International Journal of Pattern Recognition and Arti¯cial Intelligence Vol. 26, No. 4 (2012) 1256011 (14 pages) # .c World Scienti¯c Publishing Company DOI: 10.1142/S0218001412560113
TOWARDS A FAST METHOD FOR IRIS IDENTIFICATION WITH FRACTAL AND CHAOS GAME THEORY
MAHDI JAMPOUR*,§, REZA EBRAHIMZADEH*, MAHDI YAGHOOBI† and ADEL SOLEIMANI-NEZHAD‡ *Department of Arti¯cial Intelligence Islamic Azad University, Mashhad Branch, Mashhad, Iran † Department of Electrical Engineering Islamic Azad University, Mashhad Branch, Mashhad, Iran ‡Department of Library and Information Science Shahid Bahonar University of Kerman, Kerman, Iran §
[email protected]
Received 17 September 2011 Accepted 7 July 2012 Published 25 September 2012 Nowadays many techniques are being used to increase the reliability of human identi¯cation systems. Iris is a part of human body that is desirable for biometric identi¯cation and has favorable factors. We have focused on the reality that iris is a fractal phenomenon in this paper. During the production of new fractals, some features will be extracted by Chaos Game mechanism. These features are useful and e®ective in iris identi¯cation. There are three steps for iris identi¯cation with fractal and Chaos Game Theory. The ¯rst step is making a new fractal. The second step includes extracting features during the ¯rst step. Finally, the iris identi¯cation based on extracted features is the third step. We have named this technique Iris Identi¯cation based-Fractal and Chaos Game Theory (Iris-IFCGT). This technique has some fractal properties like stability against zoom, removing part of the iris image, no sensitivity on rotation and so on as well as desirable speed which helps preventing time consuming process of pattern recognition. Keywords : Biometrics; iris identi¯cation; fractal theory; Chaos Game Theory.
1. Introduction Nowadays the identi¯cation issue is considered as one of the inseparable category of human life, such as opening the automobile door, ATM cards, personal computer and so on. Identi¯cation is being used to recognize the authorized people in di®erent operations. Di®erent techniques have been used for identi¯cation since many years ago. The biometric techniques are divided into two groups according to the usage of physical characteristics and behavioral characteristics, in the ¯rst group the physical features such as ¯ngerprint, face, iris, signature, and DNA are being used for 1256011-1
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identi¯cation and in the second group, the behavioral ones such as gait recognition, typing rhythm and voice are being used.11,18 The identi¯cation techniques do not rely on human biometric features but replacing the arti¯cial keys and passwords are also used in identi¯cation techniques; in Table 1 some biometric and nonbiometric methods of identi¯cation are mentioned and analyzed assuming the interpretation of di®erent sources.12 Table 1 shows that the identi¯cation based on iris is one of the most reliable and desirable techniques in identi¯cation that is possible to improve by some kind of other techniques such as classi¯cation.10 In fact, the original idea of using iris for human identi¯cation was presented by Frank Burch in 1936 and later Leonard Flom and Aran Sa¯r raised the unique idea of the iris in 1985, then Daugman5,6 developed the automotive identifying algorithm of human being by iris. The other scientists began to investigate on the same issue and of course gave some methods on iris identi¯cation including Zhaofeng et al.,3032 Radhika et al.,25 Boles and Boashash,3 Wang et al.27 and Wildes,28,29 studies which mostly use some techniques such as di®erent methods of classi¯cation, di®erent techniques of local processing, SVM, wavelet mechanism and pattern matching to investigate the time complexion development and the Iris identi¯cation qualitative improvement.16,23,24 2. Iris Iris is the colorful part of an eye located between the pupil and the white part of the eye called sclera which is behind the cornea and it can be in di®erent colors like blue, green, brown, and honeyed. In fact, iris is one of the internal organs which are transparent because of cornea transparency. In Fig. 1, iris and eye structure are shown. 2.1. Iris features In an iris there are more than 200 analyzable features including rings, furrows and freckles9,21,26 while the ¯ngerprint has more than 80 analyzable features like core, crossroad, island, etc.4,13 We have seen suitable performance of fractal theory in analyzing of fractal phenomena and have published its results.15 But, in this paper, we improved the presented technique that causes increase in iris recognition process performance. The identi¯cation accuracy in methods based on iris as well as ¯ngerprint is according to Table 1. On the other hand, iris is more reliable than the ¯ngerprint from the point of unrealistic ampli¯ed samples and it often has biometric features. Figure 2 focuses on the existing characteristics of the iris. 3. Fractal Theory The fractal theory was given by Mandelbrot in 1975.19,20 In his opinion, fractal objects have three important properties.14 .
