Iris Recognition using Quaternionic Sparse ... - Semantic Scholar
Iris Recognition using Quaternionic Sparse Orientation Code (QSOC) Ajay Kumar, Tak-Shing Chan Department of Computing, The Hong Kong Polytechnic University, Hong Kong Email: [email protected], [email protected] In this paper, we formulate a new approach for the human identification using hypercomplex and sparse representation of biometric images. The success of this approach is evaluated † on visible illumination iris images using quaternionic sparse orientation coding (QSOC) formulation discussed in following sections.
Abstract Personal identification from the iris images acquired under less-constrained imaging environment is highly challenging problem but with several important applications in surveillance, image forensics, search for missing children and wandering elderly. In this paper, we develop and formulate a new approach for the iris recognition using hypercomplex (quaternionic or octonionic) and sparse representation of unwrapped iris images. We model iris representation problem as quaternionic sparse coding problem which is solved by convex optimization strategy. This approach essentially exploits the orientation of local iris texture elements which are efficiently extracted using a binarized dictionary of oriented atoms. The feasibility of this approach is evaluated, both for the recognition and the verification problem, on the publicly available visible illumination UBIRIS V2 database. Our experimental results using the proposed formulation illustrate significant improvement in performance (e.g., 30% improvement in rank-one recognition accuracy) over the previously studied sparse representation approach for the visible illumination iris recognition.
2. Hypercomplex Sparse Representation The key objective of our efforts is to combine hypercomplex (quaternionic or octonionic) and sparse representation to achieve more accurate biometric identification. We will prove the equivalence between hypercomplex sparse encoding and mixed 1,2-norm minimization. This equivalence enables us to perform hypercomplex sparse coding using existing software for sparse multiple measurement vector (MMV) problems [2], [5]-[6].
Problem Statement We define quaternionic sparse coding as: , (1) min α subject to Dα x D ,α ,x , and octonionic sparse coding as: min α subject to Dα x , (2) ,α ,x . D We are going to prove that the above are equivalent to: min A , subject to DA X F , ,A ,X (3) D which is an extension of single-measurement sparse recovery to the multiple-measurement case [2], [6]. The notations employed in his paper represent their conventional meaning in the related literature [2], [9]. Here we let r 4 for the equivalent quaternionic formulation and r 8 for its octonionic equivalent.
1. Introduction Iris recognition has emerged as one of the most effective technologies for the large scale human identification [1], [3]. There have been several promising efforts to segment iris images from the visible illumination face images for the personal identification and develop less cooperative alternative for the remote surveillance and forensics applications. Several publications [7], [12] detail alternative algorithms for the challenging visible illumination iris segmentation and also for the recognition [8]-[9], [17][19] from such segmented (noisy) iris images. The recognition of visible illumination iris images poses several challenges. These can be attributed to image quality degradations resulting from shadows, albedo absorption selectivity, varying iris pixel resolution, scattering and varying pigmentation. Therefore further efforts are required to develop robust feature extraction and matching techniques which can accommodate such inherent image variations in the segmented iris images.
978-1-4673-1612-5/12/$31.00 ©2012 IEEE
Quaternionic Representation Let us first prove the equivalence of α and A , . The mixed 1,2-norm is defined as A , ∑ where A denotes the j th row of [2]. A Recall that the norm of a quaternion a a i a j a i a j a k| a a a a a k is |a †
This approach can also be explored to simultaneously exploit multiple iris representations (e.g. [4]) for recognizing conventional iris images acquired under near-infrared illumination.
