Iris recognition algorithm based on point covering of high-dimensional space and neural network

Transcription

1 Irs recognton algorthm based on pont coverng of hgh-dmensonal space and neural network Wenmng Cao,, Janhu Hu, Gang Xao, Shoujue Wang The College of Informaton Engneerng, ZheJang Unversty of Technology, Hangzhou, 004, Chna Lab of Artfcal Neural Networks, Insttute of Semconductors, CAS, Bejng, 0008, Chna Abstract. In ths paper, we constructed a neuron of pont coverng of hghdmensonal space, and proposed a new method for rs recognton based on pont coverng theory of hgh-dmensonal space. In ths method, rses are traned as cognton one class by one class, and t doesn t nfluence the orgnal recognton knowledge for samples of the new added class. The results of experments show the rejecton rate s 98.9%, the correct cognton rate and the error rate are 95.7% and.5% respectvely. The expermental results demonstrate that the rejecton rate of test samples excluded n the tranng samples class s very hgh. It proves the proposed method for rs recognton s effcacy.. Introducton In recent years, wth the development of nformaton technology and the ncreasng need for securty, ntellgent personal dentfcaton has become a very mportant and urgent problem. The emergng bometrc technology can solve the problem, whch takes the unque, relable and stable bometrc features (such as fngerprnts, rs, face, palm-prnts, gat etc.) as dentfcaton body. Ths technology has very hgh securty, relablty and effectvty. As one of the bometrc technology, rs recognton has very hgh relablty. Comparng wth other bometrc dentfcaton technology, the fault acceptance rate and the fault rejecton rate of rs recognton are very low. The technology of rs recognton has many advantages,.e., stablty, non-nvasveness, unqueness. All there desrable propertes make the technology of rs recognton has very hgh commercal value. Based on the above reasons, many researchers have appled themselves to ths feld. Daugman used mult-scale quadrature wavelets to extract texture-phase structure nformaton of rs to generate a 048-bt rscode and compared the dfference between a par of rs representatons by computng ther Hammng dstance va the XOR operator [],[]. Wldes et al. represented the rs texture wth a Laplacan pyramd constructed wth four dfferent resoluton levels and used the normalzed correlaton to determne whether the nput mage and the model mage are from the same class []. Boles et al. calculated zero-crossng representaton of D wavelet transform at varous resoluton levels of a vrtual crcle on an rs mage

2 Wenmng Cao,, Janhu Hu, Gang Xao, Shoujue Wang to characterze the texture of the rs. Irs matng was based on two dssmlarty functons [4][0[]. In ths paper, from the cognton scence pont of vew, we constructed a neuron of pont coverng of hgh-dmensonal space[5][6][7], and propose a new method for rs recognton based on pont coverng theory of hghdmensonal space and neural network[8][]. The results of experments show the rejecton rate s 98.9%, the correct recognton rate and the error rate are 95.7% and.5% respectvely. The expermental results demonstrate that the rejecton rate of test samples excluded n the tranng samples class s very hgh. It proves the proposed method for rs recognton s effectve. The remander of ths paper s organzed as follows. Secton descrbes mage preprocessng. Secton ntroduces rs recognton algorthm based on pont coverng theory of mult-dmensonal space and neural network. Experments results and expermental analyss are gven n Secton 4 and Secton 5 respectvely.. Image preprocessng Irs mage preprocessng s manly composed of rs localzaton, rs normalzaton and enhancement.. Irs localzaton Irs localzaton namely s the localzaton of the nner boundary and the outer boundary of a typcal rs can approxmately be taken as crcles. It s the mportant part of the system of rs recognton, and exact localzaton s the premse of the rs dentfcaton and verfcaton... Localzaton of the nner boundary The orgnal rs mage (see Fg.(a)) has some character of the gray-scale dstrbuton. The rs s darker than the sclera, and the pupl s greatly darker than the rs, as shown n Fg.(a). From the hstogram (see Fg.(b)), we can clearly see that the low gray-scale manly converges at the frst peak value. Therefore, we adopt the bnary transform to localze the nner boundary. From the mage after bnary transform (see Fg.(a)), we fnd that the areas of zero gray-scale are almost the areas of the pupl and eyelash. Therefore, we reduce the nfluence of the eyelash by erode and dlaton (see Fg.(a)). Fg. (a) orgnal mage (b) hstogram of the rs

