Etemad, K., Chellappa, R.: Discriminant analysis for recognition of human face images. Journal of the Optical Society of America A-Optics Image Science and Vision 14 (1997) 1724--1733  Home/Search   Document Details and Download   Summary   Related Articles   Check

....about the face. The first level decomposition of an image is shown in Figure 4.2. Further decomposition is conducted on the LL sub band. Despite the equal sub band sizes, different sub bands carry different amounts of information. This observation was made at all resolutions of the image [12]. 19 Figure 4.2: Wavelet transform of an image. 20 Chapter 5 Algorithm The system as outlined in Figure 5.1 consists mainly of two stages: the training stage and the classification stage. Wavelet Transform PCA Manifold Plot Training Stage Estimated Pose Estimation Stage Wavelet Transform ....

K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. Journal of Optical Society of America A, 14(8):1724--1733, Aug 1997. 41

....proposed by Turk and Pentland [8] We omit the description of PCA due to its wide acceptance and use in the research community. The PCA representation imposes constraints on the recognition performance, but we focus on evaluating comparative performance. We adopt the statistical measures used in [4] and discussed in [3, 5] Assume that N face descriptors (e.g. a descriptor may be an intensity image, a vector of expansion coefficients, etc. of L individuals are given for training (N L) Each descriptor is defined in an M space (e.g. M is equal to the number of pixels if an intensity ....

K. Eremad and R. Chellappa, Discriminant analysis for recognition of human face images. J. of Optical Society of America. A, (14)8, 1724-1733, 1997.

....and image noise. Furthermore, they do not capture identity information. More elaborate appearance models use linear combinations of training samples. Given sufficient data, such linear combina tions can also be statistical models. This includes the use of PCA [16] Linear Discriminant Analysis [5] and Hyper Basis Function networks [8] Fig. 3. Top: Example views of 11 different subjects. Bottom: Some of the mean templates obtained by averaging filtered face prototypes at each pose from profile to profile. J.1 Linear Combination of Prototypes An image x at a given pose can be decomposed ....

K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. Optical Society of America, 14(8):1724-1733, August 1997.

....Test Date September March Version of test Group 1996 1997 Baseline Fully Automatic MIT Media Lab [4,6] U. of So. California (USC) 15] Eye Coordinates Given Baseline PCA [7,13] Baseline Correlation Excalibur Corp. MIT Media Lab 2 Michigan State U. 12] Rutgers U. 14] U Maryland [2] ffl ffl these algorithms were developed at the MIT Media Laboratory. The first was the same MIT algorithm that was tested in March 1995 [5,8] This algorithm was retested so that improvement since March 1995 could be measured. The second MIT algorithm was based on more recent work [4] ....

....1995 could be measured. The second MIT algorithm was based on more recent work [4] Algorithms were also tested from Excalibur Corp. Carlsbad, CA) Michigan State University (MSU) 12] Rutgers University [14] University of Southern California (USC) and two from University of Maryland (UMD) [2,16]. The first algorithm from UMD was tested in September 1996 and a second version of the algorithm was tested in March 1997. The final two algorithms were our implementation of normalized correlation and a principal components analysis (PCA) based algorithm [7,13] These algorithms provide a ....

K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. J. Opt. Soc. Am. A, 14:1724--1733, August 1997.

....on subspace methods. Also, among the three algorithms with best performances, two of them follow the subspace method[3] The subspace method has become a de facto standard and a common performance benchmark in face recognition[4] Extensions of the eigenface technique include Etemad and Chellappa[5] s Linear Discriminant Analysis (LDA) Swets and Weng[6] s discriminant eigenfeatures, Belhumeur, Hespanha and Kriegman[7] s fisherfaces, Pentland, Moghaddam and Stamer[8] s view based and modular eigenspaces, Moghaddam and Pentland[9] s probabilistic visual learning, and Moghaddam, Jebara and ....

....and Moghaddam, Jebara and Pentland[4] s Bayesian face recognition. The eigenface technique is based on Principle Component Analysis, which can be treated as an unsupervised method to find the optimal subspace. Many of these extensions try to overcome the unsupervised nature of this technique[5] [6] 7] However, research by Martinez and Kak pointed out that although many researchers believe that the LDA based algorithms are superior to the PCA based ones, when the training data set is small, PCA can outperform LDA. They also stated that PCA is less sensitive to different training data ....

