Multimodal Face Recognition Using

Multidimensional Clustering on Hyperspectral Face

Images

Dr. Vinayak Ashok Bharadi

Associate Professor, Head of Department- IT,

TCET, Mumbai University

Mumbai, India

Vinayak.bharadi@thakureducation.org

Ms. Payal Mishra, Mr.Bhavesh Pandya

Research Scholar, IT Department

Mumbai University

Mumbai, India

payalmishra28@gmail.com

Abstract— Human face is a very common biometric trait, with

advancement of technology it is possible to capture face images in

hyperspectral range. With the availability of such hyperspectral

face data it is possible to build systems biometrics authentication

systems working in hyperspectral range. Main focus current

research is to use hyperspectral face images for biometric

authentication. Hyperspectral face images with 33 band are used

for generation of feature vector based on Vector Quantization

(VQ) process. Popular VQ Algorithms like Kekre’s Fast Codebook

Generation (KFCG) Algorithm and Kekre’s Median Codebook

Generation (KMCG) Algorithm are used to generate codebooks.

This feature vector is used for identification of the person. K-

Nearest Neighborhood classifier (K-NN) is be used and

performance is evaluated. Here the study is extended for

Multimodal Implementation also, by combining Left, Right face

samples feature vectors. The score fusion technique is

implemented on front, left and right face images and the effect of

fusion is studied.

Keywords— Biometrics, Kekre’s Fast Codebook Generation,

Kekre’s Median Codebook Generation, K-Nearest Neighborhood

classifier, Hyperspectral images.

I. INTRODUCTION

Human body is a great gift to us, as it is unique and no other human is having the same characteristics as we have, even in the identical twins there is very minute differentiating points are present. This fact is used for the design of biometric authentication systems [1][2][3]. Biometric authentication is becoming ubiquitous, with the increasing requirement of security in the public and private premises. The technology has also advanced and new types of cost effective and efficient hardware is available. This has triggered exponential growth of the biometric authentication systems. Biometric systems can support re-designing of business processes, helping corporates to grow and reducing burdens on stressed public sector frameworks so they can be more productive for constituents; and biometrics can do all this, not at the cost of user’s confidentiality, but rather by respecting their confidentiality.

Biometric systems are in operation for decades, fingerprint, palm-print, face, handwritten signature are some of the oldest used biometric traits [2], [3]. In the recent years, with the development of new types of sensors biometric traits such as Infrared face, facial thermogram, 3D face, Finger-Knuckle

prints, hand vein geometry, online signature etc. are being implemented. Hyperspectral imaging have been in use for a long time, mainly for geo sensing purpose, in this paper the use of hyperspectral imaging in face recognition domain is studied.

A. Face Recognition

Face based biometrics have found their widespread deployment in public premises such as airports, railway stations etc. as it requires least user cooperation. Face recognition is explored for many years but with recent development in electronics devices technology have fuelled the growth of the sector. New research for algorithm developments encouraged by reducing prices of sensors and higher computing power has made the face based biometrics feasible in practical scenario. These systems are increasingly being positioned in a wide range of practical applications, and upcoming improvements promise to spread the use of face recognition. Face biometrics is relatively less accurate but requires low user co-operation. With advancement in technology variations such as facial thermogram (temperature distribution on a face) and 3D face mapping are also being implemented [2].

With advancement of technology newer methods such as 3D face, Facial Thermogram, IR Imaging and Hyperspectral Imaging are used with conventional biometric systems for improving accuracy [2],[6],[7]. Hyperspectral images contain a lot amount of data, but extracting Information out of this data requires an understanding of exactly what properties of the source are being measured, and how they connect to the measurements by the hyperspectral sensor.

B. Hyperspectral Images

Multispectral and hyperspectral imaging can get a set of spatially co-registered images at spectrally-contiguous wavelengths, this method was first used for remote sensing purpose [3], and now widely used in agriculture, forest, mineral, exploration and environment exploration[3],[4],[5]. Hyperspectral imaging can obtain the essential spectral details of the skin at various minute wavelengths, adding to the spatial information, which may reveal the skin details in proportion of reflected, absorbed and emitted electromagnetic energy. It can capture distinguishing personal identification patterns based on their molecular configurations that relates to tissue, blood, and structure, this clues to the possible application of hyperspectral

imaging to face biometrics, and has the capability to surpass the problems in conventional face recognition, such as the changes of face positions and expression. Near infrared spectrum face images have been used by Wei Di, Lei Zhang et. al. in[7], [8], Figure below shows a set of 33 hyper spectral face bands. Fig. 1 shows a set of hyperspectral face images from Honk Kong Polytechnic University’s Hyperspectral face database [7].