3 Irs recognton algorthm based on pont coverng of hgh-dmensonal space and neural network Fg.(a) bnary mage (b) bnary mage after erode and dlaton (c) localzed mage From the Fg (b), we can fnd that the length and the mdpont of the longest chord can be taken as the approxmate dameter and center of the pupl respectvely. Namely, accordng the geometry knowledge, let the length of the longest chord s da max, and the coordnates of the frst pont of the chord are xbegn and ybegn, then da max xpupl = xbegn +, ypupl = ybegn, rpupl = da max () Where xpupl and ypupl denote the center coordnates of the pupl, and rpupl denotes the radus of the pupl. When the qualty of the mage s relable, ths algorthm can localze the pupl quckly and exactly. Otherwse, we can correct the method as follow:. We can reduce the searchng area by subtractng the pxels on the edge of the mage.. We can get k chords, whch are less than a certan threshold near the longest chord, and take the average value of center coordnates of k chord as the center of the pupl... Localzaton of the outer boundary The exact parameters of the outer boundary are obtaned by usng edge detecton (Canny operator n our experments) and Hough transform. The mage after Edge detecton ncludes some useless ponts. For elmnatng the nfluence, we remove the useless ponts between the areas of [ 0 ] o, 50 o and [ 5 ] o, 5 o accordng to the center of the pupl. Then, Hough transform s adopted to localze the outer boundary. By the above method, we can localze the nner boundary and the outer boundary of the rs exactly. The localzatons results of the rs are showed n Fg.(c).. Irs normalzaton and enhancement Irses from dfferent people may be captured n dfferent sze, and even for rses from the same eye, the sze may change because of llumnaton varatons and other factors (the pupl s very senstve to lghtng changes). Such elastc deformaton n rs texture wll nfluence the results of rs recognton. For the purpose of achevng more accurate recognton results, t s necessary to compensate for such deformaton.

4 4 Wenmng Cao,, Janhu Hu, Gang Xao, Shoujue Wang In our experment, every pont of the rs mage s mapped to the polar coordnates by the followng formula. x y ( r θ ) = ( r) x p ( θ ) + rxs ( θ ) ( r, θ ) = ( r) y ( θ ) + ry ( θ ), () In whch, ( x ( θ ), y ( θ ) ) and ( x ( θ ) y ( θ ) p p p s p ) denote the pont of ntersecton wth the nner boundary and the outer boundary respectvely. In our experment, the sector areas ( [ 0 ] o, 0 o and [ 0 ] o, 40 o ) are ntercepted for normalzaton accordng the pupl center. In ths way, one hand, t s smple; on the other hand, the segment texture nformaton s enough to dentfy the dfferent persons. Then, the rs rng s unwrapped to a rectangular texture block wth 64 56, and the rows correspond to the radus and the columns a fxed sze ( ) correspond to the angles (see Fg.(a)). The normalzed rs mage stll has low contrast and may have non-unform brghtness caused by the poston of lght sources. All these may affect the feature analyss. Therefore, we enhance the normalzed mage by means of hstogram equalzaton. Such processng compensates for nonunform llumnaton, as well as mprovng the contrast of the mage. The enhanced mage s shown n Fg.(b). s Fg.(a) normalzed mage (b)enhanced mage. Irs recognton algorthm based on pont coverng of multdmensonal space and neural network Mult-weghted neuron can be represented as followng formula: Y = f [ Φ ( X, W, W, L, Wm ) Th] () In whch, Φ X, W, W, L, W ) denotes the relaton between the nput pont ( m X and m weght ( W, W, L, Wm ). Let m = ps. And ps can be descrbed as follow:, t s -weghted neuron, named Y = f [ Φ( X, W, W ) Th] (4)

5 Irs recognton algorthm based on pont coverng of hgh-dmensonal space and neural network 5 ( X, W, W ) X θ W Φ = (, W W ), (5) In whch, θ ( W, W ) denotes the fnte area, whch s enclosed by three ponts( W W W ), and t s a trangle area. Namely, θ ( W, W ) can be represented as follow: θ = Y = α [ α W + ( α ) W ] + ( α ) W, α [0, ], α [0, ]} ( W, W W ), {.. Y (6) Then, Φ( X, W, W ) -Th actually s the Eucld dstance from X to the trangle area of the ps neuron. The model of actvaton functon s:, x Th f ( x) =, x > Th (7) In mult-dmensonal space, we use every three sample s ponts of the same class to construct a fnte D plane, namely, a trangle. Then several D spaces can be constructed, and we cover these planes by the ps neuron to approxmate the complcated shape, whch s formed by many sample ponts of the rs n multdmensonal space.. Constructon of pont coverng area of mult-dmensonal space Step : Let the sample ponts of the tranng set are α ={ A, A,, } L. In whch, N s the number of the total sample ponts. To fgure out the dstance of every two ponts, the two ponts havng the least dstance are defned as B and B. Let B denotes the nearest pont away from B and B, and B must doesn t n the lne formed by B and B. In ths way, B B and B construct the frst trangle plane represented as θ, whch s covered by a ps neuron, the coverng area s: P { X Th X R n } = ρ, (8) Xθ θ = Y = α [ α B + ( α ) B ] + ( α ) B, α [0,], α [0, ]} Y (9) {.. A N

