Robust Face Recognition using Curvelet Transform Gyanendra K. Verma
Shitala Prasad
Gohel Bakul
Indian Institute of Information Technology, Allahabad Allahabad India
Indian Institute of Information Technology, Allahabad Allahabad India
National Institute for Mathematical Science, Daejeon Daejeon, South Korea
[email protected]
[email protected]
[email protected]
The recognition process includes comparison the features of images with a set of valid reference features already enrolled with the system. The simplified model of face recognition system is illustrated in figure 1. Feature extraction is very important task in face recognition system as the success of this kind of systems is depends on the robust features extracted from images. Curvelet Transform is relatively new approach used in multi-scale image analysis. In recent year curvelet transform has been used successfully in pattern recognition problems specially in image processing [1, 2].
ABSTRACT In this paper, we perform the face recognition using curvelet transform. In literature, multi resolution analyses of image through wavelet and Gabor transform have been quite exploited successfully for pattern recognition and so far, for face recognition. In contrast to wavelet transform, curvelet transform very efficiently approximate the curved edges with very few coefficients in addition to space-frequency information. Edges information is very important to pattern recognition task in image, hence for face recognition. Various statistical features from curvelet coefficient have used and evaluated with Indian face dataset of IIT Kanpur having 60 multi-pose different objects, using machine learning approach. The results achieved are very promising with 92.0 % accuracy for 500 images. Some popular existing methods based on wavelet transform are also evaluated for comparison in this study.
A lot of research work already done in the area of face recognition. Classical techniques are Principal Component Analysis (PCA) [3, 4] and Linear Discriminate Analysis (LDA) [5, 6]; however PCA based system having good performance in face recognition. Curvelet Transform is relatively new approach used in face recognition.
Categories and Subject Descriptors I.4.8 [Image Processing and Computer Vision]: Scene Analysis- Object recognition.
General Terms Performance, Design.
Keywords Curvelet Transform (CT), Wavelet Transform, Face Recognition
1. INTRODUCTION Face recognition is one of the prime application of biometric identification received significant attention in areas such as computer vision and surveillance. This is used in many other applications like human computer interaction (HCI), image retrieval and security systems. The objective of face recognition system is to identify persons by their facial images. The application of curvelet coefficients in face recognition started only in last few years.
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Figure 1. A generic Face Recognition System
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spatial domain. The shaded area is one of the wedge. The wedges are formed by dividing the frequency plane into different partitions and the spatial plane is divided in respect to ș (angular division). The angular division divides each subband image into different angles.
In this paper we proposed a robust face recognition system based on multi-scale analysis. The Curvelet Transform is applied to decompose the input image in order to get curvelet coefficient. The curvelet features for each input image are obtained from 4th and 6th level curvelet coefficients. Min-max algorithm has been used for feature set normalization in order to improve the recognition accuracy. Then similarity between the extracted features and a set of reference features is calculated by means of K-NN classifier. IIT Kanpur face dataset is used to evaluate the proposed system for face recognition. The results obtained from proposed system are very promising. The rest of the paper is organized as follows: review of curvelet transform is given in section II. Feature extraction approach is described in Section III. Proposed approach is presented in Section IV. Experiment results are discussed in section V and concluding remarks are given in section VI.
2. CURVELET TRANSFORM The Curvelet transform is a higher dimensional generalization of the Wavelet transform designed to represent images at different scales and different angles [7]. The benefit of using Curvelet transform is that curved singularities can be well approximated with very few coefficients and in a non-adaptive manner [7]. Curvelet transform is extension of the wavelet concept [8]. The limitation of wavelet transform is that it fails to represents objects containing randomly oriented edges and curves as it is not good at representing line singularities [9]. The curvelet transform is able to catch the edge singularities efficiently. Fig.2 shows the curvelet construction.
Figure 2. Curvelets in frequency domain (left) and spatial domain (Right)
3. FEATURE EXTRACTION The performance of the face recognition system depends upon the features extracted from images. The features should have high intraclass similarity and low interclass similarity. In our system discrete curvelet transform (4th and 6th level) is used to extract features from images. The feature vector obtained from curvelet coefficients provides multi-scale representation. To extract the curvelet coefficients we applied fast discrete curvelet transform to images with 4th and 6th level decomposition using Curvelab-2.1.2 [11]. We used only basic software of Curvelab and further modifications are done by us.