59
∑ α . If we rewrite the quaternionic entries in α a ,a ,a ,a and that the l -norm of a vector α is α as row vectors in the form a , a , a , a we obtain an isomorphic representation A and the following equivalence is immediately established: ∑ ∑ , 4 We further rewrite the entries of in this isomorphic form yielding and proceed to prove the equivalence of and . By definition we have; ∑ ∑ and . (5) | ∑ | and Moreover the Euclidean and Frobenius norms are defined as ∑
∑
∑
. Thus
and | | we have
|
|
, where ,
,
,
∑
| . Since
| ∑
extract the 1, , ,
parts of
, respectively,
. 6 Putting this back into original equation (1) and observing the relationships between , , , , we can finally write;
. 7
Octonionic Representation A similar argument can be used to prove the octonionic case. We first prove the equivalence of and , . is | The norm of an octonion , , , , , , , and | we again obtain an isomorphic by writing the octonionic elements in as row vectors , , , , , , , representation with the following equivalence: ,
Further let
. 8
be the isomorphic row-vector form of the entries in . The Euclidean and Frobenius norms are ∑
|
| and
∑
60
∑
. Therefore we can further rewrite;
∑ 1,
,
,
,
,
,
|
| ,
parts of
| . As , where , respectively, we obtain; ∑
| ∑
,
,
,
and , ,
| | , ,
extract
the
. 9 Finally, we substitute it back to the original equation (2) and observe the relationship between , , , :
. 10
Figure 1: Block diagram for quaternionic sparse orientation representation using visible illumination iris images.
61
inndependent teest data consiisting of all the t remainingg 904 images froom the 152 subbjects.
3. Quaternionic Sp parse Orien ntation Cod de The blockk diagram forr encoding unw wrapped iris images acquired under visible illuminatioon iris imaging is shown inn figure 1. In thhis diagram, RGB R denotes vector -valued signals and H denotes quaternion-v valued Q Im mage Patch (llet us call it ) and signals. Quaternion Real Dictionary with Six S Oriented Atoms A (let us call it ) are vectorized into 1-D coolumn vectorrs and standardiized before passing p them on to quaterrnionic basis purrsuit denoisingg: argm min s.t. 11 Here denotes the quaternion coefficients to be optimizedd and denootes the presscribed noise level. The dictiionary with six oriented attoms is consttructed using a set s of binarizeed masks whhich are designned to estimate spatial orientaation of local texture elemeents in unwrappeed and enhancced iris imagees. The compuutation of orientaation featuress from the elements of dicttionary is similarr to as in [13]. The quaternnion coefficiennts can be estimaated by the coonventional convex c optimiization approachhes, similar to t as in [111]. The orienntation estimatioon and respecttive encoding scheme is reppeated thrice too cover all the channeels (RGB) of o the segmenteed/normalizedd iris imagees. The ressulting quaternioonic sparse orientation code c (QSOC C) has template size which is three times as a large as thaat from the orienntation schem me in [9]. Thhe matching scores between the two iris feature templlates R and T, T with their corrresponding maasks AR and AT, can be gennerated similar too as in [13]: , , , ,
∑
∑
, ∑
∑
,
, ,
,
,
,
,
,
(a))
(c)
(d)
Figure 2: Image samples (aa), (c) from UBIRIS F U V2 Irris im mages and corrrespondinglyy iris segmentaation masks (bb), (dd), as generateed in [9], empployed in our experiments. e The automaated segmenttation of iris images wass saame as detailled in [12] foor the UBIRIS S V2 images. F Figure 2 illustrrates the sampple iris/eye imaages from thiss dataset and thheir corresponndingly segm mented results. T size of unw The wrapped iris im mages was 51 12 64 pixels. W employedd leave-one-oout strategy to ascertainn We avverage of the experim mental resultts from thee inndependent test data. T Therefore thhis approachh generated 904 genuine and 136504 impoostor matchingg sccores. The paarameters for the algorithm m, i.e. the linee w width w and mask m size l, werre automaticaally extracted
,
,
(b)
(12)
where is the registtered feature template with the and 2 width andd height expannded to 2 . We partition the templatees into conneccted sub-regioons to generate the best maatching score.. This strateggy has shown to t be succeessful in acccommodatingg the influencee of local im mage variationns by matchinng the corresponnding templatte sub-regionss with small amount of shiftinng and was alsso employed inn this work.
4. Expeeriments an nd Results The hypeercomplex foormulation forr the represenntation and identtification of visible v illuminnation iris imaages is investigaated on publiclly available UBIRIS U V2 daatabase [7]. The imaging distance for UB BIRIS V2 daatabase ranges frrom 4-8 meterrs and we empployed 1000 images from 1711 subjects for the experimeents. This dataset is same as released for tthe NICE II competition c [88]. We employedd 96 images from f the first 19 subjects for f the training. The experimeental results are a illustrated on the
Figure 3: Cuumulative Maatch Characteristics usingg F prroposed and prior p approachhes on UBIRIS S V2 databasee. Figure 3: Cuumulative Maatch Characteristics usingg F Q QSOC and basseline methodss on UBIRIS V2 V database.