Etemad K, Chellappa R. Discriminant Analysis for Recognition of Human Face Images. Journal of the Optical Society of America A: Optics image science and vision, 14(8), 1997: 1724-1733.

....which describe a new space. It should be noted that this space is not necessarily optimised to allow dimensionality reduction as with PCA, however the first components describe inter class variation and can as such be used as a data classifier. This has been used recently for face recognition [2] and gait classification [3] Sw = 1 n t n c X i=1 n i X j=1 (y i;j Gamma i ) y i;j Gamma i ) T (1) 2 S b = 1 n t n c X i=1 ( i Gamma y ) i Gamma y ) T (2) S b E = SwE (3) Where: Sw = Intra class Covariance Matrix S b = Inter class Covariance Matrix n t = Total ....

K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. In First International Conference on Audio and Video Based Biometric Person Authentication, pages 127--142, 1997.

.... database (a publicly available data set) As additional evidence in support of our claim, we should also draw the attention of the reader to some of the results of the September 96 FERET competition [15] In particular, we wish to point to the LDA results obtained by the University of Maryland [2] that compare unfavorably with respect to a standard PCA approach as described in [18] A notable characteristic of the data used in such experiments was that only one or two learning samples per class were given to the system. Of course, as one would expect, given large and representative ....

K. Etemad and R. Chellapa, "Discriminant analysis for recognition of human face images," Journal of Optics of American A 14(8):1724-1733, 1997.

....bounded regions in the eigenspace. Sozou et al. [14] try to solve the linearity problem of PDMs by constraining shapes to deform along polynomial paths in the eigenspace rather than simply along the axes. There has also been work on further eigen analysis of eigenspace to form a canonical space [9, 6] for which may be useful for classification purposes. These developments, however, restrict the model to a given eigenspace (i.e. a given number of reference points) In the real world we wish to classify classes of shapes that deform non linearly such that features are occluded and a fixed number ....

K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. In First International Conference of the AVBPA, pages 127--142, 1997.

....which describe a new space. It should be noted that this space is not necessarily optimised to allow dimensionality reduction as with PCA, however the first components describe inter class variation and can as such be used as a data classifier. This has been used recently for face recognition [4, 10], image retrieval systems [10] and gait classification [5] Sw = 1 n t n c X i=1 n i X j=1 (y i;j Gamma i ) y i;j Gamma i ) T (1) 2.3 Eigenfaces and High Dimensionality PCA S b = 1 n t n c X i=1 ( i Gamma y ) i Gamma y ) T (2) S b E = SwE (3) Where: Sw = Intra class ....

K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. In First InternationalConference on Audio and Video Based Biometric Person Authentication, pages 127--142, 1997.

....onto the eigen space. In the classification phase, the input face image is projected to the same eigen space and classified by an appropriate method. Many different methods have been used for face recognition, such as the Euclidean distance [15] Bayesian [9] and Linear Discriminant Analysis (LDA) [14, 1, 3, 19, 8]. Unlike the PCA which encodes information in an orthogonal linear space, the LDA encodes discriminatory information in a linear separable space of which bases are not necessarily orthogonal. Researchers have demonstrated that the LDA based algorithms outperform the PCA algorithm for many ....

....when the number of training samples is smaller than the dimension of the sample vector. This is the case for most face recognition tasks. For example, a small size of image of 64x64 turns into a 4096 dimensional vector when vectorized. The solution to this problem is to perform two projections [14, 1, 3, 20]: 1. Perform PCA to project the dimensional image space onto a lower dimensional sub space; 2. Perform discriminant projection using LDA. The PCA step helps to remove null spaces from both and S w . However, this step potentially loses useful information. In fact, the null space of S w ....

K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. Journal of the Optical Society of America A, 14(8):1724--1733, 1997.

....the ratio j t b j = j t w j [1] This ratio is maximized when consists of the eigenvectors of the matrix 1 w b [21] 1 w b = 7) where ; are the eigenvector and eigenvalue matrices of 1 w b . FLD is behind several face recognition methods [21] 1] [11], 17] As the original image space is high dimensional, most methods first perform dimensionality reduction using PCA, as it is the 10 case with the Fisherfaces method suggested by Belhumeur, Hespanha, and Kriegman [1] Using similar arguments, Swets and Weng [21] point out that the Eigenfaces ....