Self-similarity, 1256011-2
DNA Ear Face Fingerprint Gait Hand geometry Iris Keystroke Odor Retina Signature Voice
Biometric Identi¯er
Distinctiveness
H M L H L M H L H H L L
Universality
H M H M M M H L H H L M
H H M H L M H L H M L L
Permanence L M H M H H H M L L H M
Collectability H M L H L M H L L H L L
Performance L H H M H M H M M L H H
Acceptability L M H M M M H M L L H H
Circumvention
Table 1. Comparison of physiological and behavioral biometrics based on their characteristics.11
15 16 16 17 13 15 16 10 14 14 13 13
Total Evaluation H ¼ 3, M ¼ 2, L ¼ 1
Towards a Fast Method for Iris-IFCGT
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Fig. 1. Iris and eye structure.22
. .
Iterative formation, Fractional dimension.
It means that fractal body parts are similar to body and are produced by a repetitive process. If we calculate the object's dimension, the fractal object dimension would be decimal unlike objects such as line and page that have dimensions of one and two in order. In Fig. 3, a fractal sample has been shown as Longon.17 Figure 4 shows another fractal which is also called Sierpinski and it has the fractal dimension of 1.58.
4. Chaos Game Theory The Chaos Game Theory has been introduced by Barnsley in 1988,1,2 it states that a new fractal can be produced by Random Walk process and polygons of a fractal. This theory has two important points; ¯rst, operating a Chaos Game mechanism makes a new fractal and second which is more important is that during the Chaos Game mechanism in producing a new fractal, some parameters can be extracted so that they are useful for identi¯cation. 4.1. Chaos Game mechanism If we apply a Chaos Game mechanism on a triangle, the process would be: First we select a random point, this point is as the starting point and it does not matter where it is; then in the second step, we choose a random number in a domain [1 3] (because we use a triangle), if the value 1 has been selected, it means A vertex has been chosen. If 2, the vertex would be B and if 3 the vertex would be C; then we step from the running point to the chosen vertex as much as half the distance and draw a 1256011-4
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Fig. 2.
The existing characteristics of iris.
Fig. 3. An example of a fractal (Longon).17
new point, we have a random choice again and we repeat all of the process over and over again (for example 50,000 times). Thus, a shape is being produced which is the Sierpinski triangle. Figure 5 shows four steps of Chaos Game mechanism according to Ref. 1, it is also possible to use polygons to make it. Chaos Game mechanism on 1256011-5
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Fig. 4. The Sierpinski triangle fractal.
Fig. 5. Chaos Game mechanism on a trilateral that will produce the Sierpinski triangle.
polygons also leads to extract favorable parameters for identi¯cation; the di®erence is that the produced outcome fractal is di®erent which is justi¯able considering the change of fractal structure relevancy. Figure 6 shows some Chaos Game mechanism operation on di®erent polygons.
