A New Feature of Uniformity of Image Texture Directions Coinciding with the Human Eyes Perception 1

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1 A New Feature of Unformty of Image Texture Drectons Concdng wth the Human Eyes Percepton Xng-Jan He, De-Shuang Huang, Yue Zhang, Tat-Mng Lo 2, and Mchael R. Lyu 3 Intellgent Computng Lab, Insttute of Intellgent Machnes, Chnese Academy of Scences,P.O.Box 30, Hefe, Anhu 23003, Chna {xjhe,yzhang}@m.ac.cn 2 Informaton Engneerng Dept., The Chnese Unversty of Hong Kong, Shatn, Hong Kong tmlo@e.cuh.edu.h 3 Computer Scence & Engneerng Dept., The Chnese Unversty of Hong Kong, Shatn, Hong Kong lyu@cse.cuh.edu.h Abstract:In ths paper we present a new feature of texture mages whch can scale the unformty of mage texture drectons. The feature value s obtaned by examnng the statstc characterstc of the gradent nformaton of the mage. The smulaton result llustrates that ths feature can exactly concde wth the unformty degree of mage texture drectons accordng to the percepton of human eyes.. Introducton Texture features are one nd of features whch can reflect the vsual property of homogenous performance n mages and are ndependent of color and brghtness. The research of mage texture features has been a hot topc for long. Many methods, such as the wdely used grey level co-occurrence matrx method, to portray the mage texture characterstcs have been proposed n a large number of lteratures [-3]. In resent years, some ntellgent methods such as neural networ based technques have been presented [4-9]. A very mportant characterstc of texture mage s the dstrbutng trat of texture drectons. For mages wth strong texture structures (e.g., bar, cloth, roc), the statstc propertes of texture drectons are generally very useful n practcal applcatons such as object recognton and mage retreval. But pecular features to reflect the dstrbutng property of texture drectons have been seldom studed. The Tamura feature of drectonalty s one of these pecular features. The Tamura features, ncludng coarseness, contrast, drectonalty, lneleness, regularty, and roughness, are constructed n accordance wth psychologcal studes on the human Ths wor was supported by the Natonal Natural Scence Foundaton of Chna (Nos and ), and ree grants from the Hong Kong Specal Admnstratve Regon, Chna: RGC Project No.CUHK 470/04E, RGC Project No. CUHK4205/04E and UGC Project No.AoE/E-0/99.

2 percepton of texture [0]. The drectonalty s obtaned by examnng the sharp degree of a hstogram whch s constructed from the gradent vectors of all the mage pxels. But the Tamura feature of drectonalty behaves not so well n reflectng another mportant property,.e., texture drecton unformty, of mages. Undoubtedly, a feature reflectng the unformty degree of mage texture drectons accordng to the percepton of human eyes s very useful n many felds. Ths paper s organzed as follows. Secton 2 brefly revews the extracton method of Tamura feature of drectonalty. A new feature that can scale the unformty of mage texture drectons s presented n Secton 3. Secton 4 gves some smulaton results. Fnally, some conclusve remars are ncluded n Secton Tamura Feature of Drectonalty When we compute the Tamura feature of drectonalty, mages need to be convoluted wth Prewtt mass as shown n fgure to obtan the horzontal and vertcal dfferences, H and V, of the mage. Then, gradent vector at each pxel can be computed as follows: G = ( H + V )/2. θ = tan ( V + H) + π / 2. where G s magntude and θ s angle. Then, by quantzng θ and countng the pxels wth the correspondng magntude G greater than a threshold, a hstogram ofθ, denoted as H D, can be constructed. Ths hstogram wll exhbt strong peas for hghly drectonal mages and wll be relatvely flat for mages wthout strong drectonalty. So we can obtan an overall drectonalty measure from the entre hstogram as follows: F np 2 dr = ( φ φp ) HD ( φ) p φ wp. () where p s ranged over n p peas; and for each pea p, w p s the set of bns dstrbuted over the pea; whle φ p s the bn that taes the pea value. Ths equaton reflects the sharpness of the peas,.e., a smaller value of F dr wll correspondng to the mage whch gets a sharper peas hstogram. In addton, we can also see from eqn. (3) that the angle dstances between the peas can not be reflected out, so the unformty of texture drectons can not be obtaned. In alluson to ths shortage, we present a new feature n the next secton.