62
biometric identification using hypercomplex and sparse representation of normalized biometric images. We develop quanternionic sparse orientation codes (QSOC) that can simultaneously exploit information from multiple channels using widely studied convex optimization strategy. Our experimental results on publicly available visible illumination UBIRIS V2 database have illustrated significant improvement in the performance over the baseline approaches. We have considered three baseline approaches for the comparison, i.e., using 1-D log-Gabor filter, monogenic log-Gabor filter and sparse representation of orientation features in [9]. The experimental results illustrated in this paper suggest superiority of QSOC for the visible illumination iris recognition and also for the corresponding verification problem. The capability to simultaneously exploit the available information from the multiple representations of the same biometric image is the key reason for the achieved performance improvement from this approach. The use of binarized masks as the dictionary of oriented atoms also achieves computational simplicity as it requires simple summation operations (as compared to those using Gabor, sDOG or other spatial filters). The experimental results presented in this paper from the visible illumination database are quite encouraging but require further improvement for any deployment in real applications. The average rank-one recognition accuracy (figure 3) from the iris images in this database is not high but appears to be the best from prior work which have also attempted to exploit discriminating iris information from this database. The current possible estimates for the iris identification accuracy point towards its possible application in image forensics or for the surveillance from at-adistant images when iris matching scores are employed to improve the performance for face or periocular (as in [19]) region based human identification. The key reason for the lower recognition accuracy from iris images can be attributed to the imaging resolution. According to the ISO Standard 19794-6 for iris data [15], the iris diameter should be at least 200 pixels. However, the average iris diameter from UBIRIS V2 database fails to meet such criteria. Our experiments in [9] have estimated that the average iris diameter from this database is 122.48 pixels. The average iris diameter from this database was generated using the ground truth masks employed in earlier study [12]. In our experiments, we did not make any attempt to discriminate or reject iris images based on imaging resolution or quality, primarily to benchmark and ensure repeatability of the experiments. Reference [11] has recently exploited sparse representation of Gabor filter based phase information from multiple iris sectors and presented exciting results but on near
Figure 4: Receiver Operating Characteristics using QSOC and baseline methods on UBIRIS V2 database. from the independent training images (consisting of 96 images from the first 19 subjects) and are detailed in Appendix A. The average cumulative match characteristics from the recognition experiments are shown in figure 3. This figure also illustrates the corresponding performance when monogenic log Gabor [9] and 1-D log Gabor [16] are employed for the verification experiments. The template size for the 1-D log Gabor filters is two bits per pixel while the monogenic (quadrature) log Gabor filters [20] generated template size of three bits per pixel. The matching distance between the binarized iris image template generated from the monogenic log Gabor filter is also computed using normalized Hamming distance (like those for 1-D log Gabor filter based approach). The average rank-one recognition accuracy using QSOC is 48.01% while those using sparse orientation is 36.95%. The experimental results in figure 3 suggest that the visible illumination iris recognition using quaternionic sparse orientation representation can achieve significant improvement (~30%) in the rank-one recognition accuracy as compared to the nearest best performing approach [9]. The receiver operating characteristics from the iris verification experiments are shown in figure 4. This figure also illustrates the corresponding performance using other baseline approaches. The experimental results in this figure suggest that the quaternionic sparse representation of local orientation features generate significant improvement in the performance for the verification experiments similar to those trends observed from the recognition experiments.
