In this paper a new approach for image feature extraction is presented. We used the Compressive Sensing (CS) concept to generate the measurement matrix. The new measurement matrix is different from the measurement matrices in literature as it was constructed using both zero mean and nonzero mean rows. The image is simply projected into a new space using the measurement matrix to obtain the feature vector. Another proposed measurement matrix is a random matrix constructed from binary entries. Face recognition problem was used as an example for testing the feature extraction capability of the proposed matrices. Experiments were carried out using two well-known face databases, namely, ORL and FERET databases. System performance is very promising and comparable with the classical baseline feature extraction algorithms. © Springer International Publishing Switzerland 2014

A. Eleyan

D. Donoho

E. Candes

L. Liu

L. Shen

L. Sirovich

L. Wiskott

M. Kirby

P. Belhumeur

P.J. Philipps

R. Brunelli

R. Chellappa

R.G. Baraniuk

Z.M. Hafed

Eleyan, A.

Kose, K.

Cetin, A.E.

Bilkent University Institutional Repository

Image Feature Extraction UsingCompressive SensingAlaa Eleyan1, Kivanc Kose2, and A. Enis Cetin21 Mevlana UniversityElectrical and Electronics Engineering Dept., Konya, Turkeyaeleyan@mevlana.edu.tr2 Bilkent UniversityElectrical and Electronics Engineering Dept., Ankara, Turkeycetin@bilkent.edu.tr, kkivanc@ee.bilkent.edu.trSummary. In this paper a new approach for image feature extraction ispresented. We used the Compressive Sensing (CS) concept to generate themeasurement matrix. The new measurement matrix is different from the mea-surement matrices in literature as it was constructed using both zero meanand nonzero mean rows. The image is simply projected into a new space usingthe measurement matrix to obtain the feature vector. Another proposed mea-surement matrix is a random matrix constructed from binary entries. Facerecognition problem was used as an example for testing the feature extractioncapability of the proposed matrices. Experiments were carried out using twowell-known face databases, namely, ORL and FERET databases. System per-formance is very promising and comparable with the classical baseline featureextraction algorithms.1 IntroductionReliable automated face recognition is useful in several applications such assecurity and access control systems. There are many other possible uses forfacial recognition that are currently being developed. For example, the tech-nology could be used as a security measure at ATMs and airports in orderto intensify security. The same concept could also be applied to comput-ers where facial images would replace passwords in the login process. Givenstill or video images of a scene, the system should identify or verify one ormore persons in the scene using a stored database of faces. The face repre-sentation falls into two categories[1]. The first category is global approachor appearance-based, which uses holistic texture features and is applied tothe face or specific region of it. Many applied well-known algorithms falls inthis category such as principal components analysis (PCA) [2, 3], which isalso called eigenfaces [4, 5], linear discriminant analysis (LDA) [6, 7], Ga-bor wavelet transform[8, 9], and Discrete cosine transform[10]. The secondR.S. Choraś (ed.), Image Processing and Communications Challenges 5, 177Advances in Intelligent Systems and Computing 233,DOI: 10.1007/978-3-319-01622-1_21, © Springer International Publishing Switzerland 2014178 A. Eleyan, K. Kose, and A.E. Cetincategory is feature-based or component-based, which uses the geometric re-lationship among the facial features like mouth, nose, and eyes. Wiskott etal. [11] implemented feature-based approach by a geometrical model of a faceby 2-D elastic graph. Another example of feature-based was done by inde-pendently matching templates of three facial regions (eyes, mouth and nose)and the configuration of the features was unconstrained because the systemdid not include any geometrical model [12]. In this paper we used the con-cept of compressive sensing (CS) to generate a random measurement matrix.The CS is based on the fact that we can represent images and signals witha small number of coefficients which, in turn, makes CS powerful as a fea-ture extractor [13] [14]. In our proposed