leif e. peterson* kirill v....

Int. J. Knowledge Engineering and Soft Data Paradigms, Vol. 1, No. 3, 2009 239

Copyright © 2009 Inderscience Enterprises Ltd.

Image classification of artificial fingerprints using Gabor wavelet filters, self-organising maps and Hermite/Laguerre neural networks

Leif E. Peterson* Center for Biostatistics, The Methodist Hospital Research Institute, 6565 Fannin Street, Suite MGJ6-031, Houston, Texas 77030, USA E-mail: [email protected] *Corresponding author

Kirill V. Larin Biomedical Optics Laboratory, Biomedical Engineering Program, University of Houston, 4800 Calhoun Road, N207 Engineering Bldg. 1, Houston, Texas 77204, USA E-mail: [email protected]

Abstract: Image classification was performed using Gabor wavelet filters for image feature extraction, self-organising maps (SOM) for dimensional reduction of Gabor wavelet filters, and forward (FNN), Hermite (HNN) and Laguerre (LNN) neural networks to classify real and artificial fingerprint images from optical coherence tomography (OCT). Use of a SOM after Gabor edge detection of OCT images of fingerprint and material surfaces resulted in the greatest classification performance when compared with moments based on colour, texture and shape. The FNN and HNN performed similarly, however, the LNN performed the worst at a low number of hidden nodes but overtook performance of the FNN and HNN as the number of hidden nodes approached n = 10.

Keywords: Hermite neural networks; HNN; Laguerre neural networks; LNN; self-organising maps; SOM; Gabor wavelet filters; image classification.

Reference to this paper should be made as follows: Peterson, L.E. and Larin, K.V. (2009) ‘Image classification of artificial fingerprints using Gabor wavelet filters, self-organising maps and Hermite/Laguerre neural networks’, Int. J. Knowledge Engineering and Soft Data Paradigms, Vol. 1, No. 3, pp.239–256.

Biographical notes: Leif Peterson received his BSc in Nuclear Medicine from Ferris State University in 1981, MPH in Radiological Physics from University of Michigan in 1986 and PhD in Epidemiology and Biostatistics from University of Texas in 1994. He is currently an Associate Professor of Public Health at Weill Cornell Medical College and the Director of the Centre for Biostatistics, The Methodist Hospital Research Institute, Houston. His research interests include machine learning and computational intelligence in bioinformatics, oncology and cardiovascular disease.

240 L.E. Peterson and K.V. Larin

Kirill Larin received his MSc in Laser Physics and Mathematics from Saratov State University (Saratov, Russia) in 1995, MSc in Cellular Physiology and Molecular Biophysics in 2001 and PhD in Biomedical Sciences and Biomedical Engineering from the University of Texas Medical Branch, Galveston in 2002. He is currently an Assistant Professor of Electrical and Computer Engineering, and the Director of the Biomedical Optics Laboratory, Department of Mechanical Engineering, Cullen College of Engineering, University of Houston. His interests cover development of new methods for tissue functional imaging (based on optical coherence tomography) and protein biosensing (based on nano-optics).

1 Introduction

Identity detection via machine learning techniques is a rapidly growing focus in the development of security systems. Commonly used biometric techniques include behavioural characteristics such as keystroke and signature dynamics, physical characteristics such as iris, face and fingerprint recognition. Among all biometric techniques, fingerprint recognition is the most popular method (Prabhakar et al., 2003) and has the following advantages:

1 universality – the size of the population with legible fingerprints exceeds the size of the population with passports

2 high distinctiveness – even identical twins who share the same DNA have different fingerprints

3 high performance – fingerprints are one of the most accurate biometric characteristics with low false positive and false negative rates.

At the age of seven months, a fetus’s fingerprints are fully developed and fingerprint characteristics do not change in the absence of injury or skin disease. However, after a small injury to a fingertip, the pattern will grow back as the fingertip heals (Maltoni et al., 2003). The uniqueness of fingerprints can be determined by the pattern of minutia locations, local ridge orientation data and combination of ridge orientation and minutia locations (Vizcaya and Gerhardt, 1996). Therefore, fingerprint recognition has become a reliable method of personal identification.

