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Fourier mellin transform based face recognition

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  • 1. INTERNATIONAL JOURNAL OF COMPUTER(IJCET), ISSN IAEME– International Journal of Computer Engineering and Technology ENGINEERING 6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © 0976 & TECHNOLOGY (IJCET)ISSN 0976 – 6367(Print)ISSN 0976 – 6375(Online)Volume 4, Issue 1, January- February (2013), pp. 08-15 IJCET© IAEME: www.iaeme.com/ijcet.aspJournal Impact Factor (2012): 3.9580 (Calculated by GISI) ©IAEMEwww.jifactor.com FOURIER MELLIN TRANSFORM BASED FACE RECOGNITION Sambhunath Biswas1, Amrita Biswas2 System Analyst (GR-I), Machine Intelligence Unit, Indian Statistical Unit, Kolkata, India 1 Associate Professor, Electronics & Communication Engineering, Sikkim Manipal Institute of Technology, Majitar, India2 ABSTRACT Human face recognition is, indeed, a challenging task, especially under illumination and pose variations. We examine in the present paper effectiveness of a simple face recognition algorithm based on Fourier Mellin Transform. The algorithms convert 2-D gray level training face images into their respective depth maps or physical shape which are subsequently transformed by Fourier Mellin Transform. Experiments show that such transformed shape features are robust to illumination and pose variations. Classification for test face images is made through a k-NN classifier, based on L1 norm. Proposed algorithm has been tested on face images from the ORL database. Keywords: Face Recognition, Depth Map, Fourier Mellin Transform, Nearest Neighbour Classifier I. INTRODUCTION Face Recognition problem has been studied extensively for more than twenty years but even now the problem is not fully solved. In particular, the problem still exists when illumination and pose vary significantly. Recently, some progress [1] has been made on the problems of face recognition, especially under conditions such as smallvariations in lighting and facial expressions or pose. Of the many algorithms for face recognition, so far developed, the traditional approaches are based on Principal Component Analysis (PCA). Hyeonjoon Moon et al. [2] implemented a generic modular PCA algorithm where the numerous design decisions have been stated explicitly. They experimented with changing the illumination normalization procedure and studied its effect through the performance of compressing images with JPEG and wavelet compression algorithms. For this, they varied the number of eigen vectors in the representation of face images and changed the similarity measure in the classification process. Kamran Etemad and Rama Chellappa in their discriminant analysis algorithm [3], made an objective evaluation of the significance ofvisual information in different parts (features) of a facefor identifying the human subject. LDA of faces provides a small set of features that carries the most relevant information for classification purposes. The 8
  • 2. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976 –6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEMEfeatures are obtained through eigen vector analysis of scatter matrices with the objective ofmaximizing between-class variations and minimizing within-class variations. The algorithmuses a projection based feature extraction procedure and an automatic classification schemefor face recognition. A slightly different method, called the evolutionary pursuit method, forface recognition was described by Chengjun Liu and Harry Wechsler [4]. Their methodprocesses images in a lower dimensional whitened PCA subspace. Directed but randomrotations of the basis vectors in this subspace are searched by Genetic Algorithm, whereevolution is driven by a fitness function defined in terms of performance accuracy and classseparation. Up to now, many face representation approaches have been introduced includingsubspace based holistic features and local appearance features [17]. Typical holistic featuresinclude the well-known principal component analysis (PCA) [18], linear discriminantanalysis [19], independent component analysis (ICA)[20] etc. Recently, information fromdifferent sections, such as, scale, space and orientation, has been used for representation andrecognition of human faces by Zhen et al. [21]. This does not include the effect ofillumination change. Subspace based face recognition under the scenarios of misalignmentsand/or image occlusions has been published by Shuicheng et al. [22]. We have not consideredimage occlusions as our objective is different. The proposed research work addresses theproblem of face recognition to achieve high performance in the face recognition system. FaceRecognition method, [5] based on curvelet based PCA and tested on ORL Database, uses 5images for training and has achieved 96.6% recognition rate and, using 8 images for trainingon the Essex Grimace database, has achieved 100% recognition rate. Another algorithm [6],based on wavelet transform, uses 5 images for training from the ORL Database has achieveda recognition rate of 99.5%. But still more improvement is required to ensure that the facerecognition