K. Etemad and R. Chellappa, "Discriminant analysis for recognition of human face images," J. Opt. Soc. Am. A, vol. 14, pp. 1724--1733, 1997.

....FLD is that it requires large sample size for good generalization. As this requirement is rarely met, FLD overfits and thus generalizes poorly when compared against PCA schemes [9] One possible remedy for this drawback is to artificially generate additional data and thus increase the sample size [5]. FLD is behind several face recognition methods [16] 1] 5] As the original image space is high dimensional, most methods first perform dimensionality reduction using PCA, as it is the case with the Fisherfaces method developed by Belhumeur, Hespanha, and Kriegman [1] Using similar ....

.... As this requirement is rarely met, FLD overfits and thus generalizes poorly when compared against PCA schemes [9] One possible remedy for this drawback is to artificially generate additional data and thus increase the sample size [5] FLD is behind several face recognition methods [16] 1] [5]. As the original image space is high dimensional, most methods first perform dimensionality reduction using PCA, as it is the case with the Fisherfaces method developed by Belhumeur, Hespanha, and Kriegman [1] Using similar arguments, Swets and Weng [16] point out that the eigenfaces derive only ....

K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. J. Opt. Soc. Am. A, 14:1724--1733, 1997.

....a characteristic known to have great functional significance in biological sensory systems [9] The drawback of FLD is that it requires large sample sizes for good generalization. One possible remedy for this drawback is to artificially generate additional data and thus increase the sample size [12]. FLD is behind several face recognition methods [40] 2] 12] 25] As the original image space is high dimensional, most methods first perform dimensionality reduction using PCA, as it is the case with the Fisherfaces method suggested by Belhumeur, Hespanha, and Kriegman [2] Using similar ....

....biological sensory systems [9] The drawback of FLD is that it requires large sample sizes for good generalization. One possible remedy for this drawback is to artificially generate additional data and thus increase the sample size [12] FLD is behind several face recognition methods [40] 2] [12], 25] As the original image space is high dimensional, most methods first perform dimensionality reduction using PCA, as it is the case with the Fisherfaces method suggested by Belhumeur, Hespanha, and Kriegman [2] Using similar arguments, Swets and Weng [40] point out that the Eigenfaces ....

K. Etemad and R. Chellappa, "Discriminant analysis for recognition of human face images," J. Opt. Soc. Am. A, vol. 14, pp. 1724--1733, 1997.

....apply criteria not related to the Bayes error. 3.2. From Linear Discriminant Analysis (LDA) and Fisherfaces to Enhanced Fisher Models (EFM) LDA, similar to the Fisher Linear Discriminant (FLD) is yet another commonly used criterion in pattern recognition and recently in face recognition [39] [18], 4] The LDA derives a projection basis that separates the different classes as far as possible and compacts the same classes as close as possible. One representative LDA FLD based method is the Fisherfaces method [4] The Fisherfaces method specifies a face space by combining the PCA and the ....

.... PCA space, leads often to overfitting [31] Overfitting is more likely to occur for the small training sample size scenario, which is the typical one for face recognition [35] One possible remedy for this drawback is to artificially generate additional data and thus increase the sample size [18]. Another solution, to analyze the reasons for overfitting and propose new models with improved generalization abilities, led to our EFM method [31] The EFM method first addresses (concerning PCA) the range of principal components used and how it affects performance, and (regarding FLD) the ....

K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. J. Opt. Soc. Am. A, 14:1724--1733, 1997.

....time of this writing, there are three algorithms that have demonstrated the highest level of recognition accuracy on large databases (1196 people or more) under double blind testing conditions. These are the algorithms from University of Southern California (USC) 9] University of Maryland (UMD) [10], and the MIT Media Lab [11] All of these are participants in the FERET program. Only two of these algorithms, from USC and MIT, are capable of both minimally constrained detection and recognition; the others require approximate eye locations to operate. A fourth algorithm that was an early ....

K. Etemad and R. Chellappa, "Discriminant analysis for recognition of human face images," Journal of the Optical Society of America, vol. 14, pp. 1724--1733, 1997.

....recognition techniques can be found in [2, 3] There are several approaches in developing face recognition systems. For example, one approach employs linear projections of face images (treated as 1 D vectors) using either principal component analysis (PCA) 4] or linear discriminant analysis (LDA) [5, 6, 7]. PCA and LDA are parametric techniques closely related to matching pursuit filters that have also been applied for face identification [8] There are also techniques stemming from neural network community like the dynamic link architecture (DLA) a general object recognition technique that ....