At present, the FBI maintains more than 200 million fingerprint records on file. However, artificial finger dummies with embedded fingerprints constructed with household materials may easily spoof fingerprint systems (Matsumoto et al., 2002). Therefore fingerprint recognition systems need to be improved to minimise fraudulent methods. Over the last few years, substantial improvements have been made by several groups enhancing the robustness of fingerprint readers based on the recognition of the surface topology. Smart-card authentication systems, which merge fingerprint verification with personal identification number (PIN) verification by applying a double random phase encoding scheme, was described in Suzuki et al. (2006). By using an optimised template for core detection, the false rejection rate (FRR) was improved. Making use of a fast fingerprint enhancement algorithm, which could adaptively improve the clarity of ridge and valley structures of the input fingerprint images (based on the

Image classification of artificial fingerprints using Gabor wavelet filters 241

estimated local ridge orientation and frequency), a goodness index and verification accuracy could also be improved (Lin et al., 1998). However, these improvements in fingerprint recognition methods focused on decreasing FRR and false acceptance rate (FAR) and shortening scanning time, which do not prevent system bypass via artificial fingerprints.

Since the introduction of interferometric low-coherence methods in the late 1980s (Huang et al., 1991), the optical coherence tomography (OCT) technique has been widely applied in different fields, such as medical imaging diagnostics and material sciences. A typical time-domain OCT system is based on the Michelson interferometer configuration with a low coherent laser in a source arm, a moving mirror in a reference arm, an object under study in a sample arm and a photodetector to measure the interference signal in a detection arm. In-depth scanning of the samples is produced by adjusting the lateral position of the mirror in the reference arm. Lateral scanning is realised through a second scanning mirror in the sample arm of the interferometer. The OCT technique has the unique ability of noninvasive in-depth and lateral scanning to capture 2D and 3D images with resolutions up to a few micrometers. These features could be used for the simple identification of additional artificial layers placed above real fingers by analysing the OCT images. Furthermore, differences in optical properties between artificial materials and real skin can be employed in automatic recognition systems based on, for instance, an autocorrelation analysis. With these unique capabilities, artificial materials can be potentially recognised in a new generation of OCT-enhanced fingerprint systems.

In this paper, we present results of image classification for samples of real and artificial fingerprints and materials. Methods include image feature selection using moments for colour, texture and shape, features based on Gabor wavelet edge detection, and implementation of neural networks using Hermite and Laguerre orthonormal polynomials for activation functions.

2 Methods

2.1 Colour, texture and shape features

Thirty one images (450 × 450 pixels) were obtained from each of seven finger surfaces studied: agar, finger surface, gelatin coating on finger surface, gelatin, wax and finger surface, and wax (Chen and Larin, 2006, 2007). Overall, there were 217 samples (images) uniformly distributed in seven classes. Image feature determination included metrics for colour (Stricker and Orengo, 1995), texture (Haralick et al., 1973) and shape (Hu, 1962). The original (450 × 450) images were reduced in both dimensions by 25%, minus one pixel resulting in (111 × 111) images. We first determined the colour (grayscale) moments in terms of the mean, standard deviation and skewness of image grayscale histograms for 256 bins (Stricker and Orengo, 1995). Next, texture features were calculated to reveal repetitious patterns in image regions (Haralick et al., 1973). Image entropy and energy texture features were calculated from the gray functions. Entropy was defined as

logij iji j

Entropy C C=∑∑ (1)


where Cij is the cooccurrence matrix for displacement vector ( ),xy x yd δ δ= for gray levels , 0,1, , 256.i j = K The image texture energy is defined as

2 ,iji j

Energy C=∑∑ (2)

and texture contrast as

( )2 .iji j

Contrast i j C= −∑∑ (3)

Lastly, texture homogeneity was determined using the relationship

.1

ij

i j

CHomogenity

i j=

+ −∑∑ (4)

Image shape features were determined using invariant moments (Hu, 1962), which were introduced for recognition of objects and characters in images regardless of their orientation, size and position. For an M × M digital image with gray function ( ), , , 1,2, , ,f x y x y M= K the 2D shape moments are