3 3. The New Feature of Drecton Unformty In our algorthm, mage s also convoluted wth gradent operators, whch can be Prewtt mass or Sobel mass, as shown n fgure 2. Just le computng drectonalty of the Tamura feature, wth a selected threshold of G denoted wth letter b, we can also construct a hstogram ofθ. The area [0,π ] can be equally dvded nto m parts, each part of whch s called as one bn. These bns are ndexed wth nteger, 2, 3, m. For example, the 6th bn covers the nterval area of [(5/m)π, (6/m)π ]. Suppose that the ntal value of every bn s zero. Examnng the gradent vector of each pxel, f the magntude G s larger than the threshold, then the value of the bn n whch the angle θ s contaned n wll be added by one Fg. Prewtt mass. Fg.2 Sobel mass. When ths process s accomplshed, a probablty hstogram s obtaned by dvdng each value by the sum of the m values of the m bns. Then these bns are sorted by ther probablty values from the greatest to the smallest and the frst bns wth greater probablty values are pced out. The nteger s determned by a threshold d selected between (0, ) wth the follow condtons: p d and = p < d. (2) = Generally, the value of d s selected around 0.5. The bn values are normalzed by the followng formula: (3) prb = p / p =, 2...,. = Thus we get bns wth ther ndexes and normalzed ther probablty values p to prb. It should not be forgotten that the ndex of each bn ndcates the drecton of ths bn. In other words, for an mage, we then obtaned ts texture drectons wth largest probablty values. For each bn, we consder the acute angle wth the frst bn, whch gets the largest probablty value, as the angle dstance: m f ( m/2) (4) a = { otherwse where m s the fore mentoned number of bns.the presented new feature s computed by the followng formula:

4 2 unf = [( ln )] = = F prb prb a prb (5) a are all mentoned forward. From the formula we can deduce where, prb and that the smaller values of drectonalty and better drecton unformty. F unf correspond to the mages whch have stronger texture 4.Smulaton Results The texture mages are all comng from the wdely used Brodatz s. The algorthm mentoned above needs three parameters,.e., the number of bns m, the thresholds b and d. In our experments we adopted Prewtt mass, assume that the number of bns s 2, the threshold b s 9, and the threshold d s 0.5. Fg.3 Texture mages sorted by the values of drectonalty of Tamura feature from smallest to greatest Fg.4 The same texture mages sorted by the values of the new feature from smallest to greatest

5 From Fgures 3 and 4, t can be clearly seen that the new feature has some superorty than the Tamura feature of drectonalty n reflectng the mage texture drecton characterstc. Further more, t can also be found that the new feature of texture drecton unformty s to completely concde wth the human eye. 5.Conclusons Ths paper has presented a new mage texture feature and nvestgated ts mplementaton ablty. The smulaton result showed that the new feature s effectve n reflectng the degree of the mage texture drecton unformty and the strength of mage texture drectonalty. The mage sequence sorted by value of ths feature of each mage also llustrates that the feature can exactly concde wth the unformty degree of mage texture drectons n the lght of percepton of human eyes. References. D. Jones and P. Jacway.: Usng Granold for Texture Classfcaton. Ffth Internatonal Conference on Dgtal Image Computng, Technques and Applcatons, DICT 99, Perth, Australa, 999, pp L.Wang and J. Lu.: Texture Classfcaton usng Multresoluton Marov Random Feld Models. Pattern Recognton Letters, vol. 20, 999, pp E.S. Gadelmawla.: A vson system for surface roughness characterstczaton usng the gray level co-occurrence matrx. NDT&E Internatonal 37 (2004) D.S.Huang.: Intellgent Sgnal Processng Technque for Hgh Resoluton Radars. Publshng House of Machne Industry of Chna, February B. Lerner, H. Guterman, M. Aladjem and H. Dnsten.: A Comparatve Study of Neural Networ based Feature Extracton Paradgms. Pattern Recognton Letters, Vol. 20, 999, pp D.S.Huang.: A constructve approach for fndng arbtrary roots of polynomals by neural networs. IEEE Transactons on Neural Networs,Vol.5, No.2, pp , D.S.Huang.: Systematc Theory of Neural Networs for Pattern Recognton. Publshng House of Electronc Industry of Chna, Bejng, D.S.Huang.: Radal bass probablstc neural networs: Model and applcaton. Internatonal Journal of Pattern Recognton and Artfcal Intellgence, 3(7), 083-0, D.S.Huang, The local mnma free condton of feedforward neural networs for outersupervsed learnng, IEEE Trans on Systems, Man and Cybernetcs, Vol.28B, No.3, 998, H. Tamura, S. Mor, and T. Yamawa, Texture feature correspondng to vsual percepton, IEEE Trans. On Systems, Man, and Cybernetcs, vol. Smc-8, No. 6, June, 978.