Analysis of Texture of Froth Image in Coal Flotation

Dec.2001Journal of China University of mining & TechnologyVol. 11 No. 2Analysis of Texture of Froth Imagein coal flotationUMai-xi(路迈西), WANG Fan(王凡),1 10 Xiao-ming(刘晓), LIU Wen-li(刘文礼), WANG Yong(王勇)Department of Chemical and Environment Engineering, CUMT. Beijing, 100083. P.R. ChinaAbstract: Froth image features of coal flotation have been extracted and studied by neighboring grey leveldependence matrix, spatial grey level dependence matrix and grey level histogram. In this paper, a basic algorithm of unsupervised learning pattern classification is presented, and coal flotation froth images are clsified by means of self-organizing map(SOM). By extracting features from 51 flotation froth images withlaboratory column, four types of froth images are classified. The correct rate of soM cluster is satisfactoryKey words: Coal slurry; flotation froth; image; texture; artificial neural nets unsupervised learningCLC number: TD 91 Document code :A Article ID: 1006-1266(2001)02-0100-041 Introductionstatistical factor of first order grey levels, the greyIt has long been established that the infotones are set as x coordinate, while the sum of pix-tion about flotation operation can be obtainedIs of a grey level H, as y coordinate. The meanthrough observation on froth surface. Cipriano et grey level and standard deviation of an image areall. constructed a full set of expert system to evalumajor parameters of grey level characters. As a coalate flotation performance using the software ACE- flotation image of 256 grey levels with MXN pix-flot to extract the characteristics of bubble els, the grey level of one given pixel is f(m, n)shape, size and color about flotation froth. Mool- where m=1, 2, . M, n=1, 2,", N, and integerman [23 and Niemira et al studied the bubble sizes and grey level i covers the range from 0 to 255, so thatits distribution, the color and grey level of flotationthe sum of pixels of a given grey level i can be calcufroth, and analyzed the performance of flotationlated bymeansDue to highly blur of edges among bubblesshows a froth image of coal flotation, while Fig. 1bcoal flotation froth images have no distinct boundaryshows its grey level histogram. Its mean grey levelbetween objects and background. So it is difficult toand standard deviation are 90 04 and 57 37 respecxtract original bubbles. Since image texture showstivelexactly the information about grey level of all pixels, by studying coarseness, fineness and non-uni- 3 Textural Factorsformity of image parameters, the statistical classifi- 3. 1 Neighbouring grey level dependence matrixcation of such textural factors can be attained 4](NGLDM)Self-organizing neural nets are employed to clusterDM is a second-order grey level matrixthe image of coal flotation froth中国煤化工each element is defined2 Character of Grey LevelCNMHGwhich each pair of greyImage grey level histogram is used to depict the levels occurs while separating distance is d and difReceived date 2001-06-05Foundat数瑞ional Natural Science Foundation ofxi(1941-), female, from Yixin, Jiangsu Province, professor, engaged in the research of mineral processing, coalpreparation, modeling and simulation.a1-xI etAnalysis of Texture of Froth Image in Coal Flotationferences of grey levels is no more than a. The func-sQ(k, s)1tion is as follows(2)Q(k,s)=#{(m,n)f(m,n)k,#[(q,r)|p((m,n),(q,))≤d, f(m, n)-F(q, r)sa=sh,3)Non-uniformitywhere (m, n) is a given pixel of an image;(q, r)Q(k, s)all pixels circling the central pixel of (m, n)withinN3(3)the range of d, #t is the count of all pixels, which∑>Q(k,)constitutes the element of NGLDM, p((m, n),(q4)Second momentr))refers to the distance between pixels of (m,n)∑[Q(k,s)d (q, r), s is the possible neighbours to a pixel of(4)Characters of ngldM are defined aslQ(k, s)1)Small number emphasis5) Entropy[Q(k,)/52]Q(k, s)logo(k,s)1Q(k, s)(5)∑Q(k,s)2)Large number emplFig 1 Coal flotation froth image and its grey level histogram3. 