FACE PROCESSING SYSTEM –WAVELET AND FSOFM

 

Face processing system

ABSTRACT

The human face is one of the most important patterns our visual system receives. It establishes a person’s identity and also plays a significant role in everyday communication. Humans can recognize familiar faces under varying lighting conditions, different scales, and even after the face has changed due to aging, hair style, glasses, or facial hair. Our ease at recognizing faces is a strong motivation for the investigation of computational models of face processing. This project deals with a newly developed face processing system that combines wavelet pre-processing of input with a fuzzy self-organizing feature map algorithm. The wavelet-derived face space is partitioned into fuzzy sets, which are characterized by face exemplars and membership values to those exemplars. This system learns faces using relatively few training epochs, has total recall for faces it has been shown, generalizes to face images that are acquired under different lighting conditions, and has rudimentary gender discrimination capabilities.

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Keywords: Face Processing, wavelet transform, multi resolution, cluster analysis, self-organization, FCM.

Introduction

This face processing system is a Feature-based system. Feature-based approaches concentrate on individual facial features such as the eyes, nose, and mouth, and define a model by measuring the position, size and the relationships among these features. Processing of the facial image is usually done in an attempt to decrease the amount of data that must be stored, while at the same time preserving the salient information. Oftentimes, the processed facial image data is used in conjunction with neural networks for recognition and categorization in the connectionist face processing systems. The feature set used is the wavelet, for efficiency of learning and recall accuracy on face recognition tests using neural networks. The wavelet feature set has the fastest convergence properties. This project develops a two-stage face processing system that is a hybrid blend of Signal processing (wavelet transform) and Connectionist (fuzzy self organizing feature map) algorithms.

 

Face processing system

The human visual system uses highly redundant, temporally filtered information for perceptual purposes [1]. Differences of the same feature as to the degree of dissimilarity were perceived differently in the two hemispheres. The other methods closest to this method of face space partitioning found in the FSOFM is dealt in Kohenen [2] and Millward and O’Toole [3] . There have been a number of studies using backpropagation networks for face processing. Wavelets have been used for face processing Manjunath et al.[4 ,5, 6, 7]. describe a feature based approach where the features are derived directly from the intensity data using Gabor wavelets [6].Topological graphs are used to represent relations between features, and deterministic graph matching scheme is used to recognize familiar faces from a database. Gross and Koch have developed an algorithm for the Gabor wavelet decomposition based on convolution products in the Fourier domain [5]. Disadvantage of Gabor feature is that, a single image process from Gabor wavelet feature generation to classification took about 390 seconds on a SGI Indigo workstation. Micheli-Tzankou et al. use the orthogonal wavelet transform of facial images to build a feature vector as input to a back propagation network [7]. These approaches that extract features from the Gabor wavelet coefficient space or use the largest wavelet coefficients as a vector, our system uses the average and detail channels of the wavelet transform. The neural network model [8] used in the second stage of the system shown in Figure 1 is a modification of the self-organizing feature maps of Kohenen [2]. Kohene’s system consisted of a two- layer feedforward network that used an influence neighborhood in the output layer. An output node was a candidate for update of its weights if the weights were found to be closest to the input vector using the Euclidean distance. Only the local neighborhood around this output node has their weights updated. The FSOFM, used here, is a member of the generalized class of clustering networks developed by Pal, Bezdek, and Tsao [9].

Figure 1. Face Processing System

In the figure 1 , the first stage performs the wavelet transform on the facial images. The first step is to decompose the image into transform coefficients by using wavelet transform. Multi resolution representations of an image are very effective for analyzing the information content of images. There are many techniques available to decompose the signal. The wavelet transform builds a multi resolution representation of the original image that captures coarse facial structure in the average channel, as well as fine facial features in the detail channels.

Many applications can take advantage of the locality property, which is supported by the wavelet transform. Because of its orthogonal property, a change of coefficients in one level would not affect the coefficients in the other level. The other advantage that the wavelet transform has is its utility in multi resolution analysis (MRA).