5. Conclusions and Further Work This paper has formulated a new approach for the
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representations random projections,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 33, no. 9, pp. 1877-1893, Sep. 2011. [12] C.-W. Tan and A. Kumar, “Automated segmentation of iris images using visible wavelength face images,” Proc. CVPR 2011, pp. 9-14, Colorado Springs, CVPRW'11, June 2011. [13] Y. Zhou and A. Kumar, “Personal identification from iris images using localized Radon transform,” Proc. ICPR 2010, Istanbul, Aug. 2010. [14] U. Park, R. R. Jillela, A. Ross, and A. K. Jain, “Periocular biometrics in the visible spectrum,” IEEE Trans. Info. Forensics & Security, vol. 6, pp. 96–106, 2011. [15] ISO/IEC 19794-6:2005. Information technology -Biometric data interchange formats -- Part 6: Iris image data. [16] L. Masek, MATLAB source code for a biometric identification system based on iris patterns, 2003 http://www.csse.uwa.edu.au/~pk/studentprojects/libor/index. html [17] P. Li, Z. Liu and N. Zhao, “Weighted co-occurrence phase histogram for iris recognition,” Pattern Recognition Letters, pp.1000-1005, vol.33, no. 8, Jun. 2012. [18] M. De Marsico, M. Nappi and D. Riccio, “Noisy iris recognition integration scheme,” Pattern Recognition Letters, pp. 1006-1011, vol. 33, no. 8, Jun. 2012. [19] T. Tan, X. Zhang, Z Sun, and H. Zhang, “Noisy iris image matching by using multiple cues,” Pattern Recognition Letters, pp.970-977, vol. 33, no. 8, Jun. 2012. [20] P. Kovesi, Matching image phase points using monogenic phase data, Available from: http://www.csse.uwa.edu.au/~pk/research/matlabfns/Match/ matchbymonogenicphase.m, 2005.
infrared images/videos. Recent publications [17]-[19] have also explored iris verification on the UBIRIS V2 database. The experimental results presented in this paper from the verification experiments on UBIRIS V2 database compare quite favorably, e.g. with [17] using co-occurrence phase histograms or with [18] using LBP, in terms of complexity or performance. However one to one such comparison may be quite difficult due to lack of details on the training parameters in some of such recent publications. Our experiments in this paper have only presented results from the quaternionic sparse orientation framework, primarily to limit the computations. However the iris recognition using the octonionic representation, which can exploit multi-scale representation of orientation features, similar to as explored in [13], is expected to further improve the performance and this is part of further work. Another promising use of the octonionic representation could simultaneously exploit periocular features, similar to as explored in [19], and is suggested for further work.
6. References [1] Role of biometric technology in Aadhaar enrollments, UID Authority of India, Jan 2012, Accessible from http://uidai.gov.in/images/FrontPageUpdates/role_of_biomet ric_technology_in_aadhaar_jan21_2012.pdf [2] E. van den Berg and M. P. Friedlander, “Theoretical and empirical results for recovery from multiple measurements,” IEEE Trans. Info. Theory, pp. 2516- 2527, vol. 56, 2010. [3] K. W. Bowyer, K. Hollingsworth, and P. Flynn, “Image understanding for iris biometrics: a survey,” Comp. Vision and Image Understanding, vol. 110, pp. 281-307, May 2008 [4] A. Kumar and A. Passi, “Comparison and combination of iris matchers for reliable personal identification,” Pattern Recognition, vol. 43 pp. 1016-1026, Mar. 2010. [5] E. van den Berg and M. P. Friedlander, SPGL1: A solver for large-scale sparse reconstruction, http://www.cs.ubc.ca/labs/scl/spgl1, 2010. [6] E. van den Berg and M. P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM Journal on Scientific Computing, pp. 890-912, vol. 31, no. 2, 2008. [7] H. Proença S. Filipe, R. Santos, J. Oliveira, and L. Alexandre, “The UBIRIS.v2: A database of visible wavelength images captured on the move and at-a-distance,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 32, pp. 1529– 1535, 2010. [8] NICE:II - Noisy Iris Challenge Evaluation, Part II. http://nice2.di.ubi.pt/ [9] A. Kumar, T. S. Chan, and C.-W. Tan, “Human identification from at-a-distance face images using sparse representation of local iris features,” Proc. ICB 2012, New Delhi, April 2012. [10] J. Daugman, “High confidence visual recognition of persons by a test of statistical independence,” IEEE Trans. Patt. Anal. Machine Intell., pp. 1148-1161, Nov. 1993. [11] J. K. Pillai, V. M. Patel, R. Chellappa, and N. K. Ratha, “Secure and robust iris recognition using sparse
Appendix A The parameters for the evaluation of independent test dataset were selected from the training database. The selection of parameters is illustrated in the following where R1RR denotes the average rank-one recognition accuracy, EER denotes average equal error rate from the corresponding (training) dataset. Regularization Training (w =2, l=20)
In order to use the parameters on RGB images, will be scaled by a factor of √3 because the amount of squared noise will be tripled.
