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Face Recognition Using Multiresolution Hybrid Kekre-DCT Wavelet Transform Features with Multiclass ECOC Framework
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ScienceDirect Procedia Computer Science 00 000–000 Procedia Computer Science 132 (2018) 1781–1787 Procedia Computer Science 00 (2018) (2018) 000–000
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International International Conference Conference on on Computational Computational Intelligence Intelligence and and Data Data Science Science (ICCIDS (ICCIDS 2018) 2018)
Face Recognition Using Multiresolution Hybrid Kekre-DCT Wavelet Transform Features with Multiclass ECOC Framework a b Alpa Alpa Choudhary Choudharya ,, Rekha Rekha Vig Vigb a Research Scholar, The NorthCap University, Gurugram and 122017, India a Research Scholar, The NorthCap University, Gurugram and 122017, India b Associate Professor,The NorthCap University, Gurugram and 122017, India b Associate Professor,The NorthCap University, Gurugram and 122017, India
Abstract Abstract Error Error Correcting Correcting Output Output Codes Codes (ECOC) (ECOC) framework framework is is efficient efficient approach approach for for multiclass multiclass classification classification problems problems by by reducing reducing them them to to binary classifiers.In this paper Face recognition system is implemented by extracting features using novel multiresolution binary classifiers.In this paper Face recognition system is implemented by extracting features using novel multiresolution hybrid hybrid wavelet wavelet transform transform approach.This approach.This approach approach combines combines two two orthogonal orthogonal transform transform like like Kekre Kekre and and DCT DCT transform transform using using Kronceker Kronceker product product to to generate generate hybrid hybrid wavelet wavelet transform transform which which gives gives different different levels levels of of resolution.The resolution.The generated generated transform transform also also uses uses energy energy compaction compaction technique technique to to obtain obtain dimensionality dimensionality reduction. reduction. The The extracted extracted features features are are then then passed passed for for classification classification via via ECOC ECOC approach approach where where binary binary classifiers classifiers are are coded coded using using Sparse Sparse random random coding coding design design and and decoded decoded using using Hamming Hamming distance.The distance.The final final model predicts predicts the the class class labels.The labels.The best best accuracy accuracy of of 99.67% 99.67% is is obtained obtained at at 99% 99% of of energy energy threshold. threshold. model
© 2018 The Authors. Published by Elsevier Ltd. 2018 The The Authors. Authors. Published Published by by Elsevier Elsevier B.V. B.V. cc 2018 This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the scientific committee of of the the International International Conference Conference on on Computational Computational Intelligence Intelligence and and Peer-review under responsibility of the scientific committee Data Science Science (ICCIDS (ICCIDS 2018). 2018). Data Keywords: Face Keywords: Face Recognition; Recognition; Multiclass Multiclass Classification;ECOC;orthogonal Classification;ECOC;orthogonal transform;wavelet transform;wavelet transform;energy transform;energy compaction compaction
1. 1. Introduction Introduction Face Face recognition recognition is is one one of of the the most most efficient efficient and and widely widely used used biometric biometric modality modality in in today’s today’s scenario.Different scenario.Different algorithms have been proposed for implementing face recognition system. The most widely algorithms have been proposed for implementing face recognition system. The most widely used used algorithm algorithm like like PrinPrincipal Component Analysis(PCA),Linear Discriminant Analysis(LDA) uses dimensionality reduction to achieve cipal Component Analysis(PCA),Linear Discriminant Analysis(LDA) uses dimensionality reduction to achieve high high dimensional dimensional data data classification classification [1]. [1]. Face Face recognition recognition system system also also uses uses transform transform domain domain techniques techniques to to achieve achieve challenges challenges like like illumination illumination