A Texture Feature Extraction Based On Two Fractal Dimensions for Content_based Image Retrieval

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1 9 Wold Congess on Compute Science and nfomation Engineeing A Textue Featue Extaction Based On To Factal Dimensions fo Content_based mage Retieval Zhao Hai-ying Xu Zheng-guang Penghong (. College of Maths-physics and nfomation Sciences; Xinjiang omal Univesity; Uumqi Xinjiang 8354;. School of infomation Engineeing Univesity of Science and Technology Beijing83 zhy.yn@63.com Abstact To begin ith textue featue extactionit pesents ho to efficiently extact textue featues to descibe the content of images then based on the common methods to acquie the factal dimension of an image noadays to extacted textue featues a ne efficient algoithms of textue featue of to diffeent factal dimension is designed and ealized in image etieval system. The expeimental esults poved that factal dimension as textue featue algoithm eflects textue featue of image moe pecisely. Conclusion: Be a lage of quantity image etieval effective image featue extaction is a poeful tool in the eseach infomation classification and identification of aeas ith potential.. ntoduction The aticle [](p76 points out that the majoity of natual objects in space on the suface ae factal and the gay of these sufaces image is also Factal this fo Factal model at image analysis and application povides a theoetical foundation.textue is a basic featue of image. People have made a lot of eseach ok in the textue analysis and povided a lot of methods in desciption and measuement of the textue image. Factal dimension(fd is an expession of the image in mateial stability and it can be used to descibe the oughness of images suface. The pape based-on the factal dimension as textue featue ealizes an image etieval system.thee ae a lot of methods of calculating Factal dimension [] (p9 of hich the moe used methods ae: Based on the diffeence gay based on factal Bonian motion model of self-simila calculation method the basic Foundation item::pojects suppoted by the ational atual Science Foundation of China (o.6863 and by Xinjiang omal Univesity (o xjnu65. diffeence box count [3](p44 based on avelet decomposition method capet ovelay method. These algoithms ee based on diffeent backgound to the applicationithout compaison and evaluation.this aticle fist got some ays of calculating to five typical factal dimension using a goup of images(in the expeiment;then given a mathematical calculation method based on the textue featues though the extaction and compaisionthe esults sho that: the diffeence box count and the counting method of factal Bonian motion based on self-simila model of to algoithms fom the factal dimension of textue featue of image etieval is a ell-established one.. Five expeimental algoithms and the calculation methods Algoithm of Factal dimension Diffeence gay actal Bonian motion model Diffeence box count Wavelet decomposition Capet ovelay Table. Algoithm and Seial umbe.. Diffeence Gay-dimensional Seial numbe diffegay bonmove diffeboxcount avedivide capetovelay n the box-dimensional appoach to the pomotion of to-dimensional plane the diffeence is the gay method. Tts pinciple is to get small cube box by spliting the plane. Ode ( to the minimum numbe of gay level in the image egion to estimate contained in egion of side is hee you can imagine the gay-scale images into a thee-dimensional space in the sub-suface. Estimated to be the image of scoes of D factal dimension D ill be decided: ( c Whee c is a constant ith both sides to take a Logaithms: log ( D log + log c Then using linea topic to get slope about log ( in elation to log hich is the image scoes of factal dimension - gay /8 $5. 8 EEE DO.9/CSE

2 dimensional diffeencein this heading they should be Times -point boldface initially capitalized flush left ith one blank line befoe and one afte... Factal Bon Random Model Method [] Fo to-dimensional gay images f(x on the pixel point of X gay gading of eal andom function if the existence of self-simila function H ( <H < making distibution function F(t is unelated to ith X Δ X H F ( t P {(( f ( x + Δx f ( x / Δx } < t ( Whee f(x function called factal Bon D factal dimension can be said fo the D 3 H of hich the distibution function F ( t meet the assumptions of zeo means the nomal distibution ( σ available: F t ( t ( es πσ σds Thus the definition (-can be itten: h E[ f ( x + Δx f ( x ] Δx c ( E is the expectation; c is a constant. Fom (-take on both sides of the least-squaes method can be calculated acquie H can be obtained D..3. Diffeence box count method M M size of the image ill be split into the subblock S S s (M / s> s an integegiven m. magine a thee-dimensional image of the cuved suface space as x y plane that position z-axis epesents gay value. XY plane is patitioned by many ss gids. n each gid thee is a box s*s*s. A gayscale image in the ( i j gid of minimum and maximum espectively landed the fist k and l box then: n ( i l k + is the box numbe of coveage ( i j gid in the image and cove the entie image Box numbe thus: n ( i and factal dimension D lim ( log ( / log ( fo diffeent calculated using the least squae method can be obtained factal dimension D. [] (p7.4. Wavelet decomposition method n n As Set up an M image using ( M to tansfom one avelet then a simila lo-fequency images A and thee high-fequency details image f f f D D D3 size n n image is got. Set up n n M.To get diffeence box dimension by fou mages. the factal dimension D hich is to be estimated ill be detemined by the folloing fomula: ( D A( F (3 n (3 A ( fo the factal cuved suface of the suface aea is measued by the use of the aea elemental scale D factal dimension fo the cuved suface F is a constant. Cuved suface A ( of the suface aea of the solution ae as the folloing: The thee-dimensional space fom the suface of all cuved suface to the point ith thick capets coveed the u coveed suface on the suface and unde the suface b defined as: u ( i b ( i g( i (4 u ( i j max u ( i j + { ( }. max u m n ( m n ( i j b ( i j min b ( i. j + { ( } min b m n ( m n ( i j The volume of the capets follos as: v ( u ( i. b ( i i j Cuved suface of the suface aea: A ( v v (5 (6 By calculated (3 using the least squae method can be obtained factal dimension D of image blocks. 3. Expeimental esults made 5 algoithms The images of the expeimentation ae made of a numbe of diffeent elements of the image sets including foests lans tees bids hoses housing ates. Fo the geneal image size is (56~ and the expeimental fistly pocesses the image size and makes them nomalized. Selected 8 images in eight 384*56(Figue3 fom the images and espectively stike a factal dimension the expeimental esults as (Table. Model: pentium-366. P opo t i on of FD Factal dimensi on and t ext u e of ough at i o Range of FD:. ~3. di ffegay b onmove diffebox ca pet ove pl y aveapp oxi Figue. Factal dimension of diffeent algoithm f.5. Capet ovelay method To imagine the gay image as a thee-dimensional space of factal cuved suface. The egional image of 8

