Available online at www.sciencedirect.com
ScienceDirect Procedia Computer Science 86 (2016) 265 – 268
2016 International Electrical Engineering Congress, iEECON2016, 2-4 March 2016, Chiang Mai, Thailand
Face Recognition Performance Improvement Using Derivative of Accumulated Absolute Difference Based on Probabilistic Histogram Gatesakda Srikotea, Anupap Meesomboona,* a
Department of Electrical Engineering, Faculty of Engineering, Khon Kaen University, Khon Kaen, 40002, Thailand
Abstract In the paper we propose a face verifying algorithm for face recognition that can identify two face mismatch pairs in cases of incorrect decisions. The computational approach taken in this system is performed by the derivative of accumulated absolute difference between two faces unseen before. Unlike the traditional multi-dimensional distance measurement, the proposed algorithm also considers an increasing trend of accumulated absolute difference in respect to the Gaussian components. A Gaussian mixture model of bag-of-feature from training faces is also widely applicable to several biometric systems. Evaluation of the proposed algorithm is done on unconstrained environments using Labeled Face in the Wild (LFW) datasets. Experiments show that the proposed algorithm outperforms all conventional face recognition algorithms with advantage of about 4.92% over direct-bag-of-features and 18.05% over principal component analysis-based and is also appropriate for identification task of the face recognition systems. Furthermore, some particular advantages of our approach are that it can be applied to other verification systems. © 2016 2016 The TheAuthors. Authors.Published Published Elsevier by by Elsevier B.V.B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Organizing Committee of iEECON2016. Peer-review under responsibility of the Organizing Committee of iEECON2016 Keywords: Gaussian Mixture Model; Expectation Maximisation Algorithm; Accumulated Absolute Difference; Probabilistic Histogram.
1. Introduction Face recognition1 is the one of most successful biometric identification methods among several types of biometric information such as fingerprint, signature, palm veins, retina, hand geometry, and etc. Computers that recognise faces could be applied to wide rarity of problems including criminal identification, security systems, still image,
* Corresponding author. Tel.: +66-43-347-031; fax: +66-43-347-032. E-mail address:
[email protected]
1877-0509 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Organizing Committee of iEECON2016 doi:10.1016/j.procs.2016.05.052
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video processing, and human-computer reaction. There are two main procedures that have been proposed for face verification problem, one is based on holistic information2 and another one is feature geometry model-based which employs local features according to geometrical texture3. One issue in the real world face recognition that is still unsolved is the face recognition from uncontrolled condition. Unfortunately, pose mismatched problem is quite difficult4, because local feature information is changed from normal feature vector components. Thus to address these issues, not only distance of two faces to be considered, but also the differences between each of probabilistic information at any Gaussian component are determined. We therefore focus our research toward developing a face verifying algorithm to determine and correct an incorrect decision in case of matched test. In this paper, we therefore emphasise our research on the pose mismatched problem by reconsidering of two face verification with the differentiated accumulated absolute difference trend graph. The approach describes a recognition system for still-still face verification base from the probabilistic based multi-region histogram (MRH)5 and has advantages over other face recognition algorithms in accuracy. 2. Face verification system The face recognition system consists of detection (Haar Feature-based Cascade Classifier), face feature extraction, model parameters estimation, and face signature verification2. Each individual face can be extracted from block (or patch) via the 2D-DCT (two-dimensional discrete cosine transform)6. Each block consists of 8x8 (64 elements) subsquares with 75% overlap the neighbouring blocks (7 pixels). Based on preliminary experiments, using the 15 DCT coefficients at the top left of 8x8 coefficient matrix is sufficient7. The M-dimensional Gaussian distribution takes the form7
N x|ȝ, Ȉ
1 (2S )
M /2
Ȉ
1/ 2
1 ½ T exp ® x ȝ Ȉ1 x ȝ ¾ ¯ 2 ¿
(1)
where P k is the M-dimensional mean vector, 6 k is the M u M covariance matrix, and x denotes the random vector from DCT coefficients. Once the descriptive feature vector for a given face A is obtained by T
hA
N N ªN º « ¦ P1N1 (x n | ȝ1, Ȉ1 ), ¦ P2 N 2 ( x n | ȝ2 , Ȉ 2 ),..., ¦ Pk N k (x n | ȝk , Ȉ k ) » «¬ n 1 »¼ n 1 n 1
(2)
where Pk in hA is the k-th population fraction for Gaussian model, and k-th element is the posterior probability of vector xn according to the Gaussian model of a bag-of-feature7. The bag-of-feature is the Gaussian mixture model (GMM) which obtained by extracting descriptive features form Yale database, followed by employing the Expectation Maximisation (EM) algorithm to optimise the GMM parameters. 3. The proposed face signature comparison using accumulated absolute difference The face images corresponding to the feature vectors are then investigated for similarity by the L1 - norm based distance of each image to the other face images and compared to a predefined threshold. The drawback of this method is the incompetence to identify a contrast in each of Gaussian component. We discover that when we plot element values of the accumulated absolute difference vector daccumulated > d (1),, d ( j ),, d (k )@T , where d ( j ) is defined by j
d ( j)
¦ h[i]A hB[i] i 1
(3)
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0.2
0.1
0.15
0.05
0.1
0
0.05
-0.05
0
-0.1 0
100
200 300 400 Gaussian components
500
(a)
0.25
0.15
0.2
0.1
0.15
0.05
0.1
0
0.05
-0.05
0
Face feature B [red]
0.15 Face feature A [blue]
0.25
Face feature B [red]
Face feature A [blue]
where the superscript [i] indicates the i-th component of the feature vector. For j 1, 2, , k , against the number of Gaussian components j , we can see the distinction between the right decision and the wrong decision as shown in Fig. 1 where k 512 is applied. Therefore, this study was conducted to find out how to create a difference between right and wrong decisions.