Fig. 1. Illustration of a set of 33 hyperspectral face bands [7],[8].

II. LITERATURE SURVEY

Face biometric is the biometric coming under both the physiological and behavioral classes. While the physiological part of the face biometric has been widely investigated by the scientists, the behavioral (related to emotions on face) part is not yet fully investigated. In addition, as described in [1] face has benefit over other biometrics due to being natural, non-intrusive, and easy-to-use biometric. For example, midst the biometrics of hand, finger, finger-knuckle, face, voice, eye, DNA and handwritten-signature, the facial biometric grades first in the compatibility assessment of a machine readable travel document (MRTD) system pertaining to of six standards [6]: enrollment, renewal, machine assisted identity verification requirements, redundancy, public discernment, and data storage requirements and performance.

Many face based biometric systems have been explored in the past years. A large number of techniques are appearance based. Numerical techniques, such as PCA [9], LDA [10], ICA [11], and Bayes [12], etc., are used to extract low dimensional features from the greyscale face image directly for identification. A main issue of the light conditions and facial expression changes since they require position of uniformly illuminated object image to take benefit of the correlation among different samples.

To generate a codevector histogram; vector quantization of face has been used by Kotani and Quiu [13], the codebook is defined as a 33different variation in grey levels. They generated a codevector histogram and used it for matching. This method performs well for grey level intensity variations. Average recognition rate was 97%. DCT was also used for face recognition by Ekenel Stiefelhagen[14], they explored local

information by using block-based DCT. DCT has been used for feature extraction in various instances on face biometrics systems. So far, either DCT features have been used in a universal appearance-based sense [15], or localized appearance based sense that disregards spatial information during the classification phase. Pan and Bolouri [16] used the DCT coefficients obtained from the image blocks; which are given as an input to a MLP Neural Network, Sanderson & Paliwal [17] used the local DCT coefficients that are modeled with GMM, Scott [18] proposed a network of networks (NoN) model which is driven by DCT coefficients input. Kekre & Shah used Kekre’s transform coefficients of face for recognition purpose [19], Kekre transform is an orthogonal transform and gave faster computations. In another approach Kekre et al. [20],[22] used novel VQ algorithm, they have used Kekre’s Median Codebook Generation Algorithm (KMCG) for generating feature vector. The performance of the proposed method is compared with the well-known face recognition method based on Discrete Cosine Transform (DCT). From the results it is observed that the proposed method gives 92.67 % accuracy as compared to DCT. Further it was observed that KMCG is much faster than DCT. Another approach [21] is based on Wavelet Energy of face, we have used Kekre’s wavelet to generate energy based feature vector and compared performance with Haar wavelets. Researchers at Hong-Kong Polytechnic university have developed sensors for capturing the face images in multispectral band, the images were captured in 33 different bands [24], W. Di, L Zang et. al. [25] proposed a feature band selection based approach in visible spectrum for hyperspectral face recognition.

Vector Quantization has been used for Data and Image compression for a long time [20],[21],[22],[23]. Image compression is a rapid and energetically changing field with many different diversities of compression methods available. Image compression using Vector Quantization (VQ) has received great attention in the last decades because it‘s encouraging compression ratio and relatively simple structure. This analyzes the image as a two dimensional signal and takes advantage of redundancies associated with the human visual system. Vector Quantization (VQ) can be used as data reduction technique for the encoding of facial images.

The technique most frequently used to produce codebook is the Linde-Buzo-Gray (LBG) algorithm. We are using Kekre’s median codebook generation algorithm (KMCG) [23],[26] & Kekre’s fast codebook generation algorithm (KFCG) [22],[24] for face recognition. In this paper the KFCG and KMCG [20],[21],[22],[23] based approach is extended for hyperspectral face data. This technique is explain in coming section.

III. PROPOSED TECHNIQUE

Automatic face recognition is an appealing solution for the problem of automatic personal identification systems. In order to provide a cost effective approach, high levels of data reduction are required when storing the facial information. Image compression using Vector Quantization (VQ) has established great focus in the last decades because it‘s promising compression ratio and relatively simple structure [20], [22]. The proposed architecture is shown in Fig. 2,

Fig. 2. Architecture of the proposed system.