Best parameters:
17√3, R1RR = 73.3333%.
Sparse Orientation
The parameter estimation (process/results) for the monogenic log Gabor and 1-D log Gabor filter is same as detailed in [9].
64
Abstract Personal identification from the iris images acquired under less-constrained imaging environment is highly challenging problem but with several important applications in surveillance, image forensics, search for missing children and wandering elderly. In this paper, we develop and formulate a new approach for the iris recognition using hypercomplex (quaternionic or octonionic) and sparse representation of unwrapped iris images. We model iris representation problem as quaternionic sparse coding problem which is solved by convex optimization strategy. This approach essentially exploits the orientation of local iris texture elements which are efficiently extracted using a binarized dictionary of oriented atoms. The feasibility of this approach is evaluated, both for the recognition and the verification problem, on the publicly available visible illumination UBIRIS V2 database. Our experimental results using the proposed formulation illustrate significant improvement in performance (e.g., 30% improvement in rank-one recognition accuracy) over the previously studied sparse representation approach for the visible illumination iris recognition.
2. Hypercomplex Sparse Representation The key objective of our efforts is to combine hypercomplex (quaternionic or octonionic) and sparse representation to achieve more accurate biometric identification. We will prove the equivalence between hypercomplex sparse encoding and mixed 1,2-norm minimization. This equivalence enables us to perform hypercomplex sparse coding using existing software for sparse multiple measurement vector (MMV) problems [2], [5]-[6].
Problem Statement We define quaternionic sparse coding as: , (1) min α subject to Dα x D ,α ,x , and octonionic sparse coding as: min α subject to Dα x , (2) ,α ,x . D We are going to prove that the above are equivalent to: min A , subject to DA X F , ,A ,X (3) D which is an extension of single-measurement sparse recovery to the multiple-measurement case [2], [6]. The notations employed in his paper represent their conventional meaning in the related literature [2], [9]. Here we let r 4 for the equivalent quaternionic formulation and r 8 for its octonionic equivalent.
1. Introduction Iris recognition has emerged as one of the most effective technologies for the large scale human identification [1], [3]. There have been several promising efforts to segment iris images from the visible illumination face images for the personal identification and develop less cooperative alternative for the remote surveillance and forensics applications. Several publications [7], [12] detail alternative algorithms for the challenging visible illumination iris segmentation and also for the recognition [8]-[9], [17][19] from such segmented (noisy) iris images. The recognition of visible illumination iris images poses several challenges. These can be attributed to image quality degradations resulting from shadows, albedo absorption selectivity, varying iris pixel resolution, scattering and varying pigmentation. Therefore further efforts are required to develop robust feature extraction and matching techniques which can accommodate such inherent image variations in the segmented iris images.
978-1-4673-1612-5/12/$31.00 ©2012 IEEE
Quaternionic Representation Let us first prove the equivalence of α and A , . The mixed 1,2-norm is defined as A , ∑ where A denotes the j th row of [2]. A Recall that the norm of a quaternion a a i a j a i a j a k| a a a a a k is |a †
This approach can also be explored to simultaneously exploit multiple iris representations (e.g. [4]) for recognizing conventional iris images acquired under near-infrared illumination.
59
∑ α . If we rewrite the quaternionic entries in α a ,a ,a ,a and that the l -norm of a vector α is α as row vectors in the form a , a , a , a we obtain an isomorphic representation A and the following equivalence is immediately established: ∑ ∑ , 4 We further rewrite the entries of in this isomorphic form yielding and proceed to prove the equivalence of and . By definition we have; ∑ ∑ and . (5) | ∑ | and Moreover the Euclidean and Frobenius norms are defined as ∑
∑
∑
. Thus
and | | we have
|
|
, where ,
,
,
∑
| . Since
| ∑
extract the 1, , ,
parts of
, respectively,
. 6 Putting this back into original equation (1) and observing the relationships between , , , , we can finally write;
. 7
Octonionic Representation A similar argument can be used to prove the octonionic case. We first prove the equivalence of and , . is | The norm of an octonion , , , , , , , and | we again obtain an isomorphic by writing the octonionic elements in as row vectors , , , , , , , representation with the following equivalence: ,
Further let
. 8
be the isomorphic row-vector form of the entries in . The Euclidean and Frobenius norms are ∑
|
| and
∑
60
∑
. Therefore we can further rewrite;
∑ 1,
,
,
,
,
,
|
| ,
parts of
| . As , where , respectively, we obtain; ∑
| ∑
,
,
,
and , ,
| | , ,
extract
the
. 9 Finally, we substitute it back to the original equation (2) and observe the relationship between , , , :
. 10
Figure 1: Block diagram for quaternionic sparse orientation representation using visible illumination iris images.
