IMAGE RECOGNITION USING SIMPLIFIED FUZZY ARTMAP AUGMENTED

IMAGE RECOGNITION USING SIMPLIFIEDFUZZY ARTMAP AUGMENTED WITH AMOMENT BASED FEATURE EXTRACTOR

S. RAJASEKARAN∗ and G. A. VIJAYALAKSHMI PAI†∗Department of Civil Engineering

†Department of Mathematics & Computer ApplicationsPSG College of Technology, Coimbatore 641 004, India

∗E-mail : [email protected]†E-mail : [email protected]

The capability of Kasuba’s Simplified Fuzzy ARTMAP (SFAM) to behave as aPattern Recognizer/Classifier of images both noisy and noise free has been investigatedin this paper. This calls for augmenting the original Neuro–Fuzzy model with a modifiedmoment-based RST invariant feature extractor.

The potential of the SFAM based Pattern Recognizer to recognize patterns —monochrome and color, noisy and noise free — has been studied on two experimentalproblems. The first experiment which concerns monochrome images, pertains to recog-nition of satellite images, a problem discussed by Wang et al. The second experiment,which concerns color images, deals with the recognition of some sample test coloredpatterns. The results of the computer simulation have also been presented.

Keywords: Simplified fuzzy ARTMAP; moments; feature extraction; pattern recognition.

1. INTRODUCTION

Pattern Recognition (PR) which is a science that deals with the description or

classification (recognition) of measurements has turned out to be an important com-

ponent of a dominant technology such as Machine Intelligence. Various approaches

to pattern recognition include statistical (or decision theoretic), syntactic (or

structural) and neural approaches.1 Of the three major approaches, neural tech-

nology is emerging quickly as a powerful means to solve PR problems.

Fuzzy Logic (FL), which has turned out to be an excellent computational

methodology has significantly contributed to the solution of PR problems.2–6 The

fusion of Neural Networks and Fuzzy Systems,7 termed Neuro–Fuzzy Systems have

also been applied for the solution of various PR applications.

ARTMAP is a class of Neural Network architectures that perform incremental

supervised learning of recognition categories and multidimensional maps in response

to input vectors presented in arbitrary order.8 The first ARTMAP9 system classified

input patterns represented as binary values. Carpenter et al.4 refined the system to a

general one by incorporating Fuzzy ART dynamics and termed it Fuzzy ARTMAP.

Fuzzy ARTMAP responds to both analog and fuzzy patterns. Kasuba6 propounded

the Simplified Fuzzy ARTMAP (SFAM) system which is a vast simplification of

Fuzzy ARTMAP. The network is a step ahead of Fuzzy ARTMAP in reducing the

computational overhead and architectural redundancy of Fuzzy ARTMAP.

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International Journal of Pattern Recognition and Artificial Intelligence, Vol. 14, No. 8 (2000) 1081–1095

c© World Scientific Publishing Company

1082 S. RAJASEKARAN & G. A. V. PAI

However, Kasuba’s SFAM despite its simplicity, does not display the charac-

teristic of tolerance to pattern perturbations or noise while processing images.9,10

The aim of the investigation is therefore to enhance the pattern recognition capa-

bility of SFAM by retaining its simple architecture but by augmenting it with a

moment-based feature extractor to enable it display tolerance to pattern perturba-

tions and noise. The feature extractor extracts features from patterns, which are

“preprocessed” inputs to SFAM. Digital approximations of moment-based

invariants1 have been employed. However, these approximations which are invariant

to translation of patterns are not strictly invariant to rotation and scaling changes.

The authors therefore, in a parallel investigation11 have mathematically modified

the properties before putting it to use for SFAM. The SFAM augmented with the

above-said modified feature extractor, has been investigated for its recognition of

monochrome and color images.

In this paper, the architecture of SFAM has been presented in Sec. 2. The

moment-based feature extractor has been reviewed in Sec. 3. The recognition of

monochrome and color images by SFAM has been presented in Secs. 4 and 5,

respectively. Results of the computer simulation have also been presented in the

sections.

2. SFAM — A REVIEW

SFAM comprises of two layers viz. an input and an output layer [see Fig. 1]. The

input to the network flows through the complement coder where the input string

is stretched to double the size by adding its complement as well. The complement

coded input then flows into the input layer. Weights (W ) from each of the output

category nodes reach down to the input layer. The category layer is just an area to

hold the names of the M number of categories that the network has to learn. The

other mechanisms of the network architecture are primarily for network training. ρ

is the vigilance parameter, which can range from 0 to 1. It controls the granularity

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Fig. 1. Architecture of SFAM network.