compensacompensation and normalisation.Discrete Cosine transform(DCT) minimizes illumination variations and tion and normalisation.Discrete Cosine transform(DCT) minimizes illumination variations and is is robust robust and and can can be be implemented in real time[2]. High speed face recognition can be implemented combining DCT and Fisher implemented in real time[2]. High speed face recognition can be implemented combining DCT and Fisher Linear Linear Discriminant(FLD) Discriminant(FLD) and and Radial Radial Basis Basis Function(RBF) Function(RBF) neural neural networks.The networks.The proposed proposed system system achieves achieves excellent excellent perforperformance with training and high speed recognition, high recognition rates and illumination challenges[3]. mance with training and high speed recognition, high recognition rates and illumination challenges[3]. 3D 3D Discrete Discrete E-mail E-mail address: address: [email protected] [email protected]
1877-0509 © 2018 The TheAuthors. Authors.Published Published by Elsevier 1877-0509 2018 by Elsevier Elsevier B.V.Ltd. cc 2018 1877-0509 The article Authors. Published by B.V. This is an open access under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the scientific committee of the the International International Conference on on Computational Computational Intelligence Intelligence and and Data Data Science Science Peer-review under the scientific scientific committee committee of of Peer-review under responsibility responsibility of the the International Conference on Computational and Data (ICCIDS 2018). (ICCIDS 2018). (ICCIDS 2018). 10.1016/j.procs.2018.05.153
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Wavelet Transform(DWT) is employed for feature extraction of hyper-spectral facial analysis and achieved accuracy proves that 3D DWT method is superior to spatio-spectral classification[4].Other formal algorithms for feature extraction with multivariate statistical techniques in complex domain are fused with deep learning and results show advancement as compared to state of art methods in computer vision and pattern recognition[5]. Face recognition system is considered as a multicalss problem with supervised machine leraning problem.Error Correcting output Codes(ECOC) is a multiclass classification technique which reduces the N class problem to binary classification problem.ECOC approach has been applied in various pattern recognition applications like text recognition,traffic sign recognition, medical applications,[6],[7],[8].Supervised learning algorithms are based on labeled data samples.The survey on multiclass classification states different algorithms can be used like Neural networks,Decision trees,k- nearest neighbours, Naive Bayes , Support Vector Machines(SVM),Decomposing into binary classes: One vs One(OVO),All vs All(AVA), ECOC etc.[9].ECOC approach when compared to other classification techniques show better performance and provide reliable probability estimates and improve the perfomance on multiclass problems [10]. Different coding and decoding strategies can improve the classification using ECOC approach and experiments based on six decoding strategies show that code length also effects the performance of classification[11]. The rest of the paper is organised as follows : Section 2 descibes the generation of multiresolution hybrid wavelet transform method. Section 3 explains the concept of ECOC framework.In Section 4 implementation of propsed system model is explained. Section 5 demonstrates experiments and results performed on face recognition database. Section 6 gives the conclusion and future work for the research done. 2. Multiresolution Hybrid Kekre-DCT wavelet Transform T K D Multiresolution hybrid wavelet transform is used in feature extraction process from facial images.Two orthogonal transform Kekre transform and DCT transform are combined using Kronecker product.The basic equation of generating transform is given as: T KD = K ⊗ D
(1)
where K represents Kekre transform of size r*r and D represents DCT transform with size c*c. The size of generated transform T KD is rc*rc.Let s0 , s1 , s2 .. sn−1 be divisors of r (i.e. if r = 64 the s0 , s1 , s2 , s3 , s4 will be 2,4,8,16,32 respectively) arranged in ascending order, then T KD will be: Kr ⊗ D s(0: j1) I ⊗ (K ⊗ D ) c( j1 +1: j2 ) s0 r/s0 I s1 ⊗ (Kr/s1 ⊗ Dc( j2 +1: j3 ) ) . T KD = (2) . . . I ⊗ (K ⊗ D ) sn−1 r/sn−1 c( jn−2 +1: jn−1 ) Ir ⊗ Dc( jn−1 :c)