5. Iris Detection The iris identi¯cation process would be done in three important phases: (1) Extracting the iris from the picture. (2) Applying the Chaos Game process on iris and extracting the features. (3) Comparing the extracted features with database. 1256011-6
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Fig. 6. The results of implementing the Chaos Game mechanism on the di®erent polygons.2
5.1. Extracting the iris from images Because iris structure is a fractal phenomenon and producing a new fractal is based on this fractal, at ¯rst iris is being extracted from the eye images; here we have some images from iris database.7,8,22 The database has been chosen because of its good image quality and detail and also availability for researchers. Choosing another iris image database has no interruption in applying the presented techniques. In fact, extracting the fractal area of the iris is something that can be done on all iris image databases. As Fig. 7 shows, the images have four major parts; these parts consist of: .
The black area around eye resulted from the camera. The sclera, light area around iris and sometimes has bloody veins. . The iris that has all identifying details and it is the most desirable part of the image. . The pupil which is in the center of iris and generally is a black area. .
Two mechanisms including image histogram and statistic processing are being used to separate the iris from the other areas, removing the black area of the iris including the area around eye resulting from camera and the pupil area which is the central part of the iris has been separated and recognized by image histogram.
Fig. 7. An example of image analysis (Iris Phoenix Database).8 1256011-7
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Fig. 8. Image preprocessing and iris extraction.
The mean deviation idea is also used to detect the sclera area which may include nonwhite details of pixel level; we have de¯ned a sclera detector as relation (1). P j i;j ðmaskði; jÞ AverageðmaskÞÞj P F ði; jÞ ¼ : ð1Þ i;j ðmaskði; jÞÞ F ði; jÞ shows a value in interval [01] which is zero in monotonous area but will increase with bloody veins in some part of sclera. Relation (1) is a desirable parameter for removing the monotonous areas and also somehow monotonous areas of the sclera. Figure 8 shows the processing of the algorithm which has recognized and separated the outer areas of the iris. xnew ¼ x1 cosðÞ þ y1 sinðdegÞ; ynew ¼ y1 cosðÞ x1 sinðdegÞ:
ð2Þ
Common edge detection has been used to have a desired separation of the iris that leads to the recognition of iris and pupil borders. After recognition by the use of a rotating geometrical change, the ring shape of the pupil changes to a rectangle. This process is done by relation (2); Fig. 9 shows the border recognition and Fig. 10 shows the extraction of iris spectrum. After extracting the iris from the image, we have the image as a three-level threshold setting, and this threshold setting has a very simple mechanism which is being cleared through an image histogram; we detect two borders based on the iris
Fig. 9. Iris and Pupil boundary detection. 1256011-8
Towards a Fast Method for Iris-IFCGT
Fig. 10. Four iris image samples (¯rst row) and their extracted results (second row) during the extraction process.
Fig. 11. Investment results at 3 levels (white, gray and black) on the extracted iris images in the second row of Fig. 10.
spectrum histogram, about 30% of the iris image areas are black, about 30% of the iris areas are white and 40% are gray. As Fig. 11 shows, the image is desired fractals for Chaos Game process. 5.2. Applying the Chaos Game process on iris and extracting features The obtained images in Fig. 11 are desirable samples for using Chaos Game mechanism. Thereby we repeat Chaos Game mechanism with a rectangle for 50,000 times (as it has been described in Sec. 4.1) and in each step, we de¯ne two new points with a scale distance according to Fig. 12, we name them Point 1 and Point 2; for each two points, there are three states (black, gray and white) so 3 2 ¼ 9 states would be for each two points, Table 2 has explained each one. If we show the above three states with numbers 0, 1 and 2, Eq. (3) would be the sum of two points state whose sum is a valid value in interval [0 4]. We separate them into ¯ve groups (group 1 is related to the value of 0, group 2 is related to the value of 1, etc.), so each state lead to choose a group as we have in Table 2. X2 Group Value ¼ Pointi : ð3Þ i¼1
Fig. 12. Status of Point 1 and Point 2 based on random point (red point) and introduce a parameter as scale (color online). 1256011-9
M. Jampour et al. Table 2. Display modes may be two points (Points 1 and 2) and how each state is grouped according to a simple mathematical model (sum). Status
Point 1
Point 2
Group Value (P1þP2)
Group Name
Form Form Form Form Form Form Form Form Form
Black ¼ 0 Black ¼ 0 Black ¼ 0 Gray ¼ 1 Gray ¼ 1 Gray ¼ 1 White ¼ 2 White ¼ 2 White ¼ 2
Black ¼ 0 Gray ¼ 1 White ¼ 2 Black ¼ 0 Gray ¼ 1 White ¼ 2 Black ¼ 0 Gray ¼ 1 White ¼ 2
0 1 2 1 2 3 2 3 4
Group 1 Group 2 Group 3 Group 2 Group 3 Group 4 Group 3 Group 4 Group 5
1 2 3 4 5 6 7 8 9
Fig. 13. Fractals produced (third row) by the mechanism of Chaos Game for each of the iris in Fig. 11.
