IMAGERY TEXTURE ANALYSIS BASED ON MULTI-FEATURE FRACTAL DIMENSION

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1 IMAGERY TEXTURE ANALYSIS BASED ON MULTI-EATURE RACTAL DIMENSION Jingxue Wang a,*, Weidong Song a, eng Gao b a School o Geomatics, Liaoning Technical Univesity, uxin, Liaoning, 13, China xiaoxue1861@163.com, - song_wd@163.net b Liaoning Envionment Monitoing Cente, Shenyang 13, Liaoning, China Commission VII, WG VII/4 KEY WORDS: Textue; eatue extaction; Classiication; Reliability; Pecision ABSTRACT: Textue is the impotant spatial stuctue inomation and pimay eatue o emote sensing imagey. It contains the suace inomation o imagey and the elationship with aound envionment. istly ocusing on the basic pinciple o actal, this pape adopts ive dieent inds o actal algoithms to calculate the actal dimensions o image textue towads the eseaching image, and gains ive dieent actal eatues. Secondly, accoding to the above obtained ive actal eatues, this pape maes the eatue extaction unde the pinciple o the tansomation based on classibility citeion, and obtains two goup new eatue vectos. inally, in the expeiments, this pape caies on the image classiication using the two new eatue vectos, and gets the classiication esults. This pape adopts the usion matix to evaluate the pecision o these classiication esults, and validates the easibility, pecision, and eliability o this method. 1. INTRODUCE Textue is the impotant spatial stuctue inomation and pimay eatue o emote sensing imagey. It contains the suace inomation o imagey and the elationship with aound envionment. As caying on the classiication towad RS imagey, textue eatue is one ind o common classiication standad and judgment pinciple. Among the vaious methods o descibing textue eatue, the actal algoithm is bette than othe taditional algoithms in the aspects o anti-noise and attention the macostuctue and the micostuctue o imagey. actal algoithm mainly expesses the extent o sel-similaity and the eatue o oughness. Simultaneously, this algoithm can also detect the abundance details o imagey, and then obtain the bette classiication eect. This pape ocuses on the pinciples and techniques o image textue analysis, and validates the pinciples and methods with appopiate expeiments. istly ocusing to the basic pinciple o actal, this pape adopts ive dieent inds o actal algoithms to calculate the actal dimensions o image textue towads the eseaching image, and gains ive dieent images o actal eatues. Secondly, accoding to the above obtained ive actal eatues, this pape maes the eatue extaction unde the pinciple o the tansomation based on classibility citeion, and obtains new eatue vectos in ode to cay on the image classiication. inally, This pape adopts the usion matix to evaluate the pecision o these classiication esults, and validates that the method poposed in this pape can obtain excellent classiication esults, and can guaantee the pecision, the easibility and the eliability o image classiication.. RACTAL EATURE BASED ON THE TEXTURE O IMAGE.1 actal Algoithm Based on The Discete actal Bown Random Model The actal Bown Motion is one ind o typical mathematics model to descibe the andom actal eatue in natue. And its deinition is (Dongsheng Wang, 1995): Set Β is a andom Gauss ield, and <H<1. I the Β satisies this ollowing omula: ( x + Δx) Β y Β ( ) Ρ < y x Δ Β as the actal Bown Motion. I Δ in this omula ae discete values, then we can get the Discete actal Bown Random ield (abs. as DBR ield). Then we will call the the x and x Taing the gay values o image as the thid dimension (x, y) about the plane coodinates x and y, we can conside it as a discete cuving suace o gay, and this cuving suace will satisy the DBR ield patially. It can be expessed as: { x, y, y) ( x y) G} S, (1) 569