 

One major advantage afforded by wavelets is the ability to perform local analysis that is, to analyze a localized area of a large signal. Wavelet analysis is capable of revealing aspects of data that other signal analysis techniques miss, aspects like trends, breakdown points, discontinuities in higher derivatives, and self-similarity. Furthermore, because it affords a different view of data than those presented by traditional techniques, wavelet analysis can often compress or de-noise a signal without appreciable degradation.

Both the lowest resolution average channel and the lowest resolution detail channel

serve as inputs to the second stage, which is a fuzzy self-organizing feature map.(FSOFM)

 

a) The original image (b) Each sub image of the DWT at

level 2

 

(c) The DWT of image at level 2. (d) The approximation of image

at level 1.

 

Fig: 2 Discrete wavelet transform at different levels.

 

Fuzzy Self-Organizing Feature Map:

 

The neural network model used in the second stage of the system shown in Figure 1 is a modification of the self-organizing feature maps of Kohonen. Kohonen’s system consisted of a two-layer feed forward network that used an influence neighborhood in the output layer. An output node was a candidate for update of its weights if the weights were found to be closest to the input vector using the Euclidean distance. Only nodes within the local neighborhood around this output node have their weights updated. For a network with i input nodes and j output nodes, the update rule is:

W_k=W_k^old+?(t)*d?_k ——(1)

where d?_k = (?_i, W_k ), ? (t) is the learning rate, and W_k^old is the previous value of W_k ,0? k? j-1. The learning rate has to decrease with time in order to guarantee convergence. In addition the neighborhood size is decreased with time. Kohonen used the network with great success for matching of faces given partial information, and its use for dimensionality reduction for data visualization.

The FSOFM, shown in Figure 3, is a member of the generalized class of clustering network.

There are three layers in the FSOFM. The input layer feeds forward into a distance layer which determines the distance between the input vector and the current weights using a predefined metric (usually Euclidean). The distance layer then feeds forward into a membership layer which calculates the membership values of the input vector to the set of all output vectors. This is done using the following form derived from the fuzzy c-means algorithm and used in a previously developed computer vision system

u_ki=1/[?_l=0^(j-1)(d_ki /d_li )^2/(m-1) ] —- (2)

where j is the number of output nodes, d ki is the distance (Euclidean) between the input vector , i and weight vector W k , and m is a weighting exponent which is set within the range 2.0 to 1. These membership values u ki are then fed back into the network and participate in the weight update rule as:

W_k=W_k^old + u_ki*d?_k ——– (3)

where d?_k = (?_I -W_k ), and W_k^old is the previous value of W_k. The addition of a feedback loop allows the network to respond to the localized patterns of activity in the distance layer without the need for a neighborhood. The set of weights W k can be viewed as cluster centers that are representative of global partitioning of the input vectors into classes. The membership values u ki range from 0.0 (no membership in the fuzzy set) to 1.0 (total membership in the fuzzy set). The sum of membership values for any given input vector to all of the j sets is normalized to 1.0. This means that an input vector that is not close to any of the previously defined sets (an outlier) will have an equal membership value to all sets approximately equal to one over the number of output nodes (1/j). Such a vector would be considered to be unfamiliar.

 

Fuzzy C-means Algorithm:

s1. Randomly initialize weights W_k, 0 ?k?j-1 to

values between 0 and 1.

Set the limit value to be sufficiently small (e.g,

0.001), and set the total squared change in

weights , Dif f _total , to 0.

 

s2. For each vector input ?_I, I=1,2…. n where n is

the number of inputs and

for all weight vectors 0 ?K? j -1:

 

1. Calculate d_ki and determine the feedback

membership value u_ki, for

each input vector as u_ki=1/[?_l=0^(j-1)(d_ki /d_li )^2/(m-1]

 

2. Update the weight change factor d_?k such that

d_?k = (?_i -W_k ).

 

3. Save the current weight W_k as W_k ^old before

up dating weight.