where Dc( j:k) represents rows k to j of D matrix of size c and Kr/s represents matrix K of size r/s. As shown in equation 2 matrix K of size r and its lower order matrices of size r/s0 , r/s1 .. r/sn−1 are multiplied with certain rows of D transform matrix using Kronecker product.The properties of the T KD transform will depend on principal components used.The generated hybrid wavelet transform will have properties similar to transform applied for image analysis and image compression using energy comapction technique by calculating low energy, medium energy and high energy coefficients [12].The generated transform generates three levels of resolution : low resolution, medium resolution, high resolution. The low frequency components can be discarded to achieve the dimensionality reduction. 3. ECOC framework The Error Correcting Output codes(ECOC) model is created for classification of multiclass problems. The ECOC apporach works in two phases:
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• Coding • Decoding 3.1. Coding In coding stage the multiclass problems are reduced to binary class problems.The binary classifiers are also called as learners or dichotomizers [13].The codeword are created for each binary learner which separates the samples of each class from other class.The ECOC coding matrix is generated where each column represents the dichotomizer and row represents respective class with two values+1,-1. For example for 4 class problem if number of binary classifiers created are 6 the ECOC matrix will be of size 4*6 and can be as shown: 1 −1 −1 1 −1 1 −1 −1 −1 −1 1 −1 (3) E KD = 1 1 −1 −1 1 −1 −1 1 1 −1 −1 1
As shown in eq.3 rows represent 4 classes and coulmns represent classifier.The first classifier separates class 1 and class 3 as positive class whereas class 2 and class 4 as negative class and similarly other classifiers differentiates between classes.There are four different coding techniques: • One vs one(OVO) : In one vs one coding technique, binary learner separates one class as positive and other class as negative.The number of binary learners is euivalent to N(N − 1)/2, where N is total number of classes. • One vs All(OVA) : In this technique binary learners are coded with one class as positive and rest classes are negative.The number of binary learners is equal to N(total number of classes). • Sparse random coding : In this coding binary learners are assigned with positive and negative values with 0.25 probability and binary learners is equal to 15log2 N. • Dense Random coding : In this coding binary learners are assigned into positive and negative classes with atleast one type and binary learners is 10log2 N
3.2. Decoding In Decoding phase the codeword is decoded and distance strategies can be applied like Hamming distance, Euclidean distance is calculated for each class. The new test sample is coded and compared to each class, and is matched to class with minimum distance calculated.The distance approaches can be described as: 3.2.1. Hamming Distance The Hamming distance between test sample(n) and codeword(c-i) for ith class is given as: N Ham(n, ci ) = Σk=1 [(1 − sign(n, ci (k)]/2
3.2.2. Euclidean Distance The Euclidean distance between test sample(n) and codeword(c-i) for ith class is given as: N E(n, ci ) = Σk=1 (x(k) − yi (k))2
(4)
(5)
The minimum distance is considered as the best match to the test sample. 4. System Model
To implement face recognition system using multiresolution hybrid wavelet features with multiclass ECOC classification , supervised learning technique is used.In supervised learning labeled classes are used.The database is divided into training and test sample and classes are labeled.The known labels and known features are combined to generate
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ECOC model.In this model facial images from faces94 database is used with 51 classes represented as N1 to N51 .The 51 subjects includes male and female with 20 samples each.The database is partitioned into two parts : • Genuine users(NT rain ) : The genuine users consists of 51 classes labeled from N1 to N51 with 14 samples(n1 to n14 ).These genuine users are used for training hence they can be represented under NT rain .The size of each image is 180 by 200 pixel. • Test users(NT est ) : The test users consists of remaining 6 samples(n15 to n20 ) of 51 classes and they are used as test subjects for matching with trained samples and size of each image being 