3 Popo t i on of FD diffe gay b on move Fi ve al go i t hm and t ext u e sensi t i ve diffe box jj ca pe toveply Se i al umbe of al go i t hm avea pp oxi.. 7. ~. 699 Figue. Sensitivity of Textue Roughness ote: The contents of the plans and coodinates: Figue fom the abscissa expess the factal dimension beteen. to 3. each distance means. and longitudinal coodinates means the five kinds of algoithms in this inteval of the pobability density. Figue abscissa ae the five kinds of algoithms longitudinal coodinates ae five kinds of algoithms in this thee factal dimension of the distibution of pobability. Analysis of Figue indicates that the boxdimensional method naos the scope of application and it s moe sensitive on the less ough image; Bonian motion simila model to the application of the egula is elatively ide and the sensitivity of the ough textue is also bette. mage umbe Diffe gay Bon move diffebox count ave Capet ovelay Aveage time 57s 9s 9s 4s 5min3s Table. FD of Algoithm and Aithmetic Compae Figue 3. mage Relative to Table ote: The contents of the plans and coodinates ( in Table 3 and iamge 3 you can see that oughness feels geate in the visual e can use the above method and it can be bette identified. But fo the lo oughness ones thee is eo in identification. ( in Table and 5 can be seen thee is gap to a cetain extent in the avelet decomposition of the image of its factal dimensionand it shos limited capacity in identification. (3 FD is bette used in vaious algoithms and they eflect the oughness of the textue the calculations ae satisfied. n the application of the method in accodance ith Table 4 it indicates that the capet coveing la and avelet decomposition is the lagest. The othe method does not cove the entie scope of factal dimension of the dynamic ange. 4. mages of to factal dimension as the textue featues Txtue is the same colo as an impotant visual image chaacteistics and textue is usually defined as the image of a local natue hich in the aea of a elationship a measue. Textue featues can be used as a quantitative desciption in a cetain extent to the image of the space distibution of infomation this pape textue featue extaction is the factal dimension-based. Hoeve many of the visual natue of the big diffeences in textue its factal dimension is appoximately the same theefoe a single factal dimension can not povide enough infomation to descibe and identify textue. n ode to ovecome the deficiencies factal dimension the pape used in to kinds textue extaction algoithms ae as follos: 4.. mage Tansfom [] As mage tansfom is the factal dimension of the estimate of the commonly used method: the oiginal image fo (x y 4 additional images ( i j L if ( i j > L ( i j { otheise ( if ( i j > ( 55 L otheise 55 L 3 ( i j L ( i j ( L g min+ av / ; L g max av / Hee gmin gmax and av espectively ae image gay minimum maximum and aveage. and 3 espectively called the high value and lo gay gey value images. f the to images and J have the same FD the value of thei high-gay image and J may not have the same oughness so they ill be diffeent value of FD. Lo gey value images 3 and J3 the FD ill be the same fo simila easonsthey ae not the same. The highly diection textue if the textue is tavelling along the main diections of its textue (the main diection smooth the impact on its FD minimum and if the diection is smooth ith the main vetical diection FD ill be substantial eduction. On the othe hand if the anisotopy of the textue is lo it ill sho simila esults ith diffeent smoothing and the smooth diection has nothing to do ith it. The vetical and hoizontal image smoothing defined as: 9