IMAGE RECOGNITION USING SIMPLIFIED FUZZY ARTMAP 1083

of the output node encoding. Thus, high vigilance values make the output node

much fussier when deciding how to encode input patterns whereas low vigilance

allows much more relaxed matching criteria for the output node.

The “match tracking” portion of the network lets itself adjust its vigilance dur-

ing learning from some base level, in response to errors in classification during

the training phase. It is through match tracking that the network adjusts its own

learning parameter to decide when to sprout new output nodes or reshape its de-

cision regions. During training, match tracking is evoked when the selected output

node does not represent the same output category corresponding to the input vec-

tors given.

2.1. Input Normalization

Complement coding is used for input normalization and it represents the presence

of a particular feature in the input pattern and its absence. For example, if a is the

given input pattern vector of d features, the complement coded vector a′ representsthe absence of each feature, where a′ is defined as

a′ = 1− a . (1)

The previous equation is valid since, just as in fuzzy logic, all SFAM input values

must be within the range 0 to 1. Therefore, the complement coded input vector I

internal to SFAM is given by the two-dimensional vector:

I = (a, a′) = (a1, a2, . . . ad, a′1, a

′2 . . . a

′d) . (2)

An interesting side-effect of the complement coding is the automatic normaliza-

tion of input vectors such that

|I| = |(a, a′)| =d∑i=1

ai + (d−d∑i=1

ai) (3)

where the norm || is defined as

|p| =d∑i=1

pi . (4)

2.2. Output Node Activation

When SFAM is presented an input pattern whose complement coded representation

is I, all output nodes become active to some degree. This output activation is

denoted by Tj for the jth output node, where Wj is the corresponding weight

vector given by:

Tj(I) =|I ∧Wj |α+ |Wj | . (5)

Here, α is kept as a small value close to 0 usually about 0.0000001. The winning

output node is the node with the highest activation

Winner = max(Tj) . (6)


If more than one Tj is maximal, the output node j with the smallest index is

arbitrarily chosen to break the tie. The category associated with the winning output

node is thus, the networks classification of the current input pattern.

The match function given below helps determine if learning should occur.

|I ∧Wj ||I| . (7)

When used in conjunction with the vigilance parameter, the match function

value states whether the current input is a good enough match to a particular

output node to be encoded by that output node, or instead, whether a new output

node should be formed to encode the input pattern.

If the match function value is greater than the vigilance parameter the network

is said to be in a state of resonance. Resonance means that output node j is good

enough to encode the input I, provided that output node j represents the same

category as input I.

A network state called “mismatch reset” occurs if the match function is less

than vigilance. This state indicates that the current output node does not meet the

encoding granularity represented by the vigilance parameter and therefore cannot

update its weights even if the input patterns’ category is equal to the category of

the winning output node.

Once a winning output node j has been selected to learn a particular input pat-

tern I, the top–down weight vector Wj from the output node is updated according

to the equation.

W newj = β(I ∧W oldj ) + (1− β)W oldj (8)

where 0 < β ≤ 1. Once SFAM has been trained, the equivalent of a “feed forward”

pass for an unknown pattern classification consists of passing the input pattern

through the complement coder and into the input layer. The output node activation

function is evaluated and the winner is the one with the highest value. The category

of the input pattern is the one with which the winning output node is associated.

3. MOMENT-BASED FEATURE EXTRACTOR

Moments are extracted features that are derived from raw measurements. In prac-

tical imagery, images are subject to various geometric distortions or pattern per-

turbations. It is therefore necessary that features that are invariant to orientations

be used for purposes of recognition or classification. For 2D images, moments have

been used to achieve Rotation (R), Scaling (S), and Translation (T ) invariants.