Thus in addition to produce a new fractal by Chaos Game mechanism, which is shown for four iris cases of Fig. 11 in Fig. 13, some parameters will be extracted that are unique for each iris, these parameters are the sum of all mentioned state in Table 2. It is clear that the sum of ¯ve values of the mentioned groups in Table 2 is necessarily equal to frequency of Chaos Game mechanism, because a condition is being chosen in each repetition and the counter related to that condition is also being increased for a value, so the sum of all groups would be 50,000 (Chaos Game mechanism iterations) at the end of Chaos Game mechanism. To standardize the values, we will divide all the obtained values by 50,000 and the resulting numbers will be standards in interval [0 1] so that the sum of the values would be one.
5.3. Comparing the extracted features with database The parameters that have been extracted via Chaos Game mechanism are in [01] interval and can be evaluated with precision near to 0.02. We have ¯ve parameters and each parameter has 50 di®erent states, thereby, we can segregate 1256011-10
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Fig. 14. Spectrums produced by the mechanism of Chaos Game for each of the iris in Fig. 11.
50 5 ¼ 312; 500; 000 di®erent iris samples. Meanwhile, if we perform the Chaos Game mechanism with a new scale, we will have ¯ve similar features other than previous features with precision of 0.02. So, we can identify 50 10 ¼ 9:7 10 16 iris samples. Therefore, 10 features will be analyzed and stored per each iris for iris identi¯cation. If we calculate extracted parameters per di®erent values of scale, we can create a spectrum that is a suitable alternative for iris in identi¯cation and authentication processes. Generally according to the explained technique in this paper each iris has 10 decimal values in interval [01] saved and stored. About 9:7 10 16 of the iris is able to separate due to di®erent values of scale; a spectrum has been created for each iris that shows the latent di®erences. Figure 14 shows all the extracted spectrum of each iris in Fig. 10 that is being calculated by Chaos Game mechanism.
6. Conclusion The technique presented in this paper is a result of an appropriate mapping that originates from fractal theory and Chaos Game mechanism. Here, analyzable fractals have been created from the primitive fractals (Iris) based on Chaos Game mechanism. 1256011-11
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Figure 10 shows the similarities in a general view and to understand the di®erences in a minor one that is in fact the principle of fractal theory. The same attitude in Fig. 13 shows the accuracy of Chaos Game mechanism but this mechanism changes the nonsensible di®erences of the iris to numbers, values, and spectrums so easily that is understandable for a machine. The Iris Identi¯cation-based Fractal and Chaos Game Theory (Iris-IFCGT) System has so many advantages like huge analysis (more than1010), stability against rotation, and the use of some parts from iris images instead of all and so many things. Other advantages of this method is the fractal analysis of the iris and not to use the time consuming techniques of pattern matching and time consuming image processing which ultimately leads to increase the processing speed and identifying process. 7. Further Applications The presented technique in this paper has introduced a new approach for analyzing the fractal phenomenon and extracting features for each fractal by Chaos Game mechanism, so it can be applied in classi¯cation of historiography slides in medicine, generation of new music, signal and image compression, generation of various art forms, technical analysis of price series, and so on. References 1. M. F. Barnsley, Fractals Everywhere (Academic Press, New York, 1988). 