algorithms are robust, in particular to illumination and pose variation. A facerecognition algorithm mainly based on two dimensional graylevel images, in general, exhibitspoor performance when exposed to different lighting conditions. This is because the featuresextracted for classification are not illumination invariant. To get rid of the illuminationproblem, we have used the 3-dimensional depth images of the corresponding 2-dimensionalgray level face images. This is because the 3-D depth image depicts the physical surface ofthe face and thus, provides the shape of human face. The primary reasonis that such a shapedepends on the gradient values of thephysical surface of the face, i.e., on the differenceofintensity values and not on the absolute values of intensity. As a result, change inillumination does not affect the feature set and so the decision also remains unaffected. Sucha shape can be obtained using a shape from shading algorithm and subsequently can be usedfor feature extraction. 3-D face matching using isogeodesic stripes through a graph asdescribed in [23] is a different technique for face recognition. But it is computationallyexpensive. However, it is also a different area of research. Xiaoyang and Triggs [24], on theother hand, considered texture features for face recognition under difficult lightingconditions. Their method needs to enhance local textures but how to select the local texturesor which local textures are adequate and need be considered are not discussed. The proposedalgorithm use the shape from shading algorithm [8], and Fourier Mellin transformrespectively to compute energy for feature extraction. We have used L1 norm distance to testfor classification. With this, the outline of the paper is described as follows: In section II, webriefly review a shape from shading algorithm and in section III, the concepts of FourierMellin Transform are briefly sketched. Section IV, depicts the proposed algorithm, whileexperimental results are discussed in section V. Finally, conclusion is made in the lastsection. 9
  • 3. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976 –6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEMEII. EXTRACTION OF ILLUMINATION INDEPENDENT FEATURES The problem of recovering 3-D shape from a single monocular 2-D shaded image wasfirst addressed by B. K. P Horn [14]. He developed a method connecting the surface gradient(p,q) with the brightness values for Lambertian objects. There result is known as thereflectance map. Therefore, he computed the surface gradients (p,q) using the reflectancemap in order to get the shape. From (p,q), he also computed depth, Z. Since, orientation oftangent planes is accompanied by the orientation of their normal vectors, say (nx,ny,nz),theycan also be effectively used to represent the surface shape.As the reflectance map, in general,is non-linear, it is very difficult to find the gradient values in a straightforward way. Someother researchers, such as, Bruss [15] and Pentland [16], to simplify the problem, thought oflocal analysis to compute the shape. Thus, two different kinds of algorithms, e.g. global andlocal emerged. In global methods, Horn showed the shape can be recovered by minimizingsome cost function involving constraints such as smoothness. He used variational calculusapproach to compute the shape in the continuous domain and its iterative discrete version inthe discrete domain. Bruss showed that no shape from shading technique can provide aunique solution without additional constraint. Later on, P. S. Tsai and M. Shah [8] provided asimple method to compute shape through linearization of Horn s nonlinear reflectance map. ‟For our purpose, we have used the shape from shading algorithm described by P. S. Tsai andM. Shah [8] for its simplicity and fastness. This approach employs discrete approximationsfor p and q using finite differences, andlinearizes the reflectance in Z(x,y). The method isfast, since each operation is purely local. In addition, itgives good results for the sphericalsurfaces, unlike other linear methods. Note that the illumination change may be due to theposition change of the source keeping the strength of the source as it is or due to the changein the source strength keeping the position of the source fixed. In either case, the gradientvalues, p and q, of the surface do not change, i.e., they can be uniquely determined [14].Hence, for the linear reflectance map, the illumination will have no effect on the depth map.In other words, depth map will be illumination invariant.III. FEATURE EXTRACTION Number of methods are available for feature extraction. We have selected FourierMellin Transform based Approach. The Fourier-Mellin transform is a useful mathematicaltool for image recognition because its resulting spectrum is invariant in rotation, translationand scale. The Fourier Transform itself (FT) is translation invariant and its conversion to log-polar coordinates converts the scale and rotation differences to vertical and horizontal offsetsthat can be measured. A second FFT, called the Mellin transform (MT) gives a transform-space image that is invariant to translation, rotation and scale.The Standard Fourier–Mellin Transform is discussed in the following paragraph:Let f denote a function representing a gray-level image. The standard Fourier–Mellintransform of fis given by: (1)Where Z denotes additive group of integers and R denotes additive group of the real line.The FMT is a global transform and applies to all pixels the same way. Textured imagescannotbe taken into account directly and objects must first be localized and isolatedfrom the scene 10