4 4 + ( i j ( i j + k 5 + ( i j ( i + k j k (3 k (4 Methods used ove the five images ill seve as the image featue extaction. 4.. The image of the estimated to FD Diffeential Box counting method [9] and based on factal Bonian motion simila model method [9] espectively to the above five images factal dimension (FD is estimated that by textue featues vecto. Hee ae using the combination of to FD the easons fo this ae to diffeent methods have diffeent sensitivity to the oughness of the diffeent textues and the dimension is bigge by using the fist method than the second one.this is because the diffeence to the Bonian motion based on self-simila model can detect vey subtle textue that is it has a stong sensitivity to the textue and box counting method of the sensitivity is elatively eake (as shon in Table in the thid and fouth column indicates o.5 images based on the use of Factal Bonian motion model than diffeence test boxes to count the value of lage The image similaity calculation 5.. mage etieval expeiment To test the pefomance of the above methods e build a diffeent content of the vaious components of the 7 eal plants animals housing etc. pictue composition of the image database. The images ae 4 bits of tue colo images the size of pixels. Belo e combine fo example hich as discussed befoe by using the vaious methods fo the actual esults. Fo being bette compaed to each othe e selected the same image as a map fo the key image (see Figue 5 the basic content of the beach the tees have the backgound e eused diffeent methods (using to diffeent combinations of featues Quey and etieve the image fom the fist five ae the most simila to the image as output. Belo ae the enquiies on the expeiment: Figue 5. Key mage fo etieve As the autho of this aticle has compaed the dynamic selection of the similaly algoithms (specific analysis of the Senate [] (p57-6 so hee L distance is selected as the similaity of measuement. 5. Expemental esults anslysis discussion 5.. Extact FD of the expeimental platfom Figue 6. Textue featue of to kinds of seach esult Figue 4. mage etieval system Though the platfom fom the image of the o. 3 images calculate the coesponding to factal dimensions then applied it to the image etieval e can find a geate similaity of some of the image etievals. Figue 7. Textue featue of five kinds of seach esults 5.3. The esults can be seen fom methods n Figue Figue Table vaious algoithms oughness of the sensitivity of the textue is diffeent. n contast la and Coveage capet factal Bonian motion model of self-simila estimation methods in changing its oughness hous ae gentle in

5 compaison high-oughness in the case of the damatic changes the diffeence box-dimensional appoach on the oughness of textue is moe sensitive. The oughness of hous of thei moe damatic changes as Figue 4 as shon in Figue Discussion n many applications the evaluation of image etieval by people can only be made subjectively but the humanbeings eyes to distinguish the textue oughness capacity is limited in othe ods lo oughness of cetain small changes can not be aae. This vision of ho to adapt to fist of all e think of a vaiety of featues integated. Hoeve a diffeent image database because of its diffeent content the next step is to ok against the image of the contents and the factal dimension of the application of the stat. 6. Conclusion Whethe the images ae clusteed o etieved the selection of featues is a basic ok. Featue Selection ill diectly detemine that the meits of the ultimate outcome ae good o not. Fom the expeimental esults can be seen using to factal dimensions as textue featues of extaction hich ae applied in the image etieval is a bette ay. Hoeve due to diffeent factal dimension has the best diffeent application aea [8] (p7 if this can be consideed and using the eighted iteative pocess and inteactive feedback technology to futhe study the content of images database the essence of image collection can be moe effectively eflected and it can help us solve the key issues of CBR. [5] Fanny Cheung Lan pay Xinen mage of a textue classification Jounal Chinese Jounal of gaphic and image Beijing 9998 pp [6] Ye Yongei YAG Qinghua Wavelet and egional statistics on the textue image etieval system should be stong Jounal Jounal of Zhejiang Univesity of Technology Zhejiang Univesity 36 pp [7] Saka Chaudhui B B An Efficient Appoach to Estimate Factal Dimension of Textual mages Jounal Patten Recognition ASCE-AMER SOC CVL GEERS 995(9 pp [8] Chaudhui B BSaka Textue Segmentation Using Factal Dimension Jounal EEE Tan. PAM 9957( pp [9]T.OjalaM. Pietikainen and D. Haood"A compaative study of textue measues ith classification based featue distibutions"jounalpattenrecognition996vol.9o. pp [] Hong Liang Patten Recognition pinciples Yunnan nivesity Pess Yunnan.8. []ZHAO Hai-ying Based on an integated chaacteistics of the image etieval Jounal Fouth ational vitual eality and visual academic confeence poceedings 4.7 pp Refeences [] Yang Guang-jun Factal mathematics Yunnan nivesity Pess Yunnan.3. [] Miss Gao Hong Zhang Yu-Jin Lin Gang line Based on the natual textue self-desciption and classification of elevant Jounal Jounal of Tsinghua Univesity (atual Science Tsinghua Univesity 4 (3 pp [3] Li Houqiang Liu Zheng Kai Lin Feng Factal theoy based on neual netok and kohonen the textue image segmentation method Jounal Compute engineeing and application Beijing 7 pp [4] Li Houqiang Liu Zheng KaiLin Feng Factal theoy based on the classification of aeial images Jounal Remote Sensing Beijing pp