61
inndependent teest data consiisting of all the t remainingg 904 images froom the 152 subbjects.
3. Quaternionic Sp parse Orien ntation Cod de The blockk diagram forr encoding unw wrapped iris images acquired under visible illuminatioon iris imaging is shown inn figure 1. In thhis diagram, RGB R denotes vector -valued signals and H denotes quaternion-v valued Q Im mage Patch (llet us call it ) and signals. Quaternion Real Dictionary with Six S Oriented Atoms A (let us call it ) are vectorized into 1-D coolumn vectorrs and standardiized before passing p them on to quaterrnionic basis purrsuit denoisingg: argm min s.t. 11 Here denotes the quaternion coefficients to be optimizedd and denootes the presscribed noise level. The dictiionary with six oriented attoms is consttructed using a set s of binarizeed masks whhich are designned to estimate spatial orientaation of local texture elemeents in unwrappeed and enhancced iris imagees. The compuutation of orientaation featuress from the elements of dicttionary is similarr to as in [13]. The quaternnion coefficiennts can be estimaated by the coonventional convex c optimiization approachhes, similar to t as in [111]. The orienntation estimatioon and respecttive encoding scheme is reppeated thrice too cover all the channeels (RGB) of o the segmenteed/normalizedd iris imagees. The ressulting quaternioonic sparse orientation code c (QSOC C) has template size which is three times as a large as thaat from the orienntation schem me in [9]. Thhe matching scores between the two iris feature templlates R and T, T with their corrresponding maasks AR and AT, can be gennerated similar too as in [13]: , , , ,
∑
∑
, ∑
∑
,
, ,
,
,
,
,
,
(a))
(c)
(d)
Figure 2: Image samples (aa), (c) from UBIRIS F U V2 Irris im mages and corrrespondinglyy iris segmentaation masks (bb), (dd), as generateed in [9], empployed in our experiments. e The automaated segmenttation of iris images wass saame as detailled in [12] foor the UBIRIS S V2 images. F Figure 2 illustrrates the sampple iris/eye imaages from thiss dataset and thheir corresponndingly segm mented results. T size of unw The wrapped iris im mages was 51 12 64 pixels. W employedd leave-one-oout strategy to ascertainn We avverage of the experim mental resultts from thee inndependent test data. T Therefore thhis approachh generated 904 genuine and 136504 impoostor matchingg sccores. The paarameters for the algorithm m, i.e. the linee w width w and mask m size l, werre automaticaally extracted
,
,
(b)
(12)
where is the registtered feature template with the and 2 width andd height expannded to 2 . We partition the templatees into conneccted sub-regioons to generate the best maatching score.. This strateggy has shown to t be succeessful in acccommodatingg the influencee of local im mage variationns by matchinng the corresponnding templatte sub-regionss with small amount of shiftinng and was alsso employed inn this work.
4. Expeeriments an nd Results The hypeercomplex foormulation forr the represenntation and identtification of visible v illuminnation iris imaages is investigaated on publiclly available UBIRIS U V2 daatabase [7]. The imaging distance for UB BIRIS V2 daatabase ranges frrom 4-8 meterrs and we empployed 1000 images from 1711 subjects for the experimeents. This dataset is same as released for tthe NICE II competition c [88]. We employedd 96 images from f the first 19 subjects for f the training. The experimeental results are a illustrated on the
Figure 3: Cuumulative Maatch Characteristics usingg F prroposed and prior p approachhes on UBIRIS S V2 databasee. Figure 3: Cuumulative Maatch Characteristics usingg F Q QSOC and basseline methodss on UBIRIS V2 V database.