approach, the measurement matrixis different from the random measurement matrices used in most CS prob-lems. We used a matrix containing both zero-mean and nonzero-mean rows.We also compared this matrix with another measurement matrix which isconstructed using random binary entries. The measurement matrix will serveas a projection matrix to project image vectors to a new space resulting infeature vector with much shorter length. The matrix with both zero-meanand non-zero mean rows showed superior results using both face databaseswith various feature vector lengths.The paper is organized as follows: Section 2 discusses the compressivesensing concept; Section 3 explains the proposed approach. The experimentalresults and discussions are in Section 4 and then results are concluded at theend of this paper.2 Compressive SensingThe Nyquist-Shannon sampling theorem [15] is one of the fundamental the-orems in signal processing literature. It specifies the conditions for perfectreconstruction of a continuous signal from its samples. If a signal is sampledwith a sampling frequency that is at least two times larger than its band-width, it can be perfectly reconstructed from its samples. This approach isvery simple to implement however, it is not very efficient in terms of datarates. Sampling the signal according to the Nyquist criteria will end up inlarge amount of samples, most of which may be thrown away in the laterparts of the processing e.g. compression. For example in JPEG compression,first the sampled image is transformed into the DCT domain and then mostof the negligible valued (small amplitude) DCT coefficients are thrown away.Compressed sensing (CS) overcomes this problem by taking compressedmeasurements [16, 18, 20] from the signal. In a compressive sensing frame-work, the signal is assumed to be K-Sparse in a transformation domain,such as the wavelet domain or the DCT domain. A signal with length N isK-Sparse if it has at most K non-zero and (N − K) zero coefficients in atransform domain. The case of interest in CS problems is when K << N ,i.e., sparse in the transform domain.Image Feature Extraction Using Compressive Sensing 179In CS instead of taking individual, regularly spaced samples from the sig-nal, a composition of the values of the signal at some instances is taken. Thesenew samples are called compressed measurements y, and they are collectedas followsy = φx = φ.ψ.s = θ.s, (1)where φ is the M×N measurement matrix, M << N , and s is the K−sparsetransform domain representation of the signal x in the transform domain rep-resented by ψ. The reconstruction of the original signal x from its compressedmeasurements y cannot be achieved by simple matrix inversion or inversetransformation techniques. A sparse solution can be obtained by solving thefollowing optimization problem:sp = argmin||s||1 such that θ.s = y (2)One important characteristic of the measurement matrix φ is that it doesnot need to have a specific structure like transformation matrices or samplingmatrices. In fact, in [16, 17, 18], the authors states that the measurement ma-trix should satisfy the restricted isometry property (RIP) for a given numberof measurements. They also prove that a random matrix with entries thatare i.i.d Gaussian random variables, satisfies the RIP property. Measurementmatrix can even be constructed from binary entries [19].Reconstruction of the original signal from these compressed measurementsis another active research field in signal processing and mathematics. Differentoptimization techniques are frequently used for this purpose. However, for theproposed classification method, we are only interested in the sampling partof the CS framework. Therefore, we will not get into the details of thesetechniques since the proposed method is related to only the sampling part ofthe CS framework.As the perfect reconstruction of the original signal from these compressedmeasurements is possible, it is also possible to state that, these compressedmeasurements have descriptive information about the original signal. There-fore, they can used as features in a classification process. In the proposedframework, we are taking compressed measurements from face images us-ing gaussian and binary random measurement matrices and use the mea-surements as features in the classification. The details of the algorithm ispresented in Section 3.3 Proposed ApproachAn illustration of the proposed approach is shown in Fig. 1. The face databaseis divided into two sets; training set and testing set. Each image in bothsets are projected into new space using one of the proposed measurementmatrices. After generating the feature vectors of both training set and testingsets, an appropriate classifier is used for classifying each test image to its180 A. Eleyan, K. Kose, and A.E. CetinFig. 