A. Explanation of Block Diagram

In this architecture of the proposed system Pre-Processing

block is used to accept the hyperspectral face image data. The

PolyU Hyperspectral Face Database [24] is used for current

research. The database has face images with 33 frequency

bands. These instances of the image are taken at 33 different

frequencies. Front, Left and Right side face images are

captured. These images are stored in Hypercube MAT [22],

[25] format, they are also called as ‘Facecubes’.

Vector Quantization using KFCG & KMCG is performed on

this data. In [20],[22],[27] authors have used VQ on color image

data, these color image has R,G & B planes, but the

hyperspectral face has 33 bands or planes, hence to apply VQ

and reduce the overall dimension these 33 bands are grouped to

form sub-bands.

These 33 instance (bands) are been grouped into 11 sub-bands,

where each sub-bands contains 3 Frequencies. Then the Kekre’s

Fast Codebook Generation (KFCG) Algorithm and Kekre’s

Median Codebook Generation (KMCG) Algorithm is used in

order to generate code book for each sub-band. The procedure

discussed in [23] is applied on these sub-bands. This process

generates KFCG & KMCG Codebook for each sub-band, such

11 sub-bands are there.

All the codebooks combined together form the Feature Vector

of the Hyperspectral face. This Feature Vector is stored in the

database. Distance between two faces can be evaluated by

evaluating the Euclidean Distance between the KFCG &

KMCG codebooks of the Hyperspectral face data. Final step is

to analyze the performance of the proposed technique for

biometric authentication. FAR, FRR analysis as well as CCR

evolution will be performed on above feature vector. This data

is used to design a K-NN classifier to classify input data.

B. Proposed Algorithm For Feature Vector Generation

To generate the Feature vector the process is as follows.

Step 1: Firstly read MAT file and its face cubes, this gives a composite Array for 33 Bands of the Facecubes data.

Step 2: Read each image band data. T total 33 Bands of the face image are available. These bands of the face image are taken at 33 different frequencies (as shown below). Each image is of 180*220 Pixel size [23]. Perform Normalization on the data, so that the grey levels are in-between (0-255).

Step 3: Then these images are grouped into eleven sub-bands of three images each. This is shown in Fig. 3. Use the procedure discussed in [20], [21], [22].

For the generation of Codevectors, group 4 pixels together to form the Codevectors. Each sub-band is having 12 elements i.e

Codevector= (P11,P12,P13,P14),(P21,P22,P23,P24),(P31,P32,P33,P34),(P41,P42,P43,P44).

So the total number of Codevectors will be

No. of Codevectors = {[180*220]/4}*3

Generate all the codevectors from the subbands.

Step 4: Now Kekre’s Fast Codebook Generation (KFCG) Algorithm and Kekre’s Median Codebook Generation (KMCG) Algorithm is used in order to generate code book for each sub-band. Perfrom VQ to generate a codebook of size of 128 Codevectors.

So we are having total 12 dimensions in a codevector and such 128 codevectors each for 11 sub-bands, hence after applying KFCG and KMCG total size of codebook will be 11*128*12 elements.

Step 5: So for 3 faces we will be having 11*128*12*3 for KFCG and 11*128*12*3 for KMCG. This is for Front Left & Right instance of the hyperspectral face. Fig 4 shows such a sample.

Step 6: These codebook are the feature vectors of the hyperspectral face. In the database Front, Left and Right instances of the same face are captured. If these instances are considered to build a Multi-instance face recognition system then the same procedure is applied for them and final set of codebooks is extracted and stored in the database.

Fig. 3. Sub Bands Formation for VQ on Hyperspectral Face Data .

IV. RESULT AND DISCUSSION

The results are discussed in two aspects, first the dimensionality reduction and then the classification ability of the feature vector is discussed.

A. Dimensionality Reduction

The KFCG & KMCG based vector quantization provides huge

dimensionality reduction. This can be evaluated as follows

Calculating Actual Image Data Size:

Total 33 Bands with Image size of 180*220 Pixels:

1306800 Pixels, with 1 byte of data each.

After Vector Quantization:

Single Codebook Size for One Sub Band = 12*120 Elements

Such 11 Sub bands are there hence: 11*12*128

Total Elements in a codebook: 16896 of 1 byte of data each.

Hence the ratio (RD) by which the dimensionality is reduced is: RD =1306800/16896 = 77.343.

This is just for the give the idea that, by what size the size of codebook is less than the actual data. Evaluation metrics such as False Acceptance Rate (FAR), False Rejection Rate (FRR), Security Performance Index (SPI) and Performance Index (PI) are evaluated here for comparison purpose.