180 by 200 pixels. The new test sample is compared with trained ECOC model to generate predicted labels.The system works in two phases training phase and prediction phase which can be described as follows: 4.1. Training Phase In training phase the features are extracted to create a feature vector and pass these features with known labels to create ECOC model.The features are extracted based on Kronecker product of Kekre and DCT transform as explained in section 2.Since images in Ntrain , NT est are 180 by 200.Two transforms are generated based on size of row and column of image. The row size being 180 will give factors (45*4) so less components will be generated so it is rescaled to 192(32,16,8,4,2) and similarly column to 224.Row transform(R192∗192 ) and column transform(C224∗224 ) is given as: K32 ⊗ D6(1,:) I ⊗ (K ⊗ D ) 16 6(2,:) 2 I4 ⊗ (K8 ⊗ D6(3,:) ) R(192∗192) = (6) I8 ⊗ (K4 ⊗ D6(4,:) ) I ⊗ (K ⊗ D ) 2 6(5,:) 16 I32 ⊗ D6(6,:) and column transform is given as : K32 ⊗ D7(1,:) I ⊗ (K ⊗ D ) 16 7(2,:) 2 I4 ⊗ (K8 ⊗ D7(3,:) ) C(224∗224) = I8 ⊗ (K4 ⊗ D7(4,:) ) I ⊗ (K ⊗ D ) 2 7(5,:) 16 I32 ⊗ K7(6:7,:)
(7)
The samples under NT rain , NT est are first transformed using eq.6 and eq.7 and are transformed. The transformed images are used to compute energy coefficients by deriving the properties for generated transform as explained in section 2 and energy map is created,standard deviation of 4*4 energy block is computed to give feature vector map and hence feature vector of row and dimemsions of original image are reduced to 48*56.The feature vector for training images are created by reshaping feature vector of each image to row.Since there are 714 images in NT rain Feature Vector Train (FVT rain ) will be of size 714*2688(48*56).The block diagram of training phase is given in Fig. 1. As shown samples of classes N1 to N51 are resized to 192*224 and transformed to give images T I1 to T I51 .Reshaped feature vector is created from feature vector of each image.This feature vector is combined with known labels to create a trained classification ECOC model which is passed for prediction of test samples.The ECOC model uses dense random coding design to create ECOC model 4.2. Prediction Phase In prediction phase test sample will be first transformed to create feature vector for test image.Since NT est contains 306 images the size of Test Feature vector will be 306*2688.This feature vector is compared with stored ECOC model
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Fig. 1. (a) Block Diagram of ECOC modelling.
Fig. 2. (a)Block Diagram of Prediction Phase
created during training phase.The code word’s created during coding phase are decoded using Hamming distance approach.The class having minimum Hamming distance is classified label for test sample, for example see Fig 2.
5. Experiments and Results The accuracy of the system was calculated using T KD transform.The correct classifications were observed by changing the energy threshold value.The energy threshold was varied between 80 to 99 % and best classification accuracy was attained at 99.35% energy threshold and accuracy obtained was 99.67%. The system calculated Accuracy at different values of energy threshold as shown in Table 1,and the plot of energy threshold vs Accuracy can be as shown in Fig 3.
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Table 1. Accuracy at different values of Energy Threshold .
S.No
Energy Threshold
Accuracy
1 2 3 4 5 6 7 8 9 10
90 91 92 93 94 95 96 97 98 99
95.1% 95.4% 96.3% 96.83% 97.01% 97.2% 98.3% 98.7% 99.01% 99.67%
Fig. 3. (a)Energy Threshold vs Accuracy curve
6. Conclusion and Future Work Face recognition is widely incorporated bio metric modality and used in daily scenarios.In this paper face recognition system is implemented using novel Multiresolution Hybrid Kekre-DCT Wavelet transform.The novel algorihtm is used to generate feature vector for samples of train and test images using energy compaction technique to achieve dimensionality reduction.The feature vector and known labels are trained using dense random coding technique to generate Classifiaction ECOC model which is further used to predict test labels and posterior probabilities.The system accuracy for the proposed algorithm is 99.67%.The future scope of this research is to check the system for different challenges of face recognition and other different orthogonal transforms can be combined to test the system with increase in number of classes.
