A Ne Image Thresholdng Method Based on Graph Spectral Theory Chnese Journal of Computers(n Chnese)Vol.30 No.1pp [10] Otsu N A threshold selecton method from grey level hstograms IEEE Trans System. Man Cybernet SMC-9: [11] Lucas S M Panaretos A Sosa L et al ICDAR 003 Robust Readng Competton Proc. of 7 th Int l Conference on Document Analyss and Recognton Scotland pp Proceedngs of the 11th Jont Conference on Informaton Scences (008) 5