-0.1 0
100
200 300 400 Gaussian components
500
(b)
Fig. 1. (a) Two face feature histogram of correct decision on mismatch test; (b) Two face feature histogram of incorrect decision on match test.
Consequently, five methods of graph fitting were investigated: logarithm, exponential, least square, linear and polynomial. The results suggest that the polynomial fit method consistently leads to better discrimination efficiency than the other four algorithms. Due to some patch areas of two test faces, a dramatic difference is caused when one or two test faces do not have a normal area of face; hence the trend abnormally increases. From that hypothesis, we can increase the accuracy of face recognition systems through both analysis of increasing trend of accumulation and L1 - norm distance. The general formula for a k-th-degree polynomial can be written as k
f ( x)
a0 ¦ a j x j
(4)
j 1
The residual is given by n
R2 { ¦ [ yi (a0 a1 xi ... ak xi k )]2
(5)
i 1
The second degree polynomial is enough to explain and distinguish which one is abnormal. Thus, the derivative of f ( x ) can be found by the equation f c( x )
2 p1 x p2
(6)
and the derivative of a function depends on x . This expression indicates that the slope of the graph increases if p1 is positive. We discover that the positive value p1 indicates the abnormality of accumulated absolute difference graph which leads to incorrect decision.
4. Experimental Results To access the accuracy of the approach to face verification, we have performed experiments whether a pair of previously unseen faces was of the same or different person in case of matched test. In our experiments we used the Yale database as the training set for constructing the bag-of-feature as well as selecting the decision threshold which was optimised to obtain the highest average accuracy. The test strategy was set in verification framework, and used
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the labeled face in the wild (LFW) dataset8. Evaluation of the approach was done in comparison with principal component analysis (PCA)9. Following the suggestion by Wong et al.5, results for randomised binary trees (RBT) were obtained from the method proposed by Nowak et al.10. The results of MRH base for several configurations were from Chen et al.11. Note that the best known performance up to the present date is the MRH method. In term of performance for face verification accuracy, Table 1 shows that the proposed algorithm outperforms those methods using PCA, RBT, and MRH method. Table 1. Results of the proposed algorithm comparing with various methods Method PCA raw distance
Mean Accuracy 9
PCA normalised distance9 Randomised Binary Trees (RBT) 10 1x1MRH (probabilistic, normalised distance)
11
Standard Error
57.23
0.68
59.82
0.68
72.45
0.4
67.85
0.42
3x3 MRH (probabilistic, normalised distance)11
72.95
0.55
Proposed algorithm
77.87
0.42
5. Summary The simple similarity measurement approach to face recognition was motivated by information theory based on probabilistic histograms of visual word. The model parameters of visual dictionary are optimised by employing the EM algorithm under the maximum likelihood manner. Experiments on LFW still face datasets show that the use of trend analysis of accumulated absolute difference achieves higher accuracy when compared to the other techniques. Our experiments also show that only the second degree polynomial curve fitting method is able to distinguish between correct and incorrect decisions. Moreover, our approach has advantages over other verification methods on its accuracy, speed, and simplicity.
Acknowledgements This research is financially supported by Khon Kaen University under the Incubation Researcher Project.
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