2 The Intenational Achives o the Photogammety, Remote Sensing and Spatial Inomation Sciences. Vol. XXXVII. Pat B7. Beijing 8, then Ε Β ( x + Δx) Β C Δx. In this omula, C is a constant. Computing the log values o this equation, and we can get the ollowing omula: As the (y) obeys the nomal distibuting Ν (, σ ) lg Ε Β ( x + Δx) Β lg Δx + lgc Ate that, this actal algoithm its the data pais { lg Ε Β( x + Δx) Β, lg Δx } () using the least squae pinciple, and then calculates the value o H though the slope o itted line. The actal dimensional value D o image is deined as DN+1 H, and when N, then D3 H. Setting (x 1, y 1 ) and (x, y ) belong to the ield G, then x epesents the distance between (x 1, y 1 ) and (x, y ). I the selection methods o them ae dieent in ield G, then it will obtain dieent oms o actal dimensions. And the computation omulas o these actal dimensions in dieent diections ae shown as ollowing (Sixian Wang, 1998): ⑴ Hoizontal actal dimension D 1 : In the gay image, i x is in the hoizontal diection, and is the positive intege, then 1 ( ) M 1 N y y) y + ) M ( N ) (3). Box Dimension M. Mandelbot thins that the suace having actal eatue will have the sel-similaity (Mandelbot B. B, 198). I the limited set A is in the Euclidean space, then the actal dimension o A (expessed by D) will satisy the ollowing equations: 1 N D o log( N ) D (7) log(1/ ) But it is diicult to calculate the actal dimensions by these equations. M. B.B.Chaudhui poposed one algoithm to calculate the box-dimension. And the pinciple o this algoithm is: Consideing the image, whose size is M M, to be a 3D space, and the coodinate (x,y) epesents one D plane, and the gay value o image epesents the diection o Z axis. Then divides the D plane (x,y) into the gid with the size o s s (s is the intege, and its scope is 1<s<M/), and we have s / M. In each gid, thee ae many boxes staced one by one, whose volumes ae all s s s. In the (i, j) gid, this algoithm endows the maximum and the minimum values in the gay suace to the box and box l in the stacing. Then n ( i, j) l + 1 (8) ⑵ Vetical actal dimension D : I x is in the vetical diection, then ( Κ ) M K 1 N x y y ) ( x +, y ) N ( M ) (4) It is the box numbe o coveing the image in the gid (i, j). And the total box numbe o coveing the whole image can be calculated by omula (9): N n ( i, j) (9) i, j ⑶ Diagonal actal dimension D 3 : I x is in the diagonal diection, then 3 ( ) M N y M N y) ( x +, y + ) + y) ( x +, y ) y ( M )( N ) (5) ⑷ Integated actal dimension D 4 : 4 ( ) M N y M N y) ( x +, y) + y) y + ) y N( M ) + M ( N ) (6) Changing the omula (8) into one ind o simple oms in ode to calculate the gay values o image conveniently, lie omula (1) ( i, j) int( max I / ) int( min I / ) + 1 n (1) K I In this omula, (1,,,n) ees to the gay value o n pixels in the unit aea o. The changing o is caused by the changing o s, and the slope D can be calculated by itting the log( N ) log(1/ ) using the least squae pinciple. The accuacy o this algoithm to calculate the box dimension is excellent, especially as the change o image gay values in the neighboing ield is geat. M. Dongsheng Wang poposed one ind o impoved algoithm to calculate the box dimension: ( i, j) int[ ( max I min I ) ] + 1 n (11) 57

3 The Intenational Achives o the Photogammety, Remote Sensing and Spatial Inomation Sciences. Vol. XXXVII. Pat B7. Beijing 8 c c ni j 1 1 ( i) ( j) J Pi Pj d( x, xl ) (1) This algoithm can cove the cuving suace o image using the i 1 j 1 nin j 1 l 1 minimum numbe o cubic boxes, whose volume is also s s s. The cubic boxes will not be limited in cetain ixed In this omula, n i ees to the numbe o taining samples o positions, and they can move up and down along the Z axis. the w i categoy in set S, and P i ees to the pe-pobability This algoithm can educe the numbe o boxes, and impove o the i categoy. I P the extent o tightness to coveing the cuving suace. i is unnown, it can be instead by w / n. In many situations, the Euclidean distance is Theeoe, it can incease the measuing pecision o box i dimension. 