1. Flowchart of the proposed approachcorresponding class by comparing its feature vector with the feature vectorsof the training set.The similarity measures used in our experiments to evaluate the efficiencyof different representation and recognition methods include 1 distance mea-sure, δ1 , 2 distance measure, δ2 , and cosine similarity measure, δcos. Themeasures for n dimensional vectors are defined as followsδ1(x, y) = |x− y| (3)δ2(x, y) = ||x− y||2 (4)δcos(x, y) =xy||x||||y|| (5)Experiments were conducted on two commonly used face databases:FERET database [21] and ORL database [22]. For FERET database, 600frontal face images from 200 subjects are selected. The 600 face images wereacquired under varying illumination conditions and facial expressions. Eachsubject has three images of size 256 × 384 with 256 gray levels. Each faceimage is resized to 128×128. Fig. 2(a) shows sample images from the FERETdatabase. The first two rows are the training images while the third row showsthe test images. It can be noticed from this figure that the test images all dis-play variations in illumination and facial expression. To test the algorithms,two images of each subject are randomly chosen for training, while remainingone is used for testing.The ORL database consists of 400 face images acquired from 40 subjects(i.e., ten images per subject) with variations in facial expression and facialImage Feature Extraction Using Compressive Sensing 181(a) (b)Fig. 2. Example images from the face databases: (a) Example images from theFERET database. (b) Example images from the ORL database.details. All images are grey scale with a 92×112 pixels resolution. All imagesin the database are resized to 128×128 pixels. Fig. 2(b) shows sample imagesfrom the ORL database.4 Comparative Results and DiscussionsPreliminary experiments were conducted on both FERET and ORL databasesto study the performance of the proposed algorithm for the face recogni-tion problem. Leave-one-out strategy is used in the preparation of the re-sults in Table 1 and 2. Taking p as the number of poses for each person inthe database, p-1 poses will be used for training while remaining one posefor testing. In this strategy, test pose is changed at every run of the pro-gram and the rest p-1 is used for training making a total of ( p!p−1! = p)runs. At the end, averaging the results from all these runs will give the finalrecognition rate.Both in Table 1 and 2 results of using 3 different measurement matri-ces were recorded; measurement matrix with zero mean rows, measurementmatrix with nonzero mean rows and measurement matrix with mixed zeromean and nonzero mean rows. The measurement matrix size is M×N , whereN = 128× 128 and M can take an arbitrary value which will later representthe resulting feature vector length.In Table 1, the best performance obtained by using measurement ma-trix on FERET database with zero mean rows was 81.5%, while it reached80% by using measurement matrix with nonzero mean rows. Using measure-ment matrix with zero and nonzero mean rows gave a better performancereached 84.5%. In Table 2, the max performance obtained by using measure-ment matrix on ORL database with zero mean rows was 96.25%, while itreached 96.5% by using measurement matrix with nonzero mean rows. Usingmeasurement matrix with zero and nonzero mean rows gave a better perfor-mance reached 96.75%. It is clear from these results that using a measurement182 A. Eleyan, K. Kose, and A.E. Cetinmatrix with both zero and nonzero mean rows helped to slightly improve theperformance for both ORL and FERET databases.Table 3 has the same scenario as in Table 1 and 2. The difference is in theused random measurement matrix. In Table 3 a random measurement matrixwith binary entries is used. Normalization of the feature vectors obtained bymeasurement matrix before the classification stage dropped the performancein Table 1 and 2 by nearly 1 to 2%. On the