2. M. F. Barnsley, Super Fractals (Cambridge University Press, New York, 2006). 3. W. Boles and B. Boashash, A human identi¯cation technique using images of the iris and wavelet transform, IEEE Trans. Signal Process. 46 (1998) 11851188. 4. R. Cappelli, D. Maio, D. Maltoni, J. Wayman and A. K. Jain, Performance evaluation of ¯ngerprint veri¯cation systems, IEEE Trans. Pattern Anal. Mach. Intell. 28 (2006) 318. 5. J. Daugman, New methods in iris recognition, IEEE Trans. Syst. Man, Cybernet. 37 (2007) 11671175. 6. J. Daugman, Biometric decision landscapes, Technical Report No. TR482, University of Cambridge Computer Laboratory (2000). 7. M. Dobes, L. Machala, P. Tichavsky and J. Pospísil, Human eye iris recognition using the mutual information, Optik 115 (2004) 399405. 8. M. Dobes and L. Machala, Iris database, http://phoenix.inf.upol.cz/iris (accessed 2004). 9. M. Dobes, J. Martinek, D. Skoupil, Z. Dobesova and J. Pospísil, Human eye localization using the modi¯ed Hough transform, Optik 117 (2006) 468473. 10. X. Feng, X. Ding, Y. Wu and P. S. P. Wang, Classi¯er combination and its application in iris recognition, Int. J. Pattern Recogn. Artif. Intell. 22 (2008) 617638. 11. A. K. Jain, P. J. Flynn and A. A. Ross, Handbook of Biometrics (Springer, New York, 2008). 12. A. K. Jain, A. A. Ross and S. Prabhakar, An introduction to biometric recognition, IEEE Trans. Circuits Syst. Video Technol. 14 (2004) 420. 13. M. Jampour, H. Shojaei, M. Ashourzadeh and M. Yaghoobi, Compressing of ¯ngerprint images by means of fractals feature, in IEEE Proc. 2nd Int. Conf. ICMV Dubai (2009), pp. 1822. 1256011-12
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14. M. Jampour, M. Yaghoobi and M. Ashourzadeh, Fractal images compressing by estimating the closest neighborhood with assistance of schema theory, J. Comput. Sci. 6 (2010) 591596. 15. M. Jampour, M. Yaghoobi, M. Ashourzadeh and A. Soleymani, A new fast technique for ¯ngerprint identi¯cation with fractal and chaos game theory, Fractals 18 (2010) 293300. 16. M. Li, T. Tieniu, W. Yunhong and Z. Dexin, E±cient iris recognition by characterizing key local variations, IEEE Trans. Image Process. 13 (2004) 739750. 17. Longon, Fractal art \I sleep only to dream of you", http://www.°ickr.com/photos/ longan drink/289130767 (accessed 2011). 18. D. Maltoni, D. Maio, A. K. Jain and S. Prabhakar, Handbook of Fingerprint Recognition (Springer, London, 2009). 19. B. Mandelbrot, A multifractal walk down wall street, Sci. Am. 280 (1999) 7073. 20. B. Mandelbrot, Fractals: Form, Chance, and Dimension (W. H. Freeman and Co, San Francisco, 1977). 21. National Science and Technology Council (NSTC) subcommittee on Biometrics, iris recognition (2006), http://www.biometrics.gov/Documents/Irisrec.pdf (Accessed 2006). 22. J. Ortega-Garcia, J. Fierrez et al., The multi-scenario multi-environment BioSecure Multimodal Database (BMDB), IEEE Trans. Pattern Anal. Mach. Intell. 32 (2010) 10971112. 23. M. Plemons, E. Horvath et al., Computational imaging systems for iris recognition, Proc. SPIE 5559 (2004) 346357. 24. H. Proenca and L. A. Alexandre, Toward noncooperative iris recognition: A classi¯cation approach using multiple signatures, IEEE Trans. Pattern Anal. Mach. Intell. 29 (2007) 607612. 25. K. R. Radhika, S. V. Sheela, M. K. Venkatesha and G. N. Sekhar, Signature and iris authentication based on derived kinematic values, Int. J. Pattern Recogn. Artif. Intell. 