3. EATURE EXTRACTION BASED ON THE CLASSIBILITY CRITERION convenient to analyze and calculate. By the ollowing omula (13), the distances among categoies will each the maximum, and the distances in the categoies will each the minimum ate the tansomation (Jingxue Wang, 7): n The pinciple o eatue extaction is to extact the new eatue vecto d om the oiginal eatue vecto D, and in geneally the dimension o D is bigge than the dimension o d. uthemoe, the new eatue vecto should satisy the unction condition that the total dispesion o vaious categoies will be the smallest. By this way, the extacted seconday eatue not only gets id o the elativity among the oiginal eatues, contains the main eatues o the seven inds o actal dimensions in the lagest extent, but also can descibes the textue inomation o image well and tuly, impoves the pecision o classiication. In ode to extact one goup eective eatue o image classiication om vaious eatues, it needs to establish an accuate standad o citeion to judge the validity o these eatues o image classiication, and this is the tansomation based on classibility citeion (Song Weidong, 7). In the given eatue space, whose dimension is D, we should extact d eatues to guaantee that they can apat the categoies as a as possible. It means that we should extact a eatue vecto x, which has d eatues, and maes the aveage distance J(x) between each sample in the C categoies each the maximum, which is to say that J ( x ) max J. And the computation o J(x) can be expessed as the ollowing omula: d( x ( i), x ( j) l T ) [( x x ) ( x x )] (13) 4. EXPERIMENTS In expeiments, ocusing on the SPOT5 panchomatic image as the eseaching object, and though the lucubating to the actal pinciples and the actal eatues o textue, this pape adopts the actal dimensions in dieent diections based on the DBR and the box dimension as the actal eatues o textue images, extacts the eatue vectos o textue, and then ceates the coesponding actal images. Ate that, this pape extacts new eatue vectos om the above actal eatues using the pinciple o eatue extaction, and uses these eatue vectos into the image classiication. inally, it evaluates the pecision o classiication esults. 4.1 Computation o actal Dimension Based on Multi-Scale and Multi-eatue In the expeiments o computing the actal dimension, it needs to obtain the actal dimensions om the taining samples o the vaious categoies at ist. This pape selects twenty taining samples om each categoy, and calculates the textue eatues o these categoies using dieent actal algoithms, and then obtains the aveage actal values o them. The esults ae shown as the ollowing Table 1: l l 1 Discete actal Bown Model (DBM) Box Dimension Categoy Hoizontal actal Vetical actal Diagonal actal Integated actal Dimension Dimension Dimension Dimension actal Dimension Vegetable Plot Resident Aea Copland Table 1. Textue actal eatue values o dieent categoies In ode to classiy the image using the actal pinciples, it needs to now the actal dimension o each pixel. Similaly, this pape calculates the actal dimensions o the SPOT5 panchomatic image utilizing the above mathematics models, and obtains ive dieent actal images. In the computation o actal dimensions, this pape adopts the linea egession based on the least squae method to calculate the actal dimensions in the dieent window sizes. Though the computation analysis and compaison, it can be concluded that the eect o linea egession will each the best state when the size o selected window is 9 9 pixels. And the computed actal dimensions will luctuate in a elative steady ange. 4. eatue Extaction and Image Classiication Consideing that the textue eatues o vegetable land and esident aea ae simila in cetain degee, this pape caies on the seconday extaction to the ive goup actal eatues, and classiies the image using these new eatues. The extacted seconday eatue not only gets id o the elativity among the oiginal eatues, contains the main eatues o the seven inds 571