2 Spatial grey level dependence matrixflotation froth image are defined as(SGLDM)1) EnergySGLDM is used to quantify the textual factorsE(d,0){P(i,j)d,0)(6)based on the estimation of second order joint conditional probability density functions. Each function is2) Entropyorresponding to a statistical matrix of a given samH(d,0)=>P(i,j)ld, 0)logP(ple spacing d in the direction of0(0°,45°,90°and(7)135), therein (m, n) is set as central pixel, and (3)Inertiaj)as corresponding pixel within the area. FunctionI(d,0)(i-j)2P(i,jd,0)(8)of computing SGlDM is definedP(m,n1d,0)=#{(m,n),(i,)|p[(m,n),(i,)]≤4中国煤化工 by Means of SoMCN MH Gages are classified basedwhere: p((m,n),(i, j)) is the distance between on textural characters by means of SOM 6. Suppospixels of (m, n)and (i,j),(m, n)O(i, j) is deviat- ing input sampling set for training is X=ixi,x?ing angle of line from pixel (m,n) to (i,j)away ",Im, ",M,, where m is sampling character in-x数据 starting from pixel(m,n)putted. and as for each sample, n is the number ofTextural factors of SGLDM relating to coal characters, the maximal one is N, hence the eleJournal of China University of mining & TechnologyVol. 11 No. 2ments of sampling set are5 Results and Discussionxm1,xm2,…,xwhere m=1, 2Laboratory column flotation tests have beenSOM algorithm self-learning rules are as Koho- done for Linhuan fine coal, and 51 images of frothnen clustering nets, which dynamically update clus- were collected. These photographs were taken inter centers over the previous ones as the modified the same condition except the retention time andfunctionreagent dosage]. Characters obtained are grey level(k+1)=(k)+l1(k)[x-1(k)]histogram and textural features, and thus a matrixwhere k is times of learning; w is the vector of clus- of 51 10 is created. SOM method is employed toter center; l represents the output neuron, l=1separate froth to 4 types. Supposing experts virtuL, and L, is learning rate.al observation is as the standard of classification, theThe learning rate is modified as: L,=L,(0)(1average correct rate of som cluster is 70%( seek/K), which is initialized as L,(0).K is the max Table 1), it means that the clustering result bytraining epochs. The total error is defined asSOM is satisfactoryTable 1 Cluster results over 51 coal flotation froth imagesverage ash contentCorrect No. Correct rate/% classified by experts/%(Un(k+ 1)-wen(k))-(9)70,01,72Learning program of the SOM nets is con12,structed as1) Input all the patterns of characters X;Total70,62) Initialize the vectors of cluster center:Fig. 2 illustrates four typical flotation froth im3)Compute all the euclidean disages corresPnding to four classes of basic froth fetween X and cluster centers by using the functiontures. For class a, the bubbles are fine and uniD=‖foable and tough. In class Bsparse mid-sized bubbles are entrained within the4) The minimal Euclidean distance from clusterfine bubbles. While class C is mainly the mid-sizedcenter wins, and the weight vector is modifiedbubbles. And for class D the bubbles are large incording to updated learning rate proposed abovesize with the least coal attached on the bubble surwhile the other neurons fail to win whose weight face. The average ash content of the four types ofvectors remains the previous onesbubbles increases from class a to D respectively, as5)If△e>△E, then return to(3),shown in Table 16)If△e<△E, then training is completed.CIss AClass B中国煤化工Class DCNMHGFig 2 Bubble characters of the four types of Troth images6 Conclusionfeatures of grey level histogram, NGLDM, andUnsupervised learning algorithm is effective inSGLDM into considerationcoal flotat方数 image classification by takingCoal flotation froth can be classifiedpes, each type has different range of ash contenta1-xI etAnalysis of Texture of Froth Image in Coal FlotationReferences[1] Cipriano A. Guarini M, Vidal R. et al. A Real time visual sensor for supervision of flotation cells[J]. Minerals Engi[2 Moolman D W, Aldrich C, Deventer V, et al. Digital image processing as a tool for on-line monitoring of froth in flotation plantsLJ]. Minerals Engineering, 1994,7(9):1149-1164[3 Antti J, Niemi, Raimo Ylinen et al. On characterization of pulp and froth in cells of flotation plant [J].InternationalJournal of Mineral Processing, Australia Elsevier Science Ltd, 1997.51: 51-65[4 Wang Z C, Lu M X, Liu W L. Predicting the performance of coal flotation by using the features of froth image[A]Proceeding of 29th APCOM[C]. AA Balkema, Rotterdam, Netherland, 2001.487-490[5 Sun C J. William G W. Neighboring gray level dependence matrix for texture classification [J]. Computer VisionGraphics, and Image Processing, 1983, 23: 341-3526]殷勤业,杨宗凯,谈正.模式识别与神经网络[M].北京:机械工业出版社,1992.297-325η]刘文礼.煤泥浮选泡沫的数字图象处理[R].北京:中国矿业大学化工与环境工程系,2000.11.中国煤化工CNMHG