other hand, normalizing thefeature vectors obtained using the binary random measurement matrix helpedto improve the performance of the 1 and 2 classifiers drastically while ithad almost no effect on Cosine distance results. For example, with ORLdatabase, using normalized feature vector of length 1000 gives 96.29% using 1distance(Table 3) while it gives 47.5% without feature vector normalization.So, Table 1 and 2 were prepared without normalization of the feature vectors,while Table 3 was prepared using normalized feature vectors.Even though the results for FERET database show that by using a mea-surement matrix with both zero and nonzero mean rows (reached 84.5%)can give better performance than using a matrix with binary entries(reached81%). This improvement was not very clear in ORL database results, as itTable 1. Face recognition rates on FERET database obtained using different num-ber of features taken using different Measurement Matrices. The rates are given in3 different metrics defined in (3)-(5).zero mean rows nonzero mean rows mixed mean rowsM δ1 δ2 δcos δ1 δ2 δcos δ1 δ2 δcos50 70.50 70.50 70.00 70.50 70.00 70.00 72.00 71.75 71.50100 73.00 75.00 72.00 75.00 74.50 75.00 76.00 78.50 75.00200 78.00 79.50 78.50 79.00 80.50 77.50 80.00 82.00 79.75300 79.50 79.50 80.00 79.50 80.00 80.00 82.50 82.00 81.50500 79.00 79.50 79.00 79.75 80.50 81.00 84.50 84.00 81.501000 80.50 81.00 81.50 81.00 81.00 80.00 83.00 83.50 82.50Table 2. Face recognition rates on ORL database obtained using different numberof features taken using different Measurement Matrices. The rates are given in 3different metrics defined in (3)-(5).zero mean rows nonzero mean rows mixed mean rowsM δ1 δ2 δcos δ1 δ2 δcos δ1 δ2 δcos50 89.25 90.25 90.25 91.50 91.50 90.75 90.00 92.75 92.00100 93.75 93.75 94.00 92.75 93.50 92.75 93.75 94.00 93.75200 94.50 94.75 93.50 94.75 94.75 94.00 95.00 94.25 94.50300 95.75 95.00 95.25 95.25 95.00 95.00 95.25 95.75 95.75500 95.25 96.00 95.50 94.75 95.50 93.50 96.25 96.25 95.001000 96.00 96.25 94.50 96.50 95.75 94.50 96.75 96.50 94.75Image Feature Extraction Using Compressive Sensing 183Table 3. Face recognition rates on FERET and ORL database obtained usingdifferent number of features taken using Measurement Matrices with binary entries.The rates are given in 3 different metrics defined in (3)-(5).FERET ORLM δ1 δ2 δcos δ1 δ2 δcos50 69.50 68.25 69.75 90.50 91.00 90.25100 77.50 76.50 76.75 94.00 95.00 93.00200 80.50 80.25 80.51 94.75 95.75 94.25300 80.00 79.75 80.25 94.50 94.25 95.00500 79.50 78.75 79.25 95.50 95.75 94.251000 80.75 80.00 81.00 95.50 96.50 95.25reached 96.75% by using a measurement matrix with both zero and nonzeromean rows and 96.5% by using a matrix with binary entries, which is a veryclose performance.5 ConclusionIn this paper the compressive sensing concept is used to prepare a Gaussianor binary random measurement matrix. Measurement matrix is used as a pro-jection matrix for the image feature extraction. The proposed approach weretested on the face recognition problem. It is experimentally observed that mea-surement matrices with nonzero mean rows improve results compared to ordi-nary measurement matrices. This is due to the fact that multiplying an imagewith a zero mean row is somewhat equivalent to bandpass or highpass filtering.By including nonzero mean rows we also introduce lowpass energy to the mea-surement process. The preliminary results of the experiments conducted onboth FERET and ORL databases indicate that the proposed approach is ableto extract the salient features from the face images effectively and provides ahigh recognition performance . In our future work, more extensive experimentswill be carried out on various pattern classification problems to evaluate theperformance of the proposed approach under different conditions.References1. Chellappa, R., Wilson, C.L., Sirohey, S.: Human and machine recognition offaces: a survey. Proceedings of the IEEE 83(5), 705–741 (1995)2. 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Image feature extraction using compressive sensing

Alaa Eleyan

Kivanc Kose

A. Enis Cetin

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Image Feature Extraction Using Compressive Sensing

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Image feature extraction using compressive sensing

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