The moment transformation of an image function f(x, y) is given by

mpq =

∫ ∞−∞

∫ ∞−∞xpyqf(x, y)dxdy p, q = 0, 1, 2, . . .∞ . (9)

However in the case of a spatially discretized MXN image denoted by f(i, j), Eq. (9)

is formulated using an approximation of double summations,

mpq =M∑i=0

N∑j=0

ipjqf(i, j) . (10)


The so-called central moments are given by

µpq =M∑i=0

N∑j=0

(i− i)p(j − j)qf(i, j) (11)

where

i =m10

m00, j =

m01

m00. (12)

The central moments are still sensitive to R and S transformations. The scaling

invariant may be obtained by further normalizing µpq or by forming

ηpq =µpq

µ00

(p+ q

2+ 1

) , p+ q = 2, 3, . . . . (13)

From Eq. (13), constraining p, q ≤ 3, and using the tools of invariant algebra, a set

of seven RST invariant features as shown in Table 1 may be derived.

However, though the set of invariant moments shown in Table 1 are invariant to

translation, inspite of being computed discretely, the moments cannot be expected

to be strictly invariant under rotation and scaling changes.

Table 1. Moment-based RST invariant features.

φ1 = η20 + η02

φ2 = (η20 − η02)2 + 4η112

φ3 = (η30 − 3η12)2 + (3η21 − η03)2

φ4 = (η30 + η12)2 + (η21 + η03)2

φ5 = (η30 − 3η12)(η30 + η12)[(η30 + η12)2 − 3(η21 + η03)2]

+ (3η21 − η03)(η21 + η03)[3(η30 + η12)2 − (η21 + η03)2]

φ6 = (η20 − η02)[(η30 + η12)2 − (η21 + η03)2] + 4η11(η30 + η12)(η21 + η03)

φ7 = (3η21 − η03)(η30 + η12)[(η30 + η12)2 − 3(η21 + η03)2]

− (η30 − 3η12) (η21 + η03)[3(η30 + η12)2 − (η21 + η03)2

An investigation11 by the authors revealed that in the definition of µpq, the

contribution made by a pixel had been overlooked. The modified µpq definitions have

been presented in Table 2. The moment-based invariant functions are computed

using the new definitions as before, from the raw measurements of each image.

Those images, which are similar, are classified as belonging to the same class.

In other words, images which are perturbed (rotated, scaled or translated) versions

of the given nominal pattern are all classified as belonging to a class.

4. RECOGNITION OF MONOCHROME IMAGES

The problem of identifying air planes, tanks and helicopters from a satellite dis-

cussed by Wang et al.,12 is the test suite problem. The experiments conducted could


Table 2. Revised µpq definitions.

µ00 = M(Mass)

µ10 = 0

µ01 = 0

µ20 =n∑j=1

n∑i=1

f(xi, yj)

(xi

2 +1

12

)

µ02 =n∑j=1

n∑i=1

f(xi, yj)

(yj

2 +1

12

)

µ21 =n∑j=1

n∑i=1

f(xi, yj)(xi2yj)

µ12 =n∑j=1

n∑i=1

f(xi, yj)(xiyj2)

µ11 =n∑j=1

n∑i=1

f(xi, yj)(xiyj)

µ30 =n∑j=1

n∑i=1

f(xi, yj)(xi3)

µ03 =n∑j=1

n∑i=1

f(xi, yj)(yj3)

be categorized as under:

IMAGE TRAINING SET TESTING SET

Nominal Patterns (Noisy)

Monochrome Nominal (ideal) Rotated/Scaled/Translated/ (Noise free)

Patterns Combinations

Rotated/Scaled/Translated/ (Noisy)

Combinations

Figure 2 illustrates a set of sample nominal patterns that are trained with SFAM.

The results were observed for varying vigilance parameter values, 0.5 ≤ ρ < 1. The

number of training epochs was kept fixed to a paltry 3. The model was tested for

a set of 50 patterns absolutely noise free, but rotated or scaled or translated, or

for combinations of one or more or all of these. Figure 3 illustrates a sample set of

inference patterns. Table 3 shows the results of the experiments.

Table 3. Recognition of noise free monochrome images.

No. of Training Vigilance Training Set Testing Set Nature of the RecognitionEpochs Parameter Testing Set Rate

3 0.5 ≤ ρ < 1 3 Exemplars- 50 patterns Rotated/Scaled/ 100%(one in each Translated/category Combinations


Fig. 2. Training patterns of SFAM (monochrome, nominal).

Fig. 3. Sample inference patterns (monochrome, noise free) correctly identified by SFAM.


Fig. 4. Sample noisy patterns correctly identified by SFAM.