62
biometric identification using hypercomplex and sparse representation of normalized biometric images. We develop quanternionic sparse orientation codes (QSOC) that can simultaneously exploit information from multiple channels using widely studied convex optimization strategy. Our experimental results on publicly available visible illumination UBIRIS V2 database have illustrated significant improvement in the performance over the baseline approaches. We have considered three baseline approaches for the comparison, i.e., using 1-D log-Gabor filter, monogenic log-Gabor filter and sparse representation of orientation features in [9]. The experimental results illustrated in this paper suggest superiority of QSOC for the visible illumination iris recognition and also for the corresponding verification problem. The capability to simultaneously exploit the available information from the multiple representations of the same biometric image is the key reason for the achieved performance improvement from this approach. The use of binarized masks as the dictionary of oriented atoms also achieves computational simplicity as it requires simple summation operations (as compared to those using Gabor, sDOG or other spatial filters). The experimental results presented in this paper from the visible illumination database are quite encouraging but require further improvement for any deployment in real applications. The average rank-one recognition accuracy (figure 3) from the iris images in this database is not high but appears to be the best from prior work which have also attempted to exploit discriminating iris information from this database. The current possible estimates for the iris identification accuracy point towards its possible application in image forensics or for the surveillance from at-adistant images when iris matching scores are employed to improve the performance for face or periocular (as in [19]) region based human identification. The key reason for the lower recognition accuracy from iris images can be attributed to the imaging resolution. According to the ISO Standard 19794-6 for iris data [15], the iris diameter should be at least 200 pixels. However, the average iris diameter from UBIRIS V2 database fails to meet such criteria. Our experiments in [9] have estimated that the average iris diameter from this database is 122.48 pixels. The average iris diameter from this database was generated using the ground truth masks employed in earlier study [12]. In our experiments, we did not make any attempt to discriminate or reject iris images based on imaging resolution or quality, primarily to benchmark and ensure repeatability of the experiments. Reference [11] has recently exploited sparse representation of Gabor filter based phase information from multiple iris sectors and presented exciting results but on near
Figure 4: Receiver Operating Characteristics using QSOC and baseline methods on UBIRIS V2 database. from the independent training images (consisting of 96 images from the first 19 subjects) and are detailed in Appendix A. The average cumulative match characteristics from the recognition experiments are shown in figure 3. This figure also illustrates the corresponding performance when monogenic log Gabor [9] and 1-D log Gabor [16] are employed for the verification experiments. The template size for the 1-D log Gabor filters is two bits per pixel while the monogenic (quadrature) log Gabor filters [20] generated template size of three bits per pixel. The matching distance between the binarized iris image template generated from the monogenic log Gabor filter is also computed using normalized Hamming distance (like those for 1-D log Gabor filter based approach). The average rank-one recognition accuracy using QSOC is 48.01% while those using sparse orientation is 36.95%. The experimental results in figure 3 suggest that the visible illumination iris recognition using quaternionic sparse orientation representation can achieve significant improvement (~30%) in the rank-one recognition accuracy as compared to the nearest best performing approach [9]. The receiver operating characteristics from the iris verification experiments are shown in figure 4. This figure also illustrates the corresponding performance using other baseline approaches. The experimental results in this figure suggest that the quaternionic sparse representation of local orientation features generate significant improvement in the performance for the verification experiments similar to those trends observed from the recognition experiments.
5. Conclusions and Further Work This paper has formulated a new approach for the
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representations random projections,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 33, no. 9, pp. 1877-1893, Sep. 2011. [12] C.-W. Tan and A. Kumar, “Automated segmentation of iris images using visible wavelength face images,” Proc. CVPR 2011, pp. 9-14, Colorado Springs, CVPRW'11, June 2011. [13] Y. Zhou and A. Kumar, “Personal identification from iris images using localized Radon transform,” Proc. ICPR 2010, Istanbul, Aug. 2010. [14] U. Park, R. R. Jillela, A. Ross, and A. K. Jain, “Periocular biometrics in the visible spectrum,” IEEE Trans. Info. Forensics & Security, vol. 6, pp. 96–106, 2011. [15] ISO/IEC 19794-6:2005. Information technology -Biometric data interchange formats -- Part 6: Iris image data. [16] L. Masek, MATLAB source code for a biometric identification system based on iris patterns, 2003 http://www.csse.uwa.edu.au/~pk/studentprojects/libor/index. html [17] P. Li, Z. Liu and N. Zhao, “Weighted co-occurrence phase histogram for iris recognition,” Pattern Recognition Letters, pp.1000-1005, vol.33, no. 8, Jun. 2012. [18] M. De Marsico, M. Nappi and D. Riccio, “Noisy iris recognition integration scheme,” Pattern Recognition Letters, pp. 1006-1011, vol. 33, no. 8, Jun. 2012. [19] T. Tan, X. Zhang, Z Sun, and H. Zhang, “Noisy iris image matching by using multiple cues,” Pattern Recognition Letters, pp.970-977, vol. 33, no. 8, Jun. 2012. [20] P. Kovesi, Matching image phase points using monogenic phase data, Available from: http://www.csse.uwa.edu.au/~pk/research/matlabfns/Match/ matchbymonogenicphase.m, 2005.