.... linear projection algorithms that can be used to reduce the dimensionality of the feature vectors are the Karhunen Loeve or principal component analysis (PCA) and the linear discriminant analysis (LDA) 30] Representations based on PCA are useful to image reconstruction compression tasks [5, 7, 31]. In addition to dimensionality reduction, PCA decorrelates the feature vectors and facilitates the LDA applied subsequently in both eigenvalue eigenvector computations and September 30, 1999 DRAFT 12 matrix inversion. Let j 0 (x l ) j(x l ) Gamma m(x l ) be the normalized feature vector at ....

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K. Etemad, and R. Chellappa, "Discriminant Analysis for Recognition of Human Face Images," in Lecture Notes in Computer Science: Audio- and Video- based Biometric Person Authentication (J. Bigun, G. Chollet, and G. Borgefors, Eds.), vol. 1206, pp. 127--142, 1997.

....[10] Therefore, one approach to the classification task is to model the class conditional probability densities, p(xjC k ) for each class. This approach is explored in this work. An alternative approach is to estimate discriminant functions using, for example, Linear Discriminant Analysis [11,12]. 3.2 Face verification Face verification can be treated as a 2 class classification problem. The two classes C 0 and C 1 correspond to the cases where the claimed identity is true and false respectively. In order to maximise the posterior probability, x should be assigned to C 0 if and only if ....

K. Etemad and R. Chellappa, "Discriminant analysis for recognition of human face images," J. Opt. Soc. Am. A, vol. 14, no. 8, pp. 1724--1733, August 1997.

.... of projection to face space of the pixel level difference between two facial images is an adequate distance measure for face discrimination, under broad variations in the imaging conditions [25] Later, other holistic distance measures for face recognition were studied, based on multiple classes [24, 1, 4], and on two classed [14, 15, 17] under the general ideas of Linear Fisher Discriminant Analysis [7] which all employ an initial projection to face space. Besides of identity, classification and perception of race and sex [16] has been studied using PCA. Also, the PCA representation has been ....

K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. Journal of the Optical Society of America A, 14(8):1724--1733, Aug. 1997.

....our method are facial expression, sex, and race , however the technique may extend to other facial attributes. The method we propose here synthesizes aspects of two major approaches to facial image processing: Gaborwavelet labelled elastic graph matching [8, 12] and Fisherface algorithms [1, 7] based on statistical representation of face space. Both the eigenface and the more recent Fisherface techniques require precise normalization and registration of facial internal features. Performance of the eigenface algorithm is improved by morphing the face to a standard shape [3] By contrast, ....

....a new algorithm for automatically extracting high level information from facial images. The algorithm is a hybrid system using labelled elastic graph matching [8, 12] to register a grid with the face and extract Gabor wavelet features and a classifier similar to that used by the Fisherface method [1, 7]. Use of a representation based on the amplitude of 2 D Gabor wavelet transform relaxes the requirement for exact registration of the internal features of the face. Substantial :K L : r T 14 1 ) #e m ) L 8 #e m ) 84 ....

K. Etemad and R. Chellappa, "Discriminant Analysis for Recognition of Human Face Images," Journal the of Optical Society of America A, vol. 14, no. 8, pp. 1724-1733, 1997.

.... representations, and has been applied successfully to ensembles of facial regions [18] and full faces [8] PCA is also: used for face discrimination [20] and recognition [15, 10, 13] used to build probabilistic models [10, 13] serves as a the basis of Linear and Fisher Discriminant Analysis [19, 1, 3, 11]; has been used to investigate the perception of race and sex [12] and has been shown to be robust against known gaps in the data [4] as well as uncorrelated noise [14] Given the wide applicability of PCA, both as a representation and a probabilistic model, it is somewhat surprising that the ....

K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. Journal of the Optical Society of America A, 14(8):1724--1733, Aug. 1997.

.... problem [Turk and Pentland, 1991] This statistical approach was extended later for 3 D object recognition [Murase and Nayar, 1995] Using this image vector representation, the linear discriminant analysis (LDA) has been independently used for face recognition by several research groups, including [Etemad and Chellappa, 1994] [Belhumeur et al. 1996] Weng, 1994] Swets and Weng, 1996b] Swets and Weng, 1996a] among many other groups. It has been proposed that this type of approaches be called appearance based approach, in order to distinguish other view based approaches (e.g. aspect graph based) For distinguishing ....