Algorithm for finding the curvelet coefficients: STEP1: Take the Fourier transform of the signal STEP2: Divide the frequency plain into polar wedges (as shown in fig.2)
The curvelet coefficients are extracted using the discrete curvelet transform. The input image is transfered into Fourier domain first then the convolution of the curvelet with the image in spatial domain becomes the product in Fourier domain [10]. Finally we applied inverse Fourier transform on spectral product in order to obtain curvelet coefficients. But due to the frequency response of a curvelet is a nonrectangular wedge; the wedge needs to be wrapped into a rectangle to perform the inverse Fourier transform. The wrapping is done by periodic tiling of the spectrum using the wedge, and then collecting the rectangular coefficient area in the centre. Through this periodic tiling, the rectangular region collects the wedge’s corresponding portions from the surrounding periodic wedges.
STEP3: Find the curvelet coefficients at a particular scale (j) and angle (ș) by taking the inverse FFT of each wedge at scale j and oriented at angle ș. Discrete curvelet coefficient can be given by the equation-1taken from [10]
C D ( j , l , k1 , k 2 )
D ¦ f [m, n] M j ,l ,k1 ,k2 [m, n]
0d m E M 0d n E N
(1)
Here M Dj ,l ,k ,k [m, n] is digital curvelet transform. j is scale, l is 1 2 orientation and (k1 , k 2 ) are location parameters.
The mean and standard deviation from each subband are calculated to obtain features form curvelet coefficients. The features are extracted from each image. The curvelet features of input image are computed as shown in figure 4 then the comparison between query feature and set of reference features done using Euclidean distance through K-NN classifier.
The discrete curvelet transform can be applied using two algorithms namely Unequispaced FFT transform and Wrapping transform. In unequispaced Fast Fourier transform, the curvelet coefficients are formed by irregularly sampling the Fourier coefficients of the image. In wrapping algorithm, curvelet coefficients are formed by using a series of translations and a wraparound technique. The performance of wrapping based algorithm is fast in computation and more robust as compare to USFFT however both algorithms give the same output. Therefore we have used wrapping based algorithm to find out curvelet coefficients. Figure2 shows curvelets in frequency as well as
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Input Image FFT Image in Fourier Transform Domain
Product
Curvelet in Fourier Transform Domain
Product of Image and Curvelet in FT Domain
Wedge wrapping Wedge tiling IFFT Curvelet coefficients
(a)
Figure 4. Fast Discrete Curvelet Transform
4. FEATURE MATCHING Feature matching is done by calculating the distance between feature set (reference features) and query feature using K-NN algorithm. The training set s contains l points {x1 ,......, xl }, xi R n and their corresponding class labels
{ y1 y( x1 ),....yl y( xl )}, yi c, c {1,....., N c } where the number of different classes is Nc . Min-max normalization (equation no. 2) has been used to normalize the feature in range between -1 to 1, before applying matching process.
A'
A min( A) (newmax newmin ) newmin max( A) min( A)
(2) (b) Figure 5. Sample of Indian Face Database (a) Training (b) Testing Dataset
5. EXPERIMENTS AND RESULTS The experiments were performed on IIT Kanpur Indian face dataset [12]. The dataset comprises color images of more than 60 different persons in JPEG format. The image size is 640x480 pixels, having 256 grey levels. Each person having eleven different poses. The pose includes looking front, left, right, upward and down. The images also contain the emotions such as neutral, smile, laughter, sad and disgust. The images comprise the frontal faces of both Male and female frontal faces. The sample database is shown in figure 5. Training and testing dataset is shown in figure 5 (a) and 5(b).
The experiments comprise two modules: training and testing. Five gray scale images are being used for training and another five for testing purpose. Curvelet Transform is applied to decompose each image up to 4th and 6th level in order to extract the curvelet coefficients. Curvelet decomposition is illustrated in figure 2. In order to extract the feature vector, some statistics as mean and standard deviation applied on curvelet coefficients at each subband level. Total 48 features (16+32) obtained in 4th level decomposition {1x1 cell} {1x16 cell} {1x32 cell} {1x1 cell} and 144 features (16+32+32+64) in 6th level decomposition {1x1 cell} {1x16 cell} {1x32 cell} {1x32 cell} {1x64 cell} {1x1 cell} for each subband and for each scale. The subband distribution at different levels is illustrated in table 1. Min-max algorithm has been used for feature set normalization in order to improve the recognition accuracy before the classification for large dataset. All the experiments are performed on Mat Lab 7.0
Table 1. Curvelet Transforms Subband Distribution Curvelet transform subband distribution Levels
Subbands
4
{1x1 cell} cell}
{1x8 cell}
{1x16 cell}
6
{1x1 cell} {1x8 cell} {1x16 cell} ell} {1x64 cell} {1x1 cell}
{1x1
For classification purpose image of same person is assigned same class i.e. five images of the same person assigned the same class and so on such that person A = A1, A2, A3, A4, A5 assign class
{1x32
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“1” and for person B = B1, B2, B3, B4, B5 assign class “2”. In this way the whole training data is grouped in class. The proposed design of the face recognition system uses 600 feature vectors (52 dimensions for 4th level and 98 dimensions for 6th level) extracted from 10 images of each 60 persons. The parameters of the proposed design are the result of evaluation of different face recognition designs, evaluated using the Face Dataset. The classification results are shown in table 2 and the corresponding graph is illustrated in figure 6. The best classification accuracy is 92.0% for 500 images. We have also experiment with discrete wavelet transform using db4 and db6. The results shows that the curvelet transform provides more accurate recognition compare to the wavelet transform.