( ) ( ) ( )1 1

, , , 0,1, ,3M M

p qpq

x y

m x y f x y p q= =

= =∑∑ K (5)

with central moments

( ) ( ) ( )1 1

, ,M M

p qpq

x y

x x y y f x yμ= =

= − −∑∑ (6)

where 10 00/x m m= and 10 00/ .y m m= The scaled central moments become

( )00/ . / 2 1pq pq p qγη μ μ γ= = + +⎡ ⎤⎣ ⎦ (7)

Hu (1962) described seven normalised moments which are invariant to object scale, position and orientation:

( )( )( ) ( )( ) ( )

( )( ) ( ) ( )

( )( ) ( ) ( ) )

1 20 022 2

2 20 02 112 2

3 30 12 21 032 2

4 30 12 21 03

2 25 30 12 30 12 30 12 21 03

2 221 03 21 03 30 12 21 03

,

4 ,

3 ,

3 ,

3 3

3 3 3

M

M

M

M

M

= +

= + +

= + − −

= + + +

⎡ ⎤= + + + − +⎣ ⎦⎡ ⎤+ − + + − +⎢ ⎥⎣ ⎦

η η

η η η

η η η η

η η η η

η η η η η η η η



( ) ( ) ( )

( )( )

( )( ) ( ) ( )

( )( ) ( ) ( ) )

2 26 20 02 30 12 21 03

11 30 12 21 03

2 27 21 03 30 12 30 12 21 03

2 230 12 21 03 30 12 21 03

4 ,

3 3

3 3 .

M

M

⎡ ⎤= + + − +⎣ ⎦+ + +

⎡ ⎤= − + + − +⎣ ⎦⎡ ⎤− + + + − +⎢ ⎥⎣ ⎦

η η η η η η

η η η η η



(8)

Figure 1 shows a plot of the colour, texture and shape moment feature values for all samples. Additional feature selection via filtering was performed using a greedy plus-take-away-1 heuristic based on Mahalanobis distance and Wilks Lambda of the between- and within-class sum of squares. After which, nine features were retained: histogram mean, standard deviation, skewness, M1, entropy, energy, entropy correlogram at two pixel resolution, entropy correlogram at eight pixel resolution and entropy correlogram at 16 pixel resolution.

Figure 1 Colour, texture and shape feature values for all image samples (see online version for colours)

2.2 Edge detection using Gabor wavelet filters

Gabor wavelet filters (Daugman, 1988; Petkov, 1995) represent the light image response of a single visual neuron surrounded by neighbour neurons in a receptive field Ω. The receptive field function for a neuron is

( )

( ) ( ) ( ) ( )( ) ( ) ( ) ( )

2 2 2

2, , , , , exp cos 22

cos sin

sin cos ,

x y xg

x x y

y x y

γη σ θ ϕ π ϕσ

θ η θ

θ η θ

⎛ ⎞′ ′+ ⎛ ⎞ξ λ = − +⎜ ⎟ ⎜ ⎟⎜ ⎟ λ⎝ ⎠⎝ ⎠′ = − ξ − −

′ = − ξ + −

(9)


where ( )ηξ, ∈Ω is the centre of the field, ( ),x y ∈Ω is the location, θ is the orientation, γ is the aspect ratio (set to 0.5), ϕ is the phase offset, and σ is related to the bandwidth b through the relationship

( ) ( )( )2 1log 2

.2 2 1

b

bσ

π

+λ=

− (10)

The cos(.) term on the right side of (9) forms a sinusoidal oscillation component which when multiplied by the Gaussian filter e(.) forms a 2D bandpass filter that is selective to orientation. The convolution for Ω at phase value ϕ was determined with the linear spatial summation

( ) ( ) ( ), , , , , , ,s x y i x y g dxdyη σ θ φΩ− ξ, λ∫ ∫ (11)

where i(x, y) is the DC-adjusted pixel value of grayscale. Values of s(x, y) were determined for each pixel using a receptive field of 2σ and λ = 4, where σ = 0.5λ.