4 The Intenational Achives o the Photogammety, Remote Sensing and Spatial Inomation Sciences. Vol. XXXVII. Pat B7. Beijing 8 o actal dimensions in the lagest extent, but also can descibes the textue inomation o image well and tuly, impoves the pecision o classiication. In this expeiment, it extacts the eatue vectos towads sixty samples based on the pinciple o classibility citeion, and gets the gaph o discete samples. Analyzing om this gaph, it can be concluded that these thee inds o categoies have the divisibility in the diection o x and y axes. This pape classiies the image using the extacted seconday eatues, and obtains the gaph o classiication esults, which is shown as igue. In this igue o classiication esults, the dieences among these categoies ae obvious, and the total pecision o classiication is vey high. igue. Oiginal RS image igue 3. Classiication esults map 4.3 Pecision Evaluation o Classiication Results igue 1. Gaph o discete samples based on eatue extaction In geneal, thee is no one method can chec the classiication o evey pixel in the whole image one by one and judge whethe it is ight o wong, but have to evaluate the eos o classiication using some samples. And the ways o sample selection ae usually andom. This pape taes the pesent land use map, whose egion is coveed by RS image, as the eeence, and selects 6 samples andomly in this egion, constucts the coesponding conusion matix to cay on the pecision evaluation to the classiication esults, and the computed total pecision is 89.67%. The usion matix is shown as the Table : Sample Classiied Categoies Vegetable Plot Resident Aea Reeence Categoies Vegetable Plot Resident Aea Copland Sum Use s Accuacy % % Copland % The Total Classiication Pecision 89.67% Sum Poduce s Accuacy 85.5% 9.% 94.6% Table. The conusion matix and the pecision o classiication esults 57

5 The Intenational Achives o the Photogammety, Remote Sensing and Spatial Inomation Sciences. Vol. XXXVII. Pat B7. Beijing 8 5. CONCLUSION This pape caies on the classiication towads the SPOT5 image utilizing the actal pinciple and the eatue extaction algoithm in patten ecognition, and the computed total pecision o classiication eaches 89.67%. Saying om the eect o classiication and the evaluated pecision, it can ealize the eective classiication on the objects categoies with the eatue vectos extacted om multiply actal eatues, and impove the pecision o classiication. Simultaneously, it validates the easibility, pecision and eliability o this classiication algoithm based on the multi-eatue actal dimensions. REERENCES Sixian Wang, Bing Jiang, Mengyang Liao,1998. Textue Segmentation Based On Wavelet Tansom and Bownial actal Model. Tansaction o Wuhan Univesity. 44(1) pp Dongsheng Wang,1995. Chaos, actal and Thei Applications. Beijing: Publishment o Chinese Scientiic and Technical Univesity. Mandelbot B. B.198. The actal Geomety o Natue. New Yo,W H eeman Publishment. Song Weidong, Wang Jingxue, Qin Yong,7. The Study O Land Use Change Detection Based On Sole Peiod RS Image. In: Technique and Applications o Optical and SAR Imagey usion Coneence ISPRS WGⅦ. pp Jingxue Wang, Weidong Song,7. The Study o Uban Objects Stepping Classiication Based on Spectal eatue. In:SPIE ith Symposium on Multispectal Image Pocessing and Patten Recognition, MIPPR 7. (6787) pp. (1)1-7. ACKNOWLEDGEMENT Ou eseach poject is suppoted by the National Scientiic und Pogam (No ), the Univesity docto disciplines Scientiic und Pogam o Ministy o Education (No ), the Open Reseach und Pogam o the State Key Laboatoy o Inomation Engineeing in Suveying, Mapping and Remote Sensing o Wuhan Univesity (No. WKL(7)33), and the 4nd Postdocto Scientiic und Pogam (No ) 573

6 The Intenational Achives o the Photogammety, Remote Sensing and Spatial Inomation Sciences. Vol. XXXVII. Pat B7. Beijing 8 574