B. Euclidean Distance evaluation for classification

The PolyU HSFD [22] is used for testing for the proposed

method. Some of the subjects used for feature vector extraction,

intra & inter class matching are shown in Fig. 4. The feature

vectors are evaluated and stored in the database. When distance

between two samples of same user is evaluated, it is called intra

-class test and when it is performed on feature vectors of

different users, it is called inter-class testing. Distance between

feature vectors of faces of same user should be less than that of

different users, on this fact we build the classifier. In fig. 6

shows the performance index and security performance index

for KFCG and KMCG front face sample.

Security Performance Index (SPI) – This is a new parameter

proposed by Dr. H. B. Kekre [25], this parameter indicates how

fast the Equal Error Rate (EER) is achieved. In Fig. 5 a typical

FAR-FRR curve, the EER is given by crossover point. The Line

AB shows the distance at which FAR has started increasing and

the Line AC indicates the optimum possible FAR & FRR

achieved by the system. If the threshold corresponding to AC is

higher the EER will be achieved in slower way or delayed

resulting higher FAR. So in IDEAL case it should be low and

quickly achieved resulting in AB=AC. We define the Security

Performance index as,

SPI= AB/AC (1)

Ideally SPI = 1 (or 100%), SPI can be used to compare the

performance of Biometric Authentication Systems when two

system have equal EER. System with higher SPI is having

better performance. We evaluate the SPI of the different

feature vectors.

Fig. 4. Hyperspectral Face Samples (Front, Left & Right) used for Intra &

Inter Class Distance Evaluation [22] .

It can be seen that the Intra Class Euclidean distance between

KFCG & KMCG Codevectors for the front faces (F-KFCG &

F-KFCG) is same 70% and the SPI is Max 68% of F-KMCG

and Min 54% of F-KFCG. Fig 7. Shows the FAR- FRR analysis

for KFCG and KMCG front face feature vector

Fig. 5. A Typical FAR vs. FRR Plot Showing Crossover (ROC Curve)

For F-KFCG the FAR-FRR analysis is EER achieved is 30%,

Performance Index is 70% and Security Performance Index is

54%. For F- KMCG the FAR-FRR analysis is EER achieved is

30%, Performance Index is 70% and Security Performance

Index is 68%.

(a)

(b)

Fig. 6. PI and SPI for KFCG and KMCG Front Face sample.

So it is clearly seen that the KMCG front face feature vector is

better than KFCG face feature vector. This analysis can be

further performed on Left & Right face samples of the same

user and its PI and SPI can be evaluated. Future the analysis can

also be performed for multimodal system by combining Front,

Left and Right face sample for both KFCG and KMCG to

improve the accuracy of the system. This will be a multi-

instance biometric system, Table I shows the summary of

results. In the next section paper is concluded.

TABLE I. COMPARISON OF PERFORMANCE PARAMETRS

Sr.

Feature

Vector

Type

PI SPI Whole

Band

2D PCA

[25] PI KFCG KMCG KFCG KMCG

1 Front 70 70 54 68

(CCR)

55-75

2 Left 72 73 41 66

3 Right 68 74 28 66

4 Left + Right 72 74 33 67

5 Front + Left +

Right 73 77 33 66

Lower the EER or Higher the PI indicates that the system is

more accurate. Generally physiological biometric traits are

more accurate than behavioral biometrics [25]. These

parameters are specified as follows, proposed system has

achieved PI of 70%. The Recognition Rate achieved by Wei Di,

D. Zang et.al. [25] is in the range of 58-78%. The projected

recognition rate of the system is in the range of 65-69%. In [25]

authors have done separate study on each bands but here the

proposed technique is extracting feature vector form 33 bands

collectively.

0102030405060708090

100

0 5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95

10

0

10

5

11

0

FRR

FAR

FAR vs FRR Plot

% R

ate

Distance Threshold

EER (CER) = 22%

PI= 78%AB

AC

SPI = AB/AC = 59%

7072

68

72 7370

73 74 7477

Front Left Right Left + Right Front + Left+ Right

Performance Index (PI) Comparison for Various Level of Fusion

KFCG KMCG

54

41

2833 33

68 66 66 67 66

0

20

40

60

80

Front Left Right Left + Right Front + Left+ Right

Security Performance Index Comparison

KFCG KMCG

(a) FAR-FRR plot for F-KFCG face feature vector

(b) Genuine & Forgery plot for F-KFCG feature vector

(c) FAR-FRR plot for F-KMCG face feature vector

(d) Genuine & Forgery plot for F-KFCG feature vector

Fig. 7. FAR-FRR plot analysis and Genuine- Forgery plot analysis for KFCG & KMCG Front Face feature vector