infrared images/videos. Recent publications [17]-[19] have also explored iris verification on the UBIRIS V2 database. The experimental results presented in this paper from the verification experiments on UBIRIS V2 database compare quite favorably, e.g. with [17] using co-occurrence phase histograms or with [18] using LBP, in terms of complexity or performance. However one to one such comparison may be quite difficult due to lack of details on the training parameters in some of such recent publications. Our experiments in this paper have only presented results from the quaternionic sparse orientation framework, primarily to limit the computations. However the iris recognition using the octonionic representation, which can exploit multi-scale representation of orientation features, similar to as explored in [13], is expected to further improve the performance and this is part of further work. Another promising use of the octonionic representation could simultaneously exploit periocular features, similar to as explored in [19], and is suggested for further work.
6. References [1] Role of biometric technology in Aadhaar enrollments, UID Authority of India, Jan 2012, Accessible from http://uidai.gov.in/images/FrontPageUpdates/role_of_biomet ric_technology_in_aadhaar_jan21_2012.pdf [2] E. van den Berg and M. P. Friedlander, “Theoretical and empirical results for recovery from multiple measurements,” IEEE Trans. Info. Theory, pp. 2516- 2527, vol. 56, 2010. [3] K. W. Bowyer, K. Hollingsworth, and P. Flynn, “Image understanding for iris biometrics: a survey,” Comp. Vision and Image Understanding, vol. 110, pp. 281-307, May 2008 [4] A. Kumar and A. Passi, “Comparison and combination of iris matchers for reliable personal identification,” Pattern Recognition, vol. 43 pp. 1016-1026, Mar. 2010. [5] E. van den Berg and M. P. Friedlander, SPGL1: A solver for large-scale sparse reconstruction, http://www.cs.ubc.ca/labs/scl/spgl1, 2010. [6] E. van den Berg and M. P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM Journal on Scientific Computing, pp. 890-912, vol. 31, no. 2, 2008. [7] H. Proença S. Filipe, R. Santos, J. Oliveira, and L. Alexandre, “The UBIRIS.v2: A database of visible wavelength images captured on the move and at-a-distance,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 32, pp. 1529– 1535, 2010. [8] NICE:II - Noisy Iris Challenge Evaluation, Part II. http://nice2.di.ubi.pt/ [9] A. Kumar, T. S. Chan, and C.-W. Tan, “Human identification from at-a-distance face images using sparse representation of local iris features,” Proc. ICB 2012, New Delhi, April 2012. [10] J. Daugman, “High confidence visual recognition of persons by a test of statistical independence,” IEEE Trans. Patt. Anal. Machine Intell., pp. 1148-1161, Nov. 1993. [11] J. K. Pillai, V. M. Patel, R. Chellappa, and N. K. Ratha, “Secure and robust iris recognition using sparse
Appendix A The parameters for the evaluation of independent test dataset were selected from the training database. The selection of parameters is illustrated in the following where R1RR denotes the average rank-one recognition accuracy, EER denotes average equal error rate from the corresponding (training) dataset. Regularization Training (w =2, l=20)
In order to use the parameters on RGB images, will be scaled by a factor of √3 because the amount of squared noise will be tripled.
Best parameters:
17√3, R1RR = 73.3333%.
Sparse Orientation
The parameter estimation (process/results) for the monogenic log Gabor and 1-D log Gabor filter is same as detailed in [9].
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