7. REFERENCES [1] Jiulong, Z., Zhiyu, Z., Wei, H., Yanjun, L. and Yinghui, W. 2007. Face Recognition Based on Curvefaces. In Proceedings of the Third International Conference on Natural Computation (Haikou, Hainan, China, August 24 27, 2007). ICNC '07. IEEE 627-631 [2] Mandal, T., Majumdar, A. and Hu, J.2007. Face Recognition via Curvelet Based feature Extraction. In Proceedings of the 4th International Conference on Image Analysis and Recognition (Montreal, Canada, August 22-24, 2007). ICIAR ‘07. Springer LNCS 806-817. [3] Karim, T.F., Lipu, M.S.H., Rahman, M.L. and Sultana, F. 2010. Face recognition using PCA-based method. In Proceedings of the IEEE International Conference on Advanced Management Science (Chengdu, China, July 9-11, 2010). ICAMS’2010. IEEE, 158-162.
Table 2. Classification Results No of Images
Curvelet 6
Curvelet 4
Wavelet (db4)
Wavelet (db8)
600
91.8
88.3
79
81.6
500
92.0
88.8
81.2
82
400
90.0
86.5
76.5
78
300
88.0
82.6
75.3
76.6
200
84.0
81.0
74.0
73
100
84.0
84.0
74
78
[4] Akrouf, Samir, Sehili, Med Amine, Chakhchoukh, Abdesslem, Mostefai, Messaoud and Youssef, Chahir, 2009. Face Recognition Using PCA and DCT. In Proceedings of the 5th International Conference on MEMS, NANO, and Smart Systems (Dubai, United Arab Emirates, Dec. 28-30, 2009). ICMENS ’09 [5] Gang Xu, Shengli, Zhang and Liang, Yunyun. 2009. Using Linear Regression Analysis for Face Recognition Based on PCA and LDA. In Proceedings of the International Conference on Computational Intelligence and Software Engineering (Wuhan, China, December 11-13, 2009) CiSE ‘09 [6] Jianke Li, Baojun Zhao, Hui Zhang and Jichao Jiao. 2009. Face Recognition System Using SVM Classifier and Feature Extraction by PCA and LDA Combination. In Proceedings of the International Conference on Computational Intelligence and Software Engineering (Wuhan, China, December 11-13, 2009) CiSE ‘09 [7] Litrature on Curvelet Transform http://www.curvelet.org [8] Curvelet Litrature on Wikipedia http://en.wikipedia.org/wiki/Curvelet [9] Majumdar, A. 2007. Basic Character Recognition using Digital Curvelet Transform. Journal of Pattern Recognition Research, Vol. 2, No. 1 (Mar. 2007). 17-26.
Figure 6. Performance comparison with different approaches
[10] Sumana, I., Islam, M., Zhang D. S. and Lu, G. 2008. Content Based Image Retrieval Using Curvelet Transform. In Proc. of IEEE International Workshop on Multimedia Signal Processing (Cairns, Queensland, Australia, October 8-10, 2008). MMSP ’08
6. CONCLUSION AND FUTURE WORK A Curvelet transform based face recognition approach is proposed in this paper in order to obtain the better performance. The discrete curvelet transform is used to extract the curvelet coefficients for feature extraction and K-NN classifier which is very promising with large dataset, used successfully in this study. The experiments result shows 92.0% accuracy for 500 images which is very good in this category of systems. Our future goal is to scale invariant face reorganization system using curvelet transform to make the system robust.
[11] Curvelet software http://www.curvelet.org/software.html [12] Vidit Jain and Amitabha Mukherjee. 2002. The Indian Face database. http://viswww.cs.umass.edu/~vidit/IndianFaceDatabase/.
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