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References [1] Yu, Hua and Yang, Jie. (2001) “A direct LDA algorithm for high-dimensional datawith application to face recognition.” Pattern recognition 34 (10): 2067–2070. [2] Chen, Weilong and Er, Meng Joo and Wu, Shiqian. (2006) “Illumination compensation and normalization for robust face recognition using discrete cosine transform in logarithm domain” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 36 (2): 458–466. [3] Er, Meng Joo and Chen, Weilong and Wu, Shiqian (2005) “High-speed face recognition based on discrete cosine transform and RBF neural networks” IEEE Transactions on neural networks 16 (3): 679–691. [4] Ghasemzadeh, Aman and Demirel, Hasan (2017) “3D discrete wavelet transform-based feature extraction for hyperspectral face recognition” IET Biometrics7 (1): 49–55 [5] Tripathi, BK (2017) “On the complex domain deep machine learning for face recognition” Applied Intelligence 47(2):382–396. [6] Rennie, Jason DM. (2001) “Improving multi-class text classification with naive Bayes” [7] Bar´o, Xavier and Escalera, Sergio and Vitri`a, Jordi and Pujol, Oriol and Radeva, Petia. (2009) “Traffic sign recognition using evolutionary adaboost detection and forest-ECOC classification” IEEE Transactions on Intelligent Transportation Systems 10 (1): 113–126. [8] Li, Tao and Zhang, Chengliang and Ogihara, Mitsunori. (2004) “A comparative study of feature selection and multiclass classification methods for tissue classification based on gene expression.” Bioinformatics 20 (15): 2429–2437. [9] Aly, Mohamed.(2005)“Survey on multiclass classification methods”.Neural Netw (19):1–9. [10] Dietterich, Thomas G and Bakiri, Ghulum.(1995)“Solving multiclass learning problems via error-correcting output codes”.Journal of artificial intelligence research.2263–286. [11] Windeatt, Terry and Ghaderi, Reza.(2003).“Coding and decoding strategies for multi-class learning problems”.Information Fusion.411–21. [12] Kekre, Hemant B and Sarode, Tanuja K and Vig, Rekha.(2015)“A new multi-resolution hybrid wavelet for analysis and image compression”.International Journal of Electronics.1022108–2126 [13] Eghbali, Niloufar and Montazer, Gholam Ali.(2017)“Improving multiclass classification using neighborhood search in error correcting output codes”.Pattern Recognition Letters.10074–82
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ScienceDirect Procedia Computer Science 00 000–000 Procedia Computer Science 132 (2018) 1781–1787 Procedia Computer Science 00 (2018) (2018) 000–000
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
International International Conference Conference on on Computational Computational Intelligence Intelligence and and Data Data Science Science (ICCIDS (ICCIDS 2018) 2018)
Face Recognition Using Multiresolution Hybrid Kekre-DCT Wavelet Transform Features with Multiclass ECOC Framework a b Alpa Alpa Choudhary Choudharya ,, Rekha Rekha Vig Vigb a Research Scholar, The NorthCap University, Gurugram and 122017, India a Research Scholar, The NorthCap University, Gurugram and 122017, India b Associate Professor,The NorthCap University, Gurugram and 122017, India b Associate Professor,The NorthCap University, Gurugram and 122017, India
Abstract Abstract Error Error Correcting Correcting Output Output Codes Codes (ECOC) (ECOC) framework framework is is efficient efficient approach approach for for multiclass multiclass classification classification problems problems by by reducing reducing them them to to binary classifiers.In this paper Face recognition system is implemented by extracting features using novel multiresolution binary classifiers.In this paper Face recognition system is implemented by extracting features using novel multiresolution hybrid hybrid wavelet wavelet transform transform approach.This approach.This approach approach combines combines two two orthogonal orthogonal transform transform like like Kekre Kekre and and DCT DCT transform transform using using Kronceker Kronceker product product to to generate generate hybrid hybrid wavelet wavelet transform transform which which gives gives different different levels levels of of resolution.The resolution.The generated generated transform transform also also uses uses energy energy compaction compaction technique technique to to obtain obtain dimensionality dimensionality reduction. reduction. The The extracted extracted features features are are then then passed passed for for classification classification via via ECOC ECOC approach approach where where binary binary classifiers classifiers are are coded coded using using Sparse Sparse random random coding coding design design and and decoded decoded using using Hamming Hamming distance.The distance.The final final model predicts predicts the the class class labels.The labels.The best best accuracy accuracy of of 99.67% 99.67% is is obtained obtained at at 99% 99% of of energy energy threshold. threshold. model