  • 4. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976 –6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEMEto match one of the requirements regarding the existence of the integral inEq. (1).Due to thesingularity at the origin of coordinates, a solution generally adopted is tocancel the image over a smalldisk around the origin [9]. However, this approximation has serious effects on the numericalcomputation of the FMT because of the following reasons:(1)Image values nearer the origin have a larger effect on the FMT than image valuesremote from thecentroid because of the 1/rweighting in the measure of the Fourier–Mellinintegrals. Hence, significantinformation content of the image is lost in addition to removinga small disk in the image centroid.(2)It may cause stretching problems when images are enlarged. How large must thedisk be if theimage is scaled by an unknown factor? By cancelling a disk of constant radiusfor every image,different amounts of information are removed.More recently, a rigorous approach has been introduced to tackle the difficulties describedabove.Ghorbel[10] suggested computing the standard FMT offσ(r,θ)=rσf(r,θ) instead of f(r,θ), where σis afixed and strictly positive real number.Hence, the integral (1) exists and is called the AFMT of f,withσ>0 (2)While the classical Fourier transform converts translation into a pure phase change, the AFMTconverts a similarity transformation in the original domaininto a complex multiplication in theFourier–Mellin domain. These relations can be seenas the shift theorem for the planar similarity groupand make the AFMT appropriate forextracting features that are invariant to scale and rotationchanges.[11]The AFMT can be expressed according to theCartesiancoordinates of f as follows: (3)In this case, no resampling of the discrete image is necessary and theAFMTcan be estimateddirectlyfrom the rectangular grid.TheCartesianAFMT(C-Afmt) approximationis computed by using sums inplace of integrals: (4)The coordinates m and n correspond to a pixel position from the object centroid. Pmin, Pmax,Qminand Qmaxindicate the coordinates, with respect to the image centroid, of the smallest rectanglethat fully contains the object. For the sake of compatibility with otherapproximations, we used thetrapezoidal integration rule. The discrete image is recovered directly in rectangular coordinates. 11
  • 5. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976 –6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEMEIV. PROPOSED APPROACH We discuss in this section the proposed approach using Fourier Mellin Transform:Step1: Compute depths of all the training images using shape from shading method.Step2: Compute the Fourier Mellin Transform of the depth image and take the FMT coefficients as feature vectors.Step3: Classify the test images using the L1 norm distance measure.Step4: StopV. RESULTS AND DISCUSSION In order to test the proposed algorithms, we have used ORL. The ORL (AT and T)database contains 10 different images (92 x 112), each of 40 different subjects. All imageswere takenagainst a dark homogenous background with thesubjects in upright, frontalposition with some sidemovement. Sample images of the dataset are shown inFig. 3. Thedepth map was computed for all the images in thetraining database assuming the reflectanceof the surface to be Lambertian. The obtained depth image has the same size as the originalimage i.e. 92 x112.Depthimage computed by shape from shading algorithm for thefirst imagein ORL database is shown in Fig.1.The Fourier Mellin Transform of the depth map iscomputed for feature extraction. The Cartesian approximation of AFMT of the first image ofthe ORL database has been shown in Fig.2. To show the robustness of features againstorientation, wehave plottedthe relative error in distance measurement for all tenimages in sixclasses (of ORL database) from theirrespective mean images shown in Fig.4. Note thatthisdistance is almost zero for all the images in a class and maintains excellent constancy. Wehave tested the algorithm for different number of training images. Classification wasconducted using k-NN classifier based on L1 norm measure The results are shownin Table 1. TABLE I RESULTS TABLE Sl.No No.of Training Images Recognition % 1 5 100 2 4 100 3 3 95.7 4 2 90 Fig. 1 Image and its depth map 12