0

20

40

60

80

100

1 4 7

10

13

16

19

22

25

28

31

34

37

40

43

46

49

52

55

58

61

64

67

70

73

76

79

82

85

88

91

% R

ATE

THRESHOLD

F A R - F R R P L O T F O R K F C G F R O N T F A C E F E A T U R E V E C T O R

FAR FRR

EER = 30%PI = 70%SPI = 54%

-10

10

30

50

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91

PR

OB

AB

ILIT

Y

THRESHOLD

G E N U I N E & F O R G E R Y P L O T F O R K F C G - F R O N T F E A T U R E V E C T O R

Genuine Distance Forgery Distance

0102030405060708090

100

1 4 7

10

13

16

19

22

25

28

31

34

37

40

43

46

49

52

55

58

61

64

67

70

73

76

79

82

85

88

91

94

97

10

0

10

3

% R

ATE

F A R - F R R V S T H R E S H O L D P L O T F O R K M C G F R O N T F A C E F E A T U R E V E C T O R

FRR FAR

EER = 30%PI =70%SPI =68%

0

5

10

15

20

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

PR

OB

AB

ILIT

Y

G E N U I N E & F O R G E R Y P L O T F O R K M C G - F F E A T U R E V E C T O R

Genuine Distance Forgery Distance

V. CONCLUSION

In this research Vector quantization based Feature Vector

Generation for hyperspectral Face Recognition system is

proposed. Clustering on hyperspectral face bands is reducing

the feature vector size, comparative number of computations.

This is the main practical contribution. Theoretically KFCG and

KMCG are tested as feasible means of vector quantization on

hyperspectral image data.

Table I shows the performance of system compared with the

existing system. The system is tested on data collected, and has

given PI of Max 77% for KMCG Front, Left and Right and Min

of 73% for KFCG Front, Left and Right. Also the SPI of Max

68% for KMCG Front and Min 54% for KMCG Front is

evaluated. The results clearly indicate that the security

performance index of KMCG and KFCG Front is better than

that of Left, Right, Left + Right, Front + Left + Right. The

performance index of KFCG and KMCG Front + Left + Right

is better than other feature vector type. As compared with the

existing technique [25] where three experiment are performed

using the technique, whole band (2D)2PCA, single band

(2D)2PCA which is using decision level fusion, as well as band

subset fusion based (2D)2PCA where the performance is Max

75 and Min 55. However following are some of the issues faced

during the research.

1. The hyperspectral database has less number of samples, the

proposed algorithm needs more samples for better estimation of

performance parameters.

2. The proposed technique is performing VQ on 33 bands of the

hyperspectral data, this is computationally heavy, needs faster

processor and large memory.

3. In the current research a simple K-NN Classifier is used, this

gives sub-optimal performance.

Following are some directions for future work

1. Better design of classifier – a neural network or support

vector machine based can be used and better performance can

be achieved.

2. This is a clustering based approach, other approach such as

texture feature extraction based feature vector generation can

be used. Transforms and wavelets can be used for this purpose.

3. This methodology can be tested on other hyperspectral face

database and performance can be compared.

REFERENCES

[1] History of Biometrics, A report by National Science & Technology Council, Aug 2006

[2] J.D. Woodward, Jr.Nicholas M. Orlans, P. T. Higgins,

"Biometrics", McGraw-Hill/Osborne,ISBN-0-07-222227-1, DOI:10.1036/0072230304, 2003

[3] A. Goetz, G. Vane, J. Solomon, B. Rock, “Imaging spectrometry for earth remote sensing”, Science, vol.228, no. 4704,pp.1147-1153, Jun. 1985.

[4] D. Landgrebe, “Hyperspectral image data analysis”, IEEE Signal Processing Magazine, vol.19, no.1, pp. 17-28, Jan. 2002.

[5] G. Shaw, D. Manolakis, “Signal processing for hyperspectral image exploitation”, IEEE Signal Processing Magazine, vol.19, no.1, pp. 12-16, Jan. 2002.