 

4. Update weight W_k as W_k=W_k^old + u_ki*d?_k .

5. Return the value Diff, where

Diff = ?(W _k - W _k ^old) ². Update the value

of Diff _total using Diff _total = Diff _total + Diff.

s3 . If Diff _total > limit then go to s4, else go to s5.

 

s4. Reset Diff _total to 0 and go to s2.

 

s5. Write out weight file and determine the fuzzy

membership value u_ki , 0 ? k ? j - 1 for each

input vector ?_i by using the relation

u_ki=1/[?_l=0^(j-1)(d_ki /d_li )^2/(m-1) ]

The FSOFM algorithm has certain advantages over Generalized Linear Vector Quantization one of which is that there is no need to determine a winning output node. This property of FSOFM leads to a uniform weight update rule for all node.

Conclusions

The first experiment was designed to test the learning and recall capabilities of the Fuzzy- Face system. The wavelet transform was performed on the face databases and the average and detail channel images from 3 levels down in the hierarchy were used to train the FSOFM in the second stage of the system. The wavelet Transforms used are Biorthogonal Wavelet Transform and Daubechies wavelet Transform. The Daubechies wavelet has faster computation time compared to Biorthogonal wavelet transform. This represents a 98.5% reduction in the amount of information that is being processed for each image. Recall accuracy on the databases is 100%.

The second study tested the Fuzzy-Face system for its recognition capabilities. The images were normalized and test was performed to recognize the images under varying lighting conditions.

The system tested with 3 sets of 10 images is used as the database. Out of the 10 images in each set , 5 were trained and the remaining 5 were used as test images. Finally the ORL database consisting of 40 sets of 400 images in total was used and the system could recognize the test images and it is found to have 100% recall capability. This result is compared with the Eigenface recognition system and it is found that better accuracy is achieved in the FSOFM system.

 

This paper can be enhanced with Two FSOFM running in parallel. Thus the experiment can be examined for the exemplar building capabilities of the system for gender identification. This can be merged with Cryptography, that is coding combined with computational time, which will increase the number of users, improvement in security can be achieved.

 

 

Face Processing System

result

 

References

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W. Young and H. D. Ellis, editors, Handbook of

Research on Face Processing pages 57-92.

Elsevier Science Publishers, New York, NY,

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[2]T. Kohonen Self-Organization and Associative

Memory Springer-Verlag, Berlin, third

edition.. 1989

 

[3] R. B. Millward and A. J. O’Toole. Recognition

memory transfer between spatially transformed

faces In H.D. Ellis, Jeeves M. A., F. Young, and

A.Newcombe, editors, Aspects of Face

Processing.

Martinus Nijhoff, Dordrecht. 1986

 

[4] J. G. Daugman. High confidence visual

recognition of persons by a test of statistical

independence. IEEE Trans PAMI, 15(11):1148-

1161, November . 1993

 

[5] M. H. Gross and R. Koch. Visualization of

multi dimensional shape and texture features in

laser range data using complex valued Gabor

wavelets IEEE Transactions on Visualization and

Computer Graphics, 1(1):44-59. 1995

 

[6] B. S. Manjunath, R. Chellappa, and C. Von der

Malsburg. A feature based approach to face

recognition. In Proc. IEEE Computer Society

Conf. on Computer Vision and Pattern

Recognition pages 373-378, Champaign,

IL, June. 1992

 

[7] E. Micheli-Tzanakou, E. Uyeda, A. Sharma, R.

Ramanujan, and J. Dong. Comparison of neural

Network algorithm for face recognition.

Simulation 64(1):15-27, July . 1995

 

[8] T. L. Huntsberger and P. Ajjimarangsee. Parallel

self-organizing feature maps for unsupervised

pattern recognition. International Journal of

General systems, 16:357- 372. 1990

 

[9] N. R. Pal, J. C. Bezdek, and E. C.-K. Tsao.

Generalized clustering networks and Kohonen’s

self-organizing scheme. IEEE Trans. Neural

Networks, 4(4):549-557, July. 1993.

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