  • 6. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976 –6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME Fig. 2 Illustration of the Cartesian approximation of the AFMT of the original image in Fig.1 Fig. 3 Sample Images of the ORL Database Fig. 4 Relative error of images from the respective class meanVI. CONCLUSION We have proposed a simple algorithm based on image depth map and Fourier MellinTransform. The results show that for 4 training images we get 100% recognition percentageand for 3 training images we get a recognition percentage of 95.7%.This clearly shows thatdespite the simplicity of the algorithm we get superior results and there is scope for furtherimprovement in the recognition percentage by resorting to some superior classificationtechniques. 13
  • 7. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976 –6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEMEREFERENCES[1] W. Zhao, R. Chellappa, P. J. Phillips, “A. Rosenfeld,FaceRecognition:A LiteratureSurvey”, ACM Computing Surveys, Vol. 35, No. 4, 2003,pp.399-458.[2] Hyeonjoon Moon, P Jonathon Phillips, “Computational and Performance Aspects of PCABased Face Recognition Algorithms”, Perception 30(3),2001,pp.303 - 321[3] Kamran Etemad and Rama Chellappa, “Discriminant Analysis for Recognition of HumanFace Images”, Proc. First Int. Conf. on Audio and Video Based Biometric PersonAuthentication,Crans-Montana, Switzerland,Lecture Notes In Computer Science; Vol.1206,August 1997,pp.127 - 142[4] Chengjun Liu and Harry Wechsler, “Face Recognition using Evolutionary Pursuit”, Proc.Fifth European Conf. on Computer Vision, ECCV’98,Freiburg, Germany, Vol II, 02-06 June1998, pp.596-612.[5] Tanaya Mandal and Q. M. Jonathan Wu, “Face Recognition Using Curvelet” Based PCA,IEEE, Technical Report, 6/08, pp.978-1-4244-2175.[6] ZhengDezhong Cui Fayi, ‘Face Recognition based on Wavelet Transform and ImageComparison”, Proc. International Symposium on Computational Intelligence and Design,Volume: 2, 2008, pp. 24-29.[7] C.SydneyBurrus and A. Gopinath and HaitaoGuo, “Introduction to Wavelets and WaveletTransforms”, Prentice Hall, N.J 07458, USA, 1998.[8] Ping-Sing Tsai and Mubarak Shah “Shape From Shading Using Linear Approximation”,Image and Vision Computing, vol: 12, 1994, pp.487-498.[9] P. E. Zwicke and Z. Kiss, A new implementation of the Mellin transform and itsapplication to radar classification, IEEE Trans. Pattern Anal. Mach. Intell. 5, 1983, 191–19[10] F. Ghorbel, A complete invariant description for gray-level images by the harmonicanalysis approach, PatternRecog. Lett.15, 1994, 1043–1051.[11] St´ephaneDerrode,Robust and Efficient Fourier–Mellin Transform Approximations forGray-Level Image Reconstruction and Complete Invariant escription Computer Vision andImage Understanding 83, 57–78 (2001)[12] Peter N. Belhumeur, Joao P. Hespanha and David J. Kriegman,“EigenfacesvsFisherfaces:Recognition using Class Specific Linear Projection”,IEEE Trans.on PAMI, July 1997.[13] R. C. Gonzalez and R. E. woods,” Digital Image Processing”, Dorling Kindersley, India,Pearson Prentice Hall, 2006.[14] B.K.P Horn,” Robot Vision”, Cambridge, Massachusetts, USA , MIT Press,1986.[15] A. R. Bruss, “The Image Irradiance Equation:Its Solution and Applicaion”,TechnicalReport TR-623, MIT-AI, June 1981.[16] A. P. Pentland, “Local Shading Analysis”, IEEE Trans. on PAMI, vol.6,no.2, March1984, pp.170-187.[17] S. Z. Li and A. K. Jain, “Handbook of Face Recognition”, New York,Springer-Verlag,2005.[18] M. A. Turk and A.P. Pentland, “Face Recognition using eigenfaces”, Proc.IEEEComputer Society Conf. Comput.vs. Pattern Recognition, June 1991 pp. 586-591.[19] P. Belhumeur. J. Hespanha and D. Kriegman, “Eigenfaces vs. fisherfaces:recognitionusing class specific linear projection”, IEEE Trans. On Pattern Analysis and MachineIntelligence, vol. 26, no. 9, Sept. 2004, pp.1222-1228.[20] P. Conor, “Independent component analysis a new concept?”, Signal Processing, vol.36,1994, pp. 287-314. 14
  • 8. International Journal of Computer Engineering and Technology (IJCET), ISSN 0976 –6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 1, January- February (2013), © IAEME[21] Zhen Lei, Shengcai Liao, MattiPietikainen and Z. Li “Face recognition by exploringinformation jointly in space, scale and orientation”, IEEE Trans. on Pattern Analysis andMachine Intelligence, vol. 20, no. 1, Jan. 2011, pp.247-256.[22] Shuicheng Yan, jianzhuang Liu, Xiaoou Tang and Tomas S.Huang,”Misalignment-robust face recognition”, IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 19,no. 4, Aril2010, pp. 1087-1096.[23] Stefano Berretti, Alberto Del Bimbo and Pietro Pala,” 3D face recognition usingisogeodesic stripes”, IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 32, no.12,Dec. 2010, pp.2162-2177.[24] Xiaoyang Tan and Bill Triggs,” Enhanced local texture features sets forface recognitionunder difficult lighting conditions”, IEEE Trans. on Pattern Analysis and MachineIntelligence, vol. 19, no. 6, Jun.2010 pp.1635-1650.[25] Abhishek Choubey and Girish D. Bonde, “Face Recognition Across Pose WithEstimation Of Pose Parameters” International journal of Electronics and CommunicationEngineering &Technology (IJECET), Volume3, Issue1, 2012, pp. 311 - 316, Published byIAEME[26] Steven Lawrence Fernandes and Dr. G Josemin Bala, “Analysing Recognition Rate OfLda And Lpp Based Algorithms For Face Recognition” International journal of ComputerEngineering & Technology (IJCET), Volume3, Issue2, 2012, pp. 115 - 125, Published byIAEME 15

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