[6] Hietmeyer R., "Biometric Identification Promises Fast and Secure Processing of Airline Passengers," The International Civil Aviation Organization Journal, Vol. 55, No. 9, pp. 10- 11,2000

[7] PolyUHSFD,“,http://www.comp.polyu.edu.hk/~biometrics/hyper_face.htm”

[8] Wei Di, Lei Zhang, David Zhang, and Quan Pan “Studies on Hyperspectral Face Recognition in Visible Spectrum with Feature Band Selection” IEEE Trans. on System, Man and Cybernetics, Part A, vol. 40, issue 6, pp. 1354 – 1361, Nov. 2010

[9] M. Turk and A. Pentland, "Eigenfaces for Recognition", Journal of Cognitive Neuroscience, Vol. 3, No. 1, pp. 71-86, 1991

[10] P. N. Belhumeur, J. P. Hespanda, D. J. Kiregeman, “Eigenfacesvs. Fisherfaces: Recognition Using Class Specific LinearProjection‖”, IEEE Transactions on Pattern Analysis & Machine Intelligence, Vol. 19, No. 7, pp. 711-720, July 1997

[11] P. C. Yunen, and J. H. Lai, ―Face Representation Using Independent Component Analysis‖, The Journal of Pattern

Recognition, Vol. 35, pp. 1247-1257, 2002

[12] B. Moghaddam, T. Jebara, A. Pentland, ―Bayesian Face Recognition‖, Journal of Pattern Recognition, Vol. 33,No. 1, pp.1771-1782,2000.

[13] K. Kotani, Q. Chen, T. Ohmi, ―Face Recognition Using Vector Quantization Histogram Method‖, IEEE 2002 Int. Conference on Image Processing, pp. 105–108, 2002

[14] H. K. Ekenel, R. Stiefelhagen "Local Appearance-Based Face Recognition Using Discrete Cosine Transform", 13th European Signal Processing Conference, pp.100-110, 2005

[15] Hafed Z., Levine M., "Face Recognition Using The Discrete Cosine Transform", International Journal of Computer Vision -Special issue: Research at McGill ,Vol. 43, No.3, 2001

[16] Pan Z., Bolouri H., "High Speed Face Recognition Based on Discrete Cosine Transforms and Neural Networks", Technical report, University of Hertfordshire, 1999.

[17] Sanderson C., Paliwal K., "Features for robust face-based identity verification", Journal on Signal Processing, Vol. 83, No.5, May 2003

[18] Willie L. Scott, ―Block-Level Discrete Cosine Transform Coefficients for Autonomic Face Recognition‖, Ph.D. Thesis Submitted to Graduate Faculty of Louisiana State U. and Agricultural and Mechanical Collage , USA, May 2003

[19] H. B. Kekre, K. Shah, “Face Recognition Using Orthogonal Transforms and Vector Quantization Techniques‖”, Ph.D. Thesis submitted to NMIMS University, June 2010

[20] H. B. Kekre, T. K. Sarode, V. A. Bharadi, T. Bajaj, S. Chatterjee ,M. Bhat, K. Bihani, "A Comparative Study of DCT and Kekre‘s Median Code Book Generation Algorithm for Face Recognition", ICWET '10 Proceedings of the International Conference and Workshop on Emerging Trends in Technology, pp. 343-348, Feb. 2010

[21] H. B. Kekre, V. A. Bharadi, "Face Recognition using Kekre‘s Wavelets Energy & Performance Analysis of Feature Vector Variants", Proceedings of ACM International Conference ICWET2011, Mumbai, India, Vol. 1, pp.39-45, Feb. 2011

[22] PhD Thesis of Dr. Tanuja Sarode on "Vector Quantization", Submitted to NMIMS University, Mumbai, pp.28-49, June 2010

[23] H.B. Kekre, T. K. Sarode, "An Efficient Fast Algorithm to Generate Codebook for Vector Quantization," ICETET 2008 First IEEE International Conference on Emerging Trends in Engineering and Technology,pp.62-67, 2008

[24] PolyUHSFD,“,http://www.comp.polyu.edu.hk/~biometrics/hyper_face.htm”

[25] Wei Di, Lei Zhang, David Zhang, and Quan Pan “Studies on Hyperspectral Face Recognition in Visible Spectrum with Feature Band Selection” IEEE Trans. on System, Man and Cybernetics, Part A, vol. 40, issue 6, pp. 1354 – 1361, Nov. 2010

[26] H B kekre, V A Bharadi, V I Singh, Dynamic Signature Recognition using Hybrid Wavelets: Multidimensional Feature Vector Analysis using Hybrid Wavelets Type I & II, LAMBERT Academic Publishing GmbH & Co. KG, www.lap-publishing.com, ISBN : 978-3-659-49721-6

[27] V A Bharadi, “Biometric Authentication Systems”, PhD Thesis Submitted to NMIMS University, Dec 2011