Etemad, K. and Chellappa, R. (1994). Discriminant analysis for recognition of human face images. In Proc. Int'l Conf. Acoust., Speech, Signal Processing, pages 2148--2151, Atlanta, Georgia.

....that took the March 1995 test [6, 7] This algorithm was retested so that any improvement since March 1995 could be determined. The second algorithm was based on more recent work [5] Algorithms were also tested from Excalibur Corp. Rutgers University [12] and the University of Maryland [2]. The final two algorithms were our implementation of Turk and Pentland s eigenfaces [11] and normalized correlation. These two algorithms provide a baseline for algorithm performance. In our implementation of eigenfaces, we measured the similarity between two faces by the angle between feature ....

K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. In ICASSP '96, pages 2148--2151, 1996.

....March Version of test Group 1996 1997 Baseline Fully Automatic MIT Media Lab [4,6] ffl U. of So. California (USC) 15] ffl Eye Coordinates Given Baseline PCA [7,13] ffl Baseline Correlation ffl Excalibur Corp. ffl MIT Media Lab 2 Michigan State U. 12] ffl Rutgers U. 14] ffl U Maryland [2] ffl ffl USC ffl these algorithms were developed at the MIT Media Laboratory. The first was the same MIT algorithm that was tested in March 1995 [5,8] This algorithm was retested so that improvement since March 1995 could be measured. The second MIT algorithm was based on more recent work [4] ....

....1995 could be measured. The second MIT algorithm was based on more recent work [4] Algorithms were also tested from Excalibur Corp. Carlsbad, CA) Michigan State University (MSU) 12] Rutgers University [14] University of Southern California (USC) and two from University of Maryland (UMD) [2,16]. The first algorithm from UMD was tested in September 1996 and a second version of the algorithm was tested in March 1997. The final two algorithms were our implementation of normalized correlation and a principal components analysis (PCA) based algorithm [7,13] These algorithms provide a ....

K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. J. Opt. Soc. Am. A, 14:1724--1733, August 1997.

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K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. Journal of the Optical Society of America A, 14:1724--1733, 1997.

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K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. Journal of Optical Society of America A, pages 1724--1733, 1997.

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K. Etemad, R. Chellappa, Discriminant analysis for recognition of human face images, J. Opt. Soc. Am. A (1997) 1724--1733.

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Etemad, K. and Chellappa, R. (1997), Discriminant Analysis for Recognition of Human Face Images, Journal of Optical Society of America A 14, 1724-1733.

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K. Etemad and R. Chellappa, "Discriminant analysis for recognition of human face images," Journal of Optical Society of America A, pp. 1724--1733, 1997.

....identity from a database of known individuals, whereas in verification problems, the system needs to confirm or reject the claimed identity of the input face. Many methods have been proposed for face recognition [2, 1] Basically they can be divided into holistic template matching based systems [6, 8, 7, 10, 34, 23, 9] and geometrical localfeature based schemes [25, 11] Even though both types of systems have been successfully applied to the task of face recognition, they do have certain advantages and disadvantages. Thus appropriate schemes should be chosen based on the specific requirements of a given task. ....

....to decide on the class label (person ID) 2.4. 1 Distance Measure for Subspace LDA: Weighted or Unweighted For the pure LDA distance measure, it has been suggested that weighted Euclidean distance will give better classification than simple Euclidean distance in the context of face recognition [9], where the weights are the normalized eigenvalues defined in (5) But it turns out that this Preprocessing Photometrical Geometrical Projection LDA Yes No Metric Gallery Image Probe Image Euclidean Weighted Figure 4: The subspace LDA face recognition system weighted measure is ....

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K. Etemad and R. Chellappa, "Discriminant Analysis for Recognition of Human Face Images, " Journal of the Optical Society of America A, Vol. 14, pp. 1724-1733, 1997.

....[8] for reports on experiments. Experiments reported in [8] evaluate still to still scenarios, where the gallery and the probe set consist of both still facial images. Some well known still to still FR approaches include Principal Component Analysis (PCA) 9] Linear Discriminant Analysis (LDA) [10,11], and Elastic Graph Matching (EGM) 12] Typically, recognition is performed based on an abstract representation of the face image after suitable geometric and photometric transformations and corrections. Following [8] we de ne a still to video scenario: the gallery consists of still facial ....