In the next stage, for the same training set, a set of noisy patterns — nominal,

rotated, scaled, displaced or a combination — was presented, to test for the recog-

nition capability. Figure 4 illustrates a sample set of noisy patterns. The activation

values of the top–down weight nodes and the correctness of the classification were

observed for varying noise levels. Since the experiment pertains to monochrome

(binary) images, the noise level was determined in terms of the Hamming distance.

The recognition flag is set to 1 or 0 depending on whether the recognition is correct

or incorrect, respectively. Figure 5 illustrates the behavior of the model for varying

noise levels, when a nominal pattern was subjected to random noise. Figure 6 does

the same for a scaled and translated image and Fig. 7 for a rotated, scaled and

translated noisy image.


Fig. 5. Performance of SFAM during the recognition of noisy patterns (monochrome–noisy).

Fig. 6. Performance of SFAM during the recognition of noisy patterns (monochrome, scaled andtranslated).

5. RECOGNITION OF COLOR IMAGES

In this phase, a similar set of experiments was repeated with respect to colored

images. The problem pertained to the recognition of sample colored test patterns.

The experiments performed could be categorized as under:


Fig. 7. Performance of SFAM during the recognition of noisy patterns (monochrome, rotated,scaled and translated).

IMAGE TRAINING SET TESTING SET

Nominal Patterns (Noisy)

Color Nominal (ideal) Rotated/Scaled/Translated/ ( Noise free)

Patterns Combinations

Rotated/Scaled/Translated/ (Noisy)

Combinations

Figure 8 illustrates a sample set of nominal patterns and Fig. 9 a set of noise

free patterns but subject to perturbations — rotation, scaling, translation and

combinations of the three. Table 4 shows the results of the experiment.

Table 4. Recognition of noise free color images.

No. of Training Vigilance Training Testing Nature of the RecognitionEpochs Parameter Set Set Testing Set Rate

3 0.5 ≤ ρ < 1 4 Exemplars 93 patterns Rotated/Scaled 100%(one in each Translatedcategory) Combinations

In the case of noisy patterns, a sample of which is illustrated in Fig. 10, the

performance of the model for varying noise levels was observed. As before, the

activation value of the top–down weight vectors and the recognition capability of

the model for varying noise levels was under observation. Figure 11 illustrates the

behavior when nominal patterns were subjected to random noise. Figures 12 and

13 illustrate the behavior for scaled and translated noisy image, and rotated, scaled

and translated noisy image, respectively.


Fig. 8. Sample training patterns for SFAM (color, nominal).

Fig. 9. Sample inference patterns (color, noise free and perturbed).


Fig. 10. Sample noisy patterns (color) correctly identified by SFAM.

Fig. 11. Performance of SFAM during the recognition of noisy patterns (color, nominal).


Fig. 12. Performance of SFAM during the recognition of noisy patterns (color, translatedand scaled).

Fig. 13. Performance of SFAM during the recognition of noisy patterns (color, rotated, translatedand scaled).

6. CONCLUSION

In this paper, the pattern recognition capability of SFAM has been discussed. The

architecture augmented with a moment-based feature extractor exhibits an excellent

capability to recognize patterns by working on the RST invariant feature vectors

of the patterns rather than the patterns themselves.


The augmented architecture can handle both symmetric and asymmetric pat-

terns. In the case of asymmetric patterns the RST invariant functions φ1−φ7 turnout to be the same for all perturbations of a given pattern. Hence SFAM has no

difficulty in recognizing perturbed patterns since it only calls for associating the

same feature vectors with the top–down weight vectors which results in the invo-

cation of the same category node. This results in the correct identification of the

perturbed pattern.

However, in the case of symmetric patterns it is essential that only distinct

portions of the images be trained. This is so since in the case of doubly symmetric

or in general, multisymmetric images, their RST invariant feature vectors φ2 − φ7acquire values which are very close to 0, and φ1 tends to 1. This consequently

results in feature vectors which are almost similar leading to a misclassification of

patterns. Hence in the case of multisymmetric patterns, it is sufficient to consider12n th portion of the image.

REFERENCES

1. J. C. Bezdek and S. K. Pal (eds.), Fuzzy Models for Pattern Recognition, IEEE Press,Piscataway, NJ, 1992.

2. G. A. Carpenter and S. Grossberg, Pattern Recognition by Self Organizing NeuralNetworks, MIT Press, Cambridge, MA, 1991.

3. G. A. Carpenter, S. Grossberg, N. Markuzon, J. H. Reynolds and D