Convolutions of s(x, y) at 0,ϕ π= are symmetrical or even and at ,2 2π πϕ = are

antisymmetrical or odd. In this study, we determined the L2 norm of the symmetric and

antisymmetric s(x, y) with the form ( ) ( ) ( )2 20

2

, , , .s x y s x y s x y πϕ ϕ= == + The L2 norm

( ),s x y for each pixel was obtained at four orientations: 30, , ,4 2 4π π πθ ⎧ ⎫= ⎨ ⎬

⎩ ⎭

representing 0, 45, 90 and 135 degrees and summed to yield ( ) ( ), , .S x y s x yθ=∑

Final pixel values were based on the normalisation ( ) ( ){ }, / max ,S x y S x y multiplied by

256. A skip factor of eight pixels for each dimension was used to sample from the 12,321 total pixels in the (111 × 111) images, resulting in 196 = (14)(14) = (111/8)(111/8) feature values of Gabor results per image.

Figure 2 Gabor edge detection results: Lena input image on left panel, edge detection results on right panel


Figure 2 illustrates the Gabor edge detection results for the Lena image, showing the clearly defined edges visible throughout the entire image. For the study images, Gabor convolutions S(x, y) were obtained from each pixel in the (111 × 111) images. A skip factor of eight pixels for each dimension was used to sample from the 12,321 total pixels in the (111 × 111) images, resulting in 196 = (14)(14) = (111/8)(111/8) feature values of Gabor results per image. Figures 3 to 9 show examples of Gabor edge detection results.

Figure 3 Example OCT image (450 × 450) and Gabor edge detection results for agar by itself

Figure 4 Example OCT image (450 × 450) and Gabor edge detection results for a normal fingerprint


Figure 5 Example OCT image (450 × 450) and Gabor edge detection results for gelatin layer over normal fingerprint surface

Figure 6 Example OCT image (450 × 450) and Gabor edge detection results for gelatin by itself

Figure 7 Example OCT image (450 × 450) and Gabor edge detection results for silicone by itself


Figure 8 Example OCT image (450 × 450) and Gabor edge detection results for wax layer over fingerprint surface

Figure 9 Example OCT image (450 × 450) and Gabor edge detection results for wax by itself

2.3 Self-organising map of Gabor wavelet features

Using 196 Gabor wavelet features per image (Figure 10) for classifying 217 images is not parsimonious and would result in overparameterisation, where there are simply too many features used for the number of samples being analysed. Such overparameterisation is similar to the curse of dimensionality, however, this is not the small sample problem where the number of features greatly outweighs the number of samples, p >> N. Rather, by feeding so many features to a neural network or universal approximator, there is a risk that the network would learn all of the nuances in the large number of features, possibly leading to learning the signal plus all of the noise instead of learning only the signal. We mapped the 196-feature Gaborian space to a 2D feature space using self-organising maps (SOM). The 2D (i.e., X, Y ) SOM consisted of a seven-node by seven-node grid, where

, 1, 2, ,7.X Y = K SOM pre-processing involved mean-zero standardisation of the 196 Gabor features. The SOM incorporated a Gaussian neighbourhood function during


training with 500 iterations per run. SOM results were a pair of values for each sample, where X represented the closest row and Y represented the closest column in the 7 × 7 grid of nodes. Figure 11 illustrates the SOM-derived features for all samples.

Figure 10 196 Gabor wavelet features extracted from the 217 images (see online version for colours)

Figure 11 2D feature set derived from 7 × 7 SOM mapping of original 196-feature set generated from Gabor edge detection (see online version for colours)

2.4 Forward neural network – one hidden layer

A typical multilayer perceptron, backpropagation learning artificial neural network was used for comparison with the Hermite and Laguerre neural network (HNN and LNN) results. MSE was determined for an increasing number of hidden units ( )2,3, ,10 .n = K


For the forward neural network (FNN), the activation function at the hidden nodes was the logistic function and the softmax function was used on the output side. MSE values as a function of the number of hidden nodes n were calculated for ten, ten-fold cross-validation (CV) using 50 sweeps for each fold. Samples were randomly partitioned into ten folds, ten times, using stratification to uniformly distribute samples from the seven classes into each fold. Each sweep entailed one complete cycle in which the individual sample data were propagated forward using current weight values with the resulting gradient of MSE back-propagated through the network for weight updating. The initial learning rate was set to ε = 0.5, with weight decay γ = 1/50 and momentum α set to zero. Weight updates at cycle t were applied to weights for the previous cycle at t = 1. Before each CV fold, input-side and output-side weights were initialised using the random variates in the range [–0.5, 0.5].