....of the vector space. The task of face recognition is then to nd the closest matches in this face subspace. However, PCA might not be ecient in terms of recognition accuracy since the construction of the face subspace does not capture discrimination between humans. This motivates the use of LDA [11,10] and its variants. In LDA, the linear subspace is constructed [17] in such a manner that the within class scatter is minimized and the between class scatter is maximized. This idea is further generalized in the approach called Bayesian face recognition [18] where intra personal space (IPS) and ....

K. Etemad, R. Chellappa, Discriminant analysis for recognition of human face images, Journal of Optical Society of America A (1997) 1724-1733.

....[3] for reports on experiments. Experiments reported in [3] evaluate still to still scenarios, where the gallery and the probe set consist of both still facial images. Some well known still to still FR approaches include Principal Component Analysis (PCA) 9] Linear Discriminant Analysis (LDA) [10, 11], and Elastic Graph Matching (EGM) 12] Typically, recognition is performed based on an abstract representation of the face image after suitable geometric and photometric registrations. Following [3] we de ne a still to video scenario: the gallery consists of still facial templates and the ....

....face moving naturally, giving rise to signi cant variations across poses. However, the proposed method successfully copes with these pose variations as evidenced by the experimental results. It is worth emphasizing that (i) our model can take advantage of any still to still recognition algorithm [9, 10, 11, 12] by embedding distance measures used therein in our likelihood measurement; and (ii) it allows a variety of image representations and transformations. The organization of the paper is as follows: Section 2 reviews some related studies on video based FR recognition in the literature. Section 3 ....

Etemad, K. and Chellappa, R. (1997), Discriminant Analysis for Recognition of Human Face Images, Journal of Optical Society of America A, 1724-1733.

....for experiments on face recognition. Experiments reported in [9] evaluate still to still scenarios, where the gallery and the probe consist of both still facial images. Some well known still to still FR approaches include Principal Component Analysis (PCA) 10] Linear Discriminant Analysis (LDA) [11, 12], and Elastic Graph Matching (EGM) 13] Typically, recognition is performed based on an abstract representation of an image after suitable geometric and photometric normalizations are performed. Following [9] we define the gallery and probe as follows: the gallery consists of still facial ....

K. Etemad and R. Chellappa, "Discriminant analysis for recognition of human face images," Journal of Optical Society of America A, pp. 1724--1733, 1997.

....on the a posteriori probability of membership in the intra personal class. Performance improvement of this probabilistic matching over the eigenface approach was demonstrated. Face recognition systems using Linear Fisher Discriminant Analysis [55] as the classifier have also been very successful [56, 57, 58, 59, 60, 61, 62, 63]. LDA training is carried out via scatter matrix analysis [64] For an M class problem, the within and between class scatter matrices Sw , S b are computed as follows: Sw = M X i=1 Pr( i )C i ; 8) S b = M X i=1 Pr( i ) m i Gamma m 0 ) m i Gamma m 0 ) T (9) where Pr( i ) is the ....

....ten algorithms: ffl An algorithm from Excalibur Corporation (Carlsbad, CA) Sept. 1996) ffl Two algorithms from MIT Media Laboratory (Sept. 1996) 44, 169] ffl Three Linear Discriminant Analysis based algorithms from Michigan State University [56] Sept. 1996) and the University of Maryland [59, 60] (Sept. 1996 and March 1997) ffl A gray scale projection algorithm from Rutgers University [170] Sept. 1996) 30 ffl An Elastic Graph Matching algorithm from the University of Southern California [79, 171] March 1997) ffl A baseline PCA algorithm [44, 172, 173] ffl A baseline normalized ....

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K. Etemad and R. Chellappa, "Discriminant Analysis for Recognition of Human Face Images," Journal of the Optical Society of America A, Vol. 14, pp. 1724-1733, 1997.

....solving the generalized eigenvalue problem [10] S b W = SwW (5) The distance measure used in the matching could be a simple Euclidean, or a weighted Euclidean distance. It has been suggested that the weighted Euclidean distance will give better classification than the simple Euclidean distance [8], where the weights are the normalized versions of the eigenvalues defined in (5) But it turns out that this weighted measure is sensitive to whether the corresponding persons have been seen during the training stage or not. To account for this, we devised a simple scheme to detect whether the ....