6 6 Wenmng Cao,, Janhu Hu, Gang Xao, Shoujue Wang Where ρ X θ denotes the dstance from X toθ. Step : Frstly, The rest ponts contaned n P should be removed. Then, accordng to the method of step, defne the nearest pont away from B B and B as B. Among B B and B, two nearest ponts away from B are denoted as B and B. And B B and B construct the second trangle defned as θ, whch s covered by another ps neuron. And the coverng area s descrbed as follow: P { X Th X R n } = ρ, (0) Xθ [ α B + ( α ) B ] + ( α ) B, α [0,], [0,]} θ = { Y Y = α.. α (). Where ρ X θ denotes the dstance from X toθ. Step : Remove the rest ponts contaned n the coverng area of the front ( ) ps neurons. Let B denotes the nearest pont from the remaned ponts to the three vertexes of the ( ) th trangle. Two nearest vertexes of the ( -) trangle away from B are represented as B and B. Then, B B and B construct the th trangle, defned as θ. In the same way, θ s covered by a ps neuron. The coverng area s P { X Th X R n } = ρ, () Xθ θ = Y = α [ α B + ( α ) B ] + ( α ) B, α [0,], α [0, ]} Y ( () {.. Step 4: Repeat the step untl all sample ponts are conducted successfully. Fnally, there are m ps neurons, and ther mergence about coverng area s the coverng area of every rs class. m P = U P = (4). Irs recognton algorthm based on pont coverng of hgh-dmensonal space Takng Th =0 under recognton, the ps neuron can be descrbed as follow:

7 Irs recognton algorthm based on pont coverng of hgh-dmensonal space and neural network 7 ρ = X θ ( W, W W ), The output ρ s the dstance from X to the fnte area ( W, W ) The dstance from X to the coverng area of the th class rs s: ρ = M mn ρ j= j, =, L, 80 θ. (5) (6) In whch, M denotes the number of the ps neuron of the th rs, ρ s the dstance from X to the coverng area of the jth neuron of the th class rs. The X wll be classfed to the rs class correspondng to the least ρ. Namely, the classfcaton method s: 80 j = mn = ρ, j (, L,80) (7) 4. Expermental results Fg.4 rs samples from the tranng set Fg.5 rs samples from the second test set Fg.6 rs samples from the frst test set Images of CASIA (Insttute of Automaton, Chnese Academy of Scences) rs mage database are used n ths paper. The database ncludes 74 rs mages from 06 dfferent eyes (hence 06 dfferent classes) of 80 subjects. For each rs class, mages

8 8 Wenmng Cao,, Janhu Hu, Gang Xao, Shoujue Wang are captured n two dfferent sessons and the nterval between two sessons s one month. The experment processes and experment results are presented as follow: () In our experment, random samples from each class n the frontal 80 classes (hence, 40 samples) are chosen for tranng, and a ps neuron of mult-weghted neural network s constructed for the samples. Fve samples from the tranng set are shown n Fg.4. Then, the entre rs database s taken as test sample set. In whch, 8 ( 6 7 ) samples, whch don t belong to the classes of tranng samples, are referred to the frst sample set. The remander of total 560 ( 80 7) samples s referred to the second sample set. Fg.5 shows fve samples from the second test set and Fg.6 shows fve samples from the frst test set. () The rejecton rate=the number of samples whch are rejected correctly n the frst sample set/the total number of the frst sample set. The correct cognton rate=the number of samples whch are recognzed corrected n the second sample set / the total number of the second sample set. The error recognton rate= (the number of samples whch are recognzed mstakenly n the frst sample set +the number of samples whch are recognzed mstakenly n the second sample set) / the total number of the second sample set. () For total 74 test samples, 80 samples are rejected correctly and the other samples are recognzed mstakenly n the frst test sample; and 56 samples are recognzed correctly and the rest 4 samples are recognzed mstakenly n the second test sample. Therefore, the rejecton rate s 98.9%(80/8), the correct cognton rate and the error recognton rate are 95.7%(56/560) and.5%((+4)/74) respectvely. 5. Expermental analyss We can conclude from the above expermental results that: () Irses are traned as cognton one class by one class n our method, and t doesn t nfluence the orgnal recognton knowledge for samples of the new added class. () Although the correct cognton rate s not very well, the result of rejecton s wonderful. In our experment, the rejecton rate s 98.9%, namely, the rs classes that don t belong to the tranng test can be rejected successfully. () The rs recognton algorthm based on neuron of mult-weghted neural network s appled n the experment and the total samples of every class construct the shape of D dstrbuton. Namely, t s the network connecton of dfferent neuron. (4) The dstrbuton of the recognzed thng should be researched frstly when we apply the algorthm for rs recognton based on pont coverng theory of hghdmensonal space. Then, the coverng method of neural network s consdered. (5) In above experment, f the mage preprocessng s more perfectly, the expermental results maybe better. To sum up, t proves the proposed rs recognton algorthm based on pont coverng of hgh-dmensonal space and neural network s effectve.

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