© 2018 The Authors. Published by Elsevier Ltd. 2018 The The Authors. Authors. Published Published by by Elsevier Elsevier B.V. B.V. cc 2018 This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the scientific committee of of the the International International Conference Conference on on Computational Computational Intelligence Intelligence and and Peer-review under responsibility of the scientific committee Data Science Science (ICCIDS (ICCIDS 2018). 2018). Data Keywords: Face Keywords: Face Recognition; Recognition; Multiclass Multiclass Classification;ECOC;orthogonal Classification;ECOC;orthogonal transform;wavelet transform;wavelet transform;energy transform;energy compaction compaction
1. 1. Introduction Introduction Face Face recognition recognition is is one one of of the the most most efficient efficient and and widely widely used used biometric biometric modality modality in in today’s today’s scenario.Different scenario.Different algorithms have been proposed for implementing face recognition system. The most widely algorithms have been proposed for implementing face recognition system. The most widely used used algorithm algorithm like like PrinPrincipal Component Analysis(PCA),Linear Discriminant Analysis(LDA) uses dimensionality reduction to achieve cipal Component Analysis(PCA),Linear Discriminant Analysis(LDA) uses dimensionality reduction to achieve high high dimensional dimensional data data classification classification [1]. [1]. Face Face recognition recognition system system also also uses uses transform transform domain domain techniques techniques to to achieve achieve challenges challenges like like illumination illumination compensacompensation and normalisation.Discrete Cosine transform(DCT) minimizes illumination variations and tion and normalisation.Discrete Cosine transform(DCT) minimizes illumination variations and is is robust robust and and can can be be implemented in real time[2]. High speed face recognition can be implemented combining DCT and Fisher implemented in real time[2]. High speed face recognition can be implemented combining DCT and Fisher Linear Linear Discriminant(FLD) Discriminant(FLD) and and Radial Radial Basis Basis Function(RBF) Function(RBF) neural neural networks.The networks.The proposed proposed system system achieves achieves excellent excellent perforperformance with training and high speed recognition, high recognition rates and illumination challenges[3]. mance with training and high speed recognition, high recognition rates and illumination challenges[3]. 3D 3D Discrete Discrete E-mail E-mail address: address: [email protected] [email protected]
1877-0509 © 2018 The TheAuthors. Authors.Published Published by Elsevier 1877-0509 2018 by Elsevier Elsevier B.V.Ltd. cc 2018 1877-0509 The article Authors. Published by B.V. This is an open access under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the scientific committee of the the International International Conference on on Computational Computational Intelligence Intelligence and and Data Data Science Science Peer-review under the scientific scientific committee committee of of Peer-review under responsibility responsibility of the the International Conference on Computational and Data (ICCIDS 2018). (ICCIDS 2018). (ICCIDS 2018). 10.1016/j.procs.2018.05.153
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Wavelet Transform(DWT) is employed for feature extraction of hyper-spectral facial analysis and achieved accuracy proves that 3D DWT method is superior to spatio-spectral classification[4].Other formal algorithms for feature extraction with multivariate statistical techniques in complex domain are fused with deep learning and results show advancement as compared to state of art methods in computer vision and pattern recognition[5]. Face recognition system is considered as a multicalss problem with supervised machine leraning problem.Error Correcting output Codes(ECOC) is a multiclass classification technique which reduces the N class problem to binary classification problem.ECOC approach has been applied in various pattern recognition applications like text recognition,traffic sign recognition, medical applications,[6],[7],[8].Supervised learning algorithms are based on labeled data samples.The survey on multiclass classification states different algorithms can be used like Neural networks,Decision trees,k- nearest neighbours, Naive Bayes , Support Vector Machines(SVM),Decomposing into binary classes: One vs One(OVO),All vs All(AVA), ECOC etc.[9].ECOC approach when compared to other classification techniques show better performance and provide reliable probability estimates and improve the perfomance on multiclass problems [10]. Different coding and decoding strategies can improve the classification using ECOC approach and experiments based on six decoding strategies show that code length also effects the performance of classification[11]. The rest of the paper is organised as follows : Section 2 descibes the generation of multiresolution hybrid wavelet transform method. Section 3 explains the concept of ECOC framework.In Section 4 implementation of propsed system model is explained. Section 5 demonstrates experiments and results performed on face recognition database. Section 6 gives the conclusion and future work for the research done. 2. Multiresolution Hybrid Kekre-DCT wavelet Transform T K D Multiresolution hybrid wavelet transform is used in feature extraction process from facial images.Two orthogonal transform Kekre transform and DCT transform are combined using Kronecker product.The basic equation of generating transform is given as: T KD = K ⊗ D