....for this, we devised a simple scheme to detect whether the person in the testing image has been trained or not and then use either a weighted Euclidean distance or a simple Euclidean distance respectively. 2. 2 LDA of Principal Components Both PCA and LDA have been used for face recognition [5, 6, 7, 8, 15, 16, 11]. With PCA, the input face images usually needed to be warped to a standard face because of the large within class variance [6, 7] This preprocessing stage reduces the within class variance dramatically, thus improving the recognition rate. We first built a simple system based on pure LDA [8] ....

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K. Etemad and R. Chellappa, "Discriminant Analysis for Recognition of Human Face Images," Journal of Optical Society of America A, pp. 1724-1733, Aug. 1997.

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Etemad, K. and Chellappa, R. 1997. Discriminant Analysis for Recognition of Human Face Images. Journal of the Optical Society of America A, Vol. 14, pp. 1724-1733.

....individuals, whereas in verification problems, the system needs to confirm or reject the claimed identity of the input face. Many methods have been proposed for face recognition [2] 1] Basically they can be divided into holistic template matching based systems [7] 9] 8] 11] 34] 4] [10] and geometrical local feature based schemes [25] 12] Even though both types of systems have been successfully applied to the task of face recognition, they do have certain advantages and disadvantages. Thus appropriate schemes should be chosen based on the specific requirements of a given ....

....subspace LDA face recognition system ID) D. 1 Distance Measure for Subspace LDA: Weighted or Unweighted For the pure LDA distance measure, it has been suggested that the weighted Euclidean distance will give better classification than simple Euclidean distance in the context of face recognition [10], where the weights are the normalized eigenvalues defined in (5) But it turns out that this weighted measure is sensitive to whether the corresponding persons have been seen before during the training stage and need some additional treatment [4] Thus the preferred distance measure is the ....

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K. Etemad and R. Chellappa, "Discriminant Analysis for Recognition of Human Face Images, " Journal of the Optical Society of America A, Vol. 14, pp. 1724-1733, 1997.

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Etemad, K., Chellappa, R.: Discriminant analysis for recognition of human face images. Journal of the Optical Society of America A-Optics Image Science and Vision 14 (1997) 1724--1733

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K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. J. Opt. Soc. Am. A, 14:1724--1733, 1997.

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K. Etemad and R. Chellappa, "Discriminant analysis for recognition of human face images," Journal of the Optical Society of America A, vol. 14, pp. 1724--1733, 1997.

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K. Etemad and R. Chellappa, "Discriminant analysis for recognition of human face images," J. Opt. Soc. Amer. A, vol. 14, pp. 1724--1733, 1997.

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K. Etemad and R. Chellapa, "Discriminant analysis for recognition of human face images", Journal of Optical Socieaty of American A 14(8): 1724-1733, 1997.

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K. Etemad and R. Chellappa, "Discriminant analysis for recognition of human face images," J. Opt. Soc. Amer. A, vol. 14, pp. 1724--1733, 1997.

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K. Etemad and R. Chellappa, "Discriminant analysis for recognition of human face images," J. Opt. Soc. Am. A, vol. 14, pp. 1724--1733, 1997.

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K. Etemad and R. Chellappa, "Discriminant analysis for recognition of human face images," J. Opt. Soc. Am. A, vol. 14, pp. 1724--1733, 1997. 19

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K. Etemad and R. Chellappa, "Discriminant analysis for recognition of human face images," J. Opt. Soc. Am. A, vol. 14, pp. 1724--1733, 1997.

No context found.

K. Etemad and R. Chellappa, "Discriminant analysis for recognition of human face images," J. Opt. Soc. Am. A, vol. 14, pp. 1724--1733, 1997.

No context found.

K. Etemad and R. Chellappa, "Discriminant analysis for Recognition of Human Face Images," Journal of Optical Society of America A, pp. 1724-1733, Aug., 1997

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K. Etemad and R. Chellappa. Discriminant analysis for recognition of human face images. In Proceedings of the International Conference on Acoustics, Speech and Signal Processing, pages 2148--2151, 1994.

No context found.

K. Etemad and R. Chellappa, "Discriminant analysis for recognition of human face images," Journal of the Optical Society of America, vol. 14, pp. 1724--1733, 1997.

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K. Etemad and R.Chellappa, "Discriminant Analysis for Recognition of Human Face Images," In Proc. of AVBPA'97, pp. 127-142, 1997.

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