Figure 12 Hermite polynomials of order 0,1, ,5K (see online version for colours)

2.5 Hermite neural network

Hermite functions belong to the general class of orthonormal functions. The HNN was based on activation functions at the hidden layer using the product of a Hermite polynomial Hn(t) and a Gaussian function t

( ) ( ) 2exp

22 !n

n n

H t th tn π

⎛ ⎞−= ⎜ ⎟⎜ ⎟

⎝ ⎠ (12)

where the first Hermite polynomial H0(t) = 1 and the remaining polynomials ( )1n ≥ are based on the recurrence relationship

( ) ( ) ( )12 2 .n n nH t tH t nH t−= − (13)

Figure 12 shows Hermite activation functions for 1,2, ,10.n = K First order derivatives for the activation functions are


( ) ( ) ( )

( ) ( )

1

00

2 1

0

nn n

dh tnh t th t n

dtdh t

th t ndt

−= − ≥

= − =

(14)

MSE was determined for an increasing number of hidden units ( )2,3, ,10 ,n = K where

hn(t) and Hn(t) were calculated for the nth hidden unit, with jn ijjt x=∑ w for the nth

hidden unit and ith input sample having j features. MSE values as a function of the number of hidden nodes n were calculated for ten ten-fold CV using 50 sweeps for each fold. Initial weight values on the input-side were set to randomly sampled quantiles from the standard normal distribution ( )0,1 ,N while output-side weights were initialised in the range [–0.5, 0.5]. In addition, for the HNN, the output side activation function was the softmax function.

Figure 13 Laguerre polynomials of order 1,2, ,6K (see online version for colours)

2.6 Laguerre neural network

The LNN was based on Laguerre polynomials, which are strictly positive and are shown for 1,2, ,6n = K in Figure 13. Laguerre activation functions at the hidden level are

( )2

20

exp2/ 2 .

!

n

n

ttt

n

−⎛ ⎞⎜ ⎟⎝ ⎠=l (15)

The first order derivative of ( )20 / 2n tl with respect to t is


( )( ) ( )

22 2

0

12 exp2 4

.2 !

n n

ntn t t

d tdt t n

⎛ ⎞−⎛ ⎞− ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠=l

(16)

MSE as a function of number of hidden nodes 1, 2, ,10n = K was also determined for the LNN. The network training and testing parameters were the same as the parameters used for the HNN. However, the output-side activation function was the linear sum product of weights and outputs from the Laguerre activation functions at hidden nodes.

2.7 Feature, sample, classification summary

Altogether, a total of 31 images (450 × 450) were obtained from seven configurations (classes): agar, finger, gelatine + finger, gelatin, wax + finger and wax, resulting in 217 images. Two feature sets were developed from the 217 samples: one set with nine features based on colour, texture and shape moments, and another set based on two features derived from SOM performed on 196 Gabor wavelet features per image. The two feature sets were used in classification runs of all 217 samples using the FNN, HNN and LNN, with an increasing number ( )2,3, ,10n = K of hidden nodes in the hidden layer. This resulted in six total classification runs.

Figure 14 Seven-class MSE as a function of number of hidden nodes for FNN with one hidden layer (see online version for colours)

Note: Input data based on nine mean-zero standardised features derived from colour, texture and shape.


Figure 15 Seven-class MSE as a function of number of hidden nodes for FNN with one hidden layer (see online version for colours)

Note: Input data based on two mean-zero standardised features derived from SOM of Gabor wavelet features.

Figure 16 Seven-class MSE as a function of number of hidden nodes for HNN with one hidden layer (see online version for colours)

Note: Input data based on nine L2-norm features derived from colour, texture and shape.


Figure 17 Seven-class MSE as a function of number of hidden nodes for HNN with one hidden layer (see online version for colours)


Figure 18 Seven-class MSE as a function of number of hidden nodes for LNN with one hidden layer (see online version for colours)

Note: Input data based on nine mean-zero standardised features derived from colour, texture and shape.