(1)
where K represents Kekre transform of size r*r and D represents DCT transform with size c*c. The size of generated transform T KD is rc*rc.Let s0 , s1 , s2 .. sn−1 be divisors of r (i.e. if r = 64 the s0 , s1 , s2 , s3 , s4 will be 2,4,8,16,32 respectively) arranged in ascending order, then T KD will be: Kr ⊗ D s(0: j1) I ⊗ (K ⊗ D ) c( j1 +1: j2 ) s0 r/s0 I s1 ⊗ (Kr/s1 ⊗ Dc( j2 +1: j3 ) ) . T KD = (2) . . . I ⊗ (K ⊗ D ) sn−1 r/sn−1 c( jn−2 +1: jn−1 ) Ir ⊗ Dc( jn−1 :c)
where Dc( j:k) represents rows k to j of D matrix of size c and Kr/s represents matrix K of size r/s. As shown in equation 2 matrix K of size r and its lower order matrices of size r/s0 , r/s1 .. r/sn−1 are multiplied with certain rows of D transform matrix using Kronecker product.The properties of the T KD transform will depend on principal components used.The generated hybrid wavelet transform will have properties similar to transform applied for image analysis and image compression using energy comapction technique by calculating low energy, medium energy and high energy coefficients [12].The generated transform generates three levels of resolution : low resolution, medium resolution, high resolution. The low frequency components can be discarded to achieve the dimensionality reduction. 3. ECOC framework The Error Correcting Output codes(ECOC) model is created for classification of multiclass problems. The ECOC apporach works in two phases:
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• Coding • Decoding 3.1. Coding In coding stage the multiclass problems are reduced to binary class problems.The binary classifiers are also called as learners or dichotomizers [13].The codeword are created for each binary learner which separates the samples of each class from other class.The ECOC coding matrix is generated where each column represents the dichotomizer and row represents respective class with two values+1,-1. For example for 4 class problem if number of binary classifiers created are 6 the ECOC matrix will be of size 4*6 and can be as shown: 1 −1 −1 1 −1 1 −1 −1 −1 −1 1 −1 (3) E KD = 1 1 −1 −1 1 −1 −1 1 1 −1 −1 1
As shown in eq.3 rows represent 4 classes and coulmns represent classifier.The first classifier separates class 1 and class 3 as positive class whereas class 2 and class 4 as negative class and similarly other classifiers differentiates between classes.There are four different coding techniques: • One vs one(OVO) : In one vs one coding technique, binary learner separates one class as positive and other class as negative.The number of binary learners is euivalent to N(N − 1)/2, where N is total number of classes. • One vs All(OVA) : In this technique binary learners are coded with one class as positive and rest classes are negative.The number of binary learners is equal to N(total number of classes). • Sparse random coding : In this coding binary learners are assigned with positive and negative values with 0.25 probability and binary learners is equal to 15log2 N. • Dense Random coding : In this coding binary learners are assigned into positive and negative classes with atleast one type and binary learners is 10log2 N
3.2. Decoding In Decoding phase the codeword is decoded and distance strategies can be applied like Hamming distance, Euclidean distance is calculated for each class. The new test sample is coded and compared to each class, and is matched to class with minimum distance calculated.The distance approaches can be described as: 3.2.1. Hamming Distance The Hamming distance between test sample(n) and codeword(c-i) for ith class is given as: N Ham(n, ci ) = Σk=1 [(1 − sign(n, ci (k)]/2
3.2.2. Euclidean Distance The Euclidean distance between test sample(n) and codeword(c-i) for ith class is given as: N E(n, ci ) = Σk=1 (x(k) − yi (k))2
(4)
(5)
The minimum distance is considered as the best match to the test sample. 4. System Model
To implement face recognition system using multiresolution hybrid wavelet features with multiclass ECOC classification , supervised learning technique is used.In supervised learning labeled classes are used.The database is divided into training and test sample and classes are labeled.The known labels and known features are combined to generate
