IRIS RECOGNITION BASED ON HILBERT–HUANG TRANSFORM 1 ...

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628 Z.Yang,Z.Yang&L.Yang Hilbert marginal spectrum of xj(t). The average Hilbert marginal spectrum of X is defined as H(f) = 1 N hj(f). (4) N j=1 f H m is called as the average main frequency of X if f H m satisfies H(f H m ) ≥ H(f), ∀f. For a given set of signal series, in which signals are approximately periodic, the main frequency can characterize the approximate period very well. Unfortunately, in some cases a signal may not have a unique main frequency. To handle this situation, all the possible main frequencies have to be considered. Therefore, we can utilize the gravity frequencies, which is called the “main frequency center”, instead of the “main frequency”. Definition 3 (Main frequency center). Let H(fi) (j =1, 2,...,W)bethe average Hilbert marginal spectrum of X = {xj(t)|j =1, 2,...,N}. Assume H(fi) is monotone decreasing respect to i. The main frequency center of X is defined as fC(X) = M i=1 fiH(fi) M i=1 H(fi) , (5) where M is the minimum integer satisfying M i=1 H(fi) ≥ P W i=1 H(fi), and 0 < P < 1 is a given constant. Then e =(1/M ) M i=1 H(fi) is called the energy of fC(X). As can be seen from its definition, the main frequency center is the weighted mean of several frequencies whose Hilbert marginal spectrums are largest. There and the main frequency center is a gap between the average main frequency f H m fC, but the main frequency center will be a steadier recognition feature. Therefore the main frequency center fC is used instead of the average main frequency f H m to characterize the approximate period of signal series. 3.3. Iris feature extraction Although all normalized iris templates have the same size, eyelashes and eyelids may still appear on the templates and degrade recognition performance. We find that the upper portion of a normalized iris image (corresponding to regions closer to the pupil) provides the most useful information for recognition (see Fig. 3). Therefore, the region of interest (ROI) is selected to remove the influence of eyelashes and eyelids. That is, the features are extracted only from the upper 75% section (48 × 512) that is closer to the pupil in our experiments (see Fig. 3). It is known that an iris has a particularly interesting structure and provides abundant texture information. Furthermore if we vertically divide the ROI of a normalized image into three subregions as shown in Fig. 3, the texture information in the subregion will be more distinct.
ROI { Iris Recognition Based on Hilbert–Huang Transform 629 Fig. 3. The normalized iris image is vertically divided into four subregions. The three subregions 1,2and3aretheROI. 210 200 190 180 170 160 150 140 130 120 0 50 100 150 200 250 300 350 400 450 500 x 1 2 3 4 200 150 100 0 50 0 50 100 150 200 250 300 350 400 450 500 −50 0 50 50 100 150 200 250 300 350 400 450 500 c1 c2 c3 c4 c5 r 0 −50 0 50 50 100 150 200 250 300 350 400 450 500 0 −50 0 50 50 100 150 200 250 300 350 400 450 500 0 −50 0 50 100 150 200 250 300 350 400 450 500 20 0 −20 0 200 50 100 150 200 250 300 350 400 450 500 150 0 50 100 150 200 250 300 350 400 450 500 Fig. 4. Left, the 11th line signal of the normalized iris image in Fig. 3 along the horizontal direction. Right, the EMD decomposition result of the 11th line signal. An iris consists of some basic elements which are similar each other and interlaced each other. Hence, an iris image is generally periodic to some extent along some directions, that is, some approximate periods are embed in the iris image. As an example, let us observe the 11th line signal of the normalized iris image in Fig. 3 along the horizontal direction, as show in the left of Fig. 4. It can be seen that most of the durations of the waves are similar, i.e. some main frequencies embed in the signal. As we know, the EMD can extract the low-frequency oscillations very well. 11 With EMD, the decomposition result of the 11th line signal is shown in the right of Fig. 4. It can be seen that two main approximate periods are extracted in the third and fourth IMFs. To show it clearly, we plot the original signal (solid line) and the third IMF (dash line) together in the interval [320, 450] in the left of Fig. 5. It can be seen that this IMF characterizes the proximate period of the waveform quite well and the period is about 15 (i.e. the frequency is about 1/15 ≈ 0.067). Similarly, we plot the original signal (solid line) and the fourth IMF (dash line) together in the interval [320, 450] in the right of Fig. 5. It can be seen that this IMF characterizes the proximate period and the variety of the amplitude. This period is about 26 (i.e. the frequency is about 1/26 ≈ 0.0385). According to Eq. (3), we can compute the Hilbert marginal spectrum of the 11th line signal of the normalized iris image in Fig. 3, as shown in the left of Fig. 6. It is evident that the two main frequencies can be extracted from the Hilbert marginal spectrum correctly. Based on lots of experiments and analysis we found
Page 1 and 2: Advances in Adaptive Data Analysis
Page 3 and 4: Iris image preprocessing Iris image
Page 5: Iris Recognition Based on Hilbert-H
Page 9 and 10: α ( ) α Iris Recognition Based on
Page 11 and 12: Energy 600 400 200 Iris Recognition
Page 13 and 14: x c1 c2 c3 c4 c5 Iris Recognition B
Page 15 and 16: Main Frequency Center 0.06 0.05 0.0
Page 17 and 18: False Reject Rate(%) 0 2.5 2 1.5 1
Page 19: Iris Recognition Based on Hilbert-H

IRIS RECOGNITION BASED ON HILBERT–HUANG TRANSFORM 1 ...

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