24 (2010) 12371260. 26. P. Radu, K. Sirlantzis, G. Howells, S. Hoque and F. Deravi, Are two eyes better than one? An experimental investigation on dual iris recognition, Int. Conf. Emerging Security Technologies (2010), pp. 712. 27. Z. Wang, Q. Han and C. Busch, A novel iris location algorithm, Int. J. Pattern Recogn. Artif. Intell. 23 (2009) 5970. 28. R. P. Wildes, Iris recognition: An emerging biometric technology, Proc. IEEE. 85 (1997) 13481363. 29. R. P. Wildes, J. C. Asmuth et al., A system for automated iris recognition, in Proc. Second IEEE Workshop on Applications of Computer Vision (1994), pp. 121128. 30. H. Zhaofeng, T. Tieniu, S. Zhenan and Q. Xianchao, Toward accurate and fast iris segmentation for iris biometrics, IEEE Trans. Pattern Anal. Mach. Intell. 31 (2009) 16701684. 31. H. Zhaofeng, S. Zhenan, T. Tieniu and Q. Xianchao, Enhanced usability of iris recognition via e±cient user interface and Iris image restoration, IEEE Int. Conf. Image Processing (2008), pp. 261264. 32. S. Zhenan, W. Yunhong, T. Tieniu and C. Jiali, Improving iris recognition accuracy via cascaded classi¯ers, IEEE Trans. Syst. Man, Cybernet. 35 (2005) 435441.
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M. Jampour et al. Mahdi Jampour is a Ph.D. researcher in Computer Vision and Biometric Systems in Graz University of Technology (Graz, Austria). He received his B.S. in Computer Science from Shahid Bahonar University of Kerman in 2006 and received his M.Sc. from Islamic Azad University of Mashhad in Arti¯cial Intelligence (2009). He has received a scholarship from the Ministry of Science, Research and Technology to continue his studies towards a Ph.D. at Graz University of Technology (2010). He is a member of IEEE and IACSIT and also an editorial member of various international journals.
Mahdi Yaghoobi is a faculty member at the Arti¯cial Intelligence Department at Islamic Azad University of Mashhad. He received his B.S. in Electrical Engineering (1989) and M.Sc. in Electrical Engineering (Control) in 1993, both from Ferdowsi University of Mashhad, and he received his Ph.D. in Electrical Engineering (Control) from Islamic Azad University of Science and Research branch (2008). He is Vice-Dean of Research in the Faculty of Engineering. He is an editorial board member of various international journals. His research interests are predictive control, adaptive control, fractal and chaotic systems and evolutionary algorithms.
Reza Ebrahimzadeh is a faculty member of Computer Engineering at Islamic Azad University of Zahedan (IAUZAH). He received his B.S. and M.Sc. in Computer Science and Arti¯cial Intelligence from Islamic Azad University of Mashhad in 2006 and 2009, respectively. He is now working on iris identi¯cation project in the biometrics laboratory of IAUZAH. His research interests include biometrics systems such as iris identi¯cation, ¯ngerprint recognition, signature veri¯cation, etc.
Adel Soleimani-Nejad received his B.S. in Library and Information Science (LIS) from the National University of Tehran in 1991, and he received his M.Sc. and Ph.D. in Information Science (IS) from the National University of Shiraz and Islamic Azad University, Science and Research branch in 2000 and 2008, respectively. He is now a faculty member of the Department of Library and Information Science at Shahid Bahonar University of Kerman. His research interests focus on the Information Systems (IS), Management Information Systems (MIS) and Information Technology (IT).
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