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ECOC model.In this model facial images from faces94 database is used with 51 classes represented as N1 to N51 .The 51 subjects includes male and female with 20 samples each.The database is partitioned into two parts : • Genuine users(NT rain ) : The genuine users consists of 51 classes labeled from N1 to N51 with 14 samples(n1 to n14 ).These genuine users are used for training hence they can be represented under NT rain .The size of each image is 180 by 200 pixel. • Test users(NT est ) : The test users consists of remaining 6 samples(n15 to n20 ) of 51 classes and they are used as test subjects for matching with trained samples and size of each image being 180 by 200 pixels. The new test sample is compared with trained ECOC model to generate predicted labels.The system works in two phases training phase and prediction phase which can be described as follows: 4.1. Training Phase In training phase the features are extracted to create a feature vector and pass these features with known labels to create ECOC model.The features are extracted based on Kronecker product of Kekre and DCT transform as explained in section 2.Since images in Ntrain , NT est are 180 by 200.Two transforms are generated based on size of row and column of image. The row size being 180 will give factors (45*4) so less components will be generated so it is rescaled to 192(32,16,8,4,2) and similarly column to 224.Row transform(R192∗192 ) and column transform(C224∗224 ) is given as: K32 ⊗ D6(1,:) I ⊗ (K ⊗ D ) 16 6(2,:) 2 I4 ⊗ (K8 ⊗ D6(3,:) ) R(192∗192) = (6) I8 ⊗ (K4 ⊗ D6(4,:) ) I ⊗ (K ⊗ D ) 2 6(5,:) 16 I32 ⊗ D6(6,:) and column transform is given as : K32 ⊗ D7(1,:) I ⊗ (K ⊗ D ) 16 7(2,:) 2 I4 ⊗ (K8 ⊗ D7(3,:) ) C(224∗224) = I8 ⊗ (K4 ⊗ D7(4,:) ) I ⊗ (K ⊗ D ) 2 7(5,:) 16 I32 ⊗ K7(6:7,:)
(7)
The samples under NT rain , NT est are first transformed using eq.6 and eq.7 and are transformed. The transformed images are used to compute energy coefficients by deriving the properties for generated transform as explained in section 2 and energy map is created,standard deviation of 4*4 energy block is computed to give feature vector map and hence feature vector of row and dimemsions of original image are reduced to 48*56.The feature vector for training images are created by reshaping feature vector of each image to row.Since there are 714 images in NT rain Feature Vector Train (FVT rain ) will be of size 714*2688(48*56).The block diagram of training phase is given in Fig. 1. As shown samples of classes N1 to N51 are resized to 192*224 and transformed to give images T I1 to T I51 .Reshaped feature vector is created from feature vector of each image.This feature vector is combined with known labels to create a trained classification ECOC model which is passed for prediction of test samples.The ECOC model uses dense random coding design to create ECOC model 4.2. Prediction Phase In prediction phase test sample will be first transformed to create feature vector for test image.Since NT est contains 306 images the size of Test Feature vector will be 306*2688.This feature vector is compared with stored ECOC model
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Fig. 1. (a) Block Diagram of ECOC modelling.
Fig. 2. (a)Block Diagram of Prediction Phase
created during training phase.The code word’s created during coding phase are decoded using Hamming distance approach.The class having minimum Hamming distance is classified label for test sample, for example see Fig 2.
5. Experiments and Results The accuracy of the system was calculated using T KD transform.The correct classifications were observed by changing the energy threshold value.The energy threshold was varied between 80 to 99 % and best classification accuracy was attained at 99.35% energy threshold and accuracy obtained was 99.67%. The system calculated Accuracy at different values of energy threshold as shown in Table 1,and the plot of energy threshold vs Accuracy can be as shown in Fig 3.
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Table 1. Accuracy at different values of Energy Threshold .
S.No
Energy Threshold
Accuracy
1 2 3 4 5 6 7 8 9 10
90 91 92 93 94 95 96 97 98 99
95.1% 95.4% 96.3% 96.83% 97.01% 97.2% 98.3% 98.7% 99.01% 99.67%
Fig. 3. (a)Energy Threshold vs Accuracy curve
6. Conclusion and Future Work Face recognition is widely incorporated bio metric modality and used in daily scenarios.In this paper face recognition system is implemented using novel Multiresolution Hybrid Kekre-DCT Wavelet transform.The novel algorihtm is used to generate feature vector for samples of train and test images using energy compaction technique to achieve dimensionality reduction.The feature vector and known labels are trained using dense random coding technique to generate Classifiaction ECOC model which is further used to predict test labels and posterior probabilities.The system accuracy for the proposed algorithm is 99.67%.The future scope of this research is to check the system for different challenges of face recognition and other different orthogonal transforms can be combined to test the system with increase in number of classes.
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