Figure 19 Seven-class MSE as a function of number of hidden nodes for LNN with one hidden layer (see online version for colours)


Table 1 Classification performance (accuracy) for ten ten-fold CV as a function of the number of hidden nodes in the hidden layer of FNN, HNN and LNN

FNN HNN LNN

Nodes Moments (9)

Gabor SOM(2)

Moments (9)

Gabor SOM(2)

Moments (9)

Gabor SOM(2)

2 0.82 0.95 0.76 0.95 0.45 0.46 3 0.92 0.99 0.86 0.99 0.62 0.67 4 0.95 1.00 0.92 1.00 0.82 0.84 5 0.96 1.00 0.93 1.00 0.89 0.94 6 0.97 1.00 0.95 1.00 0.94 1.00 7 0.96 1.00 0.93 1.00 0.97 1.00 8 0.96 1.00 0.95 1.00 0.97 1.00 9 0.96 1.00 0.96 1.00 0.98 1.00 10 0.97 1.00 0.96 1.00 0.98 1.00

Notes: (9) Denotes nine moments from colour, texture, shape moments. (2) Denotes two features from SOM run on Gabor edge detection values.

3 Results

Values of MSE for the FNN decreased the most rapidly with increasing number of hidden nodes (Figures 14–19). The MSE for HNN performed quite satisfactorily but did reveal several MSE outliers at greater numbers of hidden nodes when compared with the FNN. However, MSE for the LNN decreased less rapidly with increasing number of hidden nodes compared with the FNN and HNN network architectures. Table 1 lists performance results as a function of the number of hidden nodes for FNN, HNN and LNN using the both feature extraction methods. A major finding was that the use of SOM after Gabor


edge detection resulted in the greatest performance values at the lowest number of hidden nodes (100% at four nodes for FNN and HNN, and 100% at six nodes for LNN). For the nine-feature set based on moments, the FNN and HNN performed similarly over the range of number of hidden nodes. However, the LNN performed poorly for a low number of hidden nodes and then resulted in greater performance than the FNN and HNN.

4 Discussion

Classification performance results indicate that FNN, HNN or LNN could be combined with an OCT system using 3D image acquisition as an artificial fingerprint identification system. As shown in Figures 3–9, OCT images can reveal surface ridges and valleys that constitute the fingerprint pattern in addition to tissue layers. Classification results demonstrate that surface and material differences can be accurately classified, suggesting that fingerprint patterns can be discerned from artificial coatings on a finger and the finger skin itself. Therefore, it would be possible to construct libraries of OCT images for artificial and real fingerprints for the purpose of artificial fingerprint detection.

When using SOM after Gabor edge detection, results were similar for the neural networks used. When moments of colour, texture and shape were used, the LNN performed the worst at a lower number of hidden nodes but performed the best at the greatest number of hidden nodes (n = 10).

HNN and LNN have been applied in projection pursuit learning (Kwok and Yeung, 1996), signal processing (Mackenzie and Tieu, 2003), function approximation and classification (Ma and Khorasani, 2005). LNN have also been applied to signal processing (Mackenzie and Tieu, 2004). The HNN employed in this investigation was slightly different from the constructive HNN used by Ma and Khorasani (2005) in that the softmax function rather than linear regression was used on the output-side. We also used MSE exclusively for learning evaluation instead of the fraction of variance unexplained. Our implementation of the LNN was also wholly different from the application used by Mackenzie and Tieu (2004), which combined Hermite and Laguerre filters within a hybrid neural network for signal processing.

Hermite activation functions are orthonormal and therefore minimise redundancy and promote compactness. Because they are also spectral in form, they can learn the structure of the sample space. Laguerre activation functions on the other hand, are similar to radial basis function network centres. However, they can’t be freely changed and hence the weights of the LNN do not optimally reduce MSE during learning. HNN and LNN also form closed clusters of the data, so the optimisation of the pdf results in a better model when compared with FNN. Last, Laguerre polynomials are not sinusoidal like Hermite functions and are wider than Hermite polynomials of the same order. LNN activation functions therefore exploit Gaussian-distributed input features to a greater extent when compared with sinusoidal Hermite activation functions.

5 Conclusions

In this study, we demonstrated that several neural network classification methods could be successfully applied for identifying materials used for creating fake fingerprints. Use


of a SOM after Gabor edge detection of OCT images of fingerprint or material surfaces resulted in the greatest classification performance. The LNN performed the worst at a low number of hidden nodes, but overtook the FNN and HNN as the number of hidden nodes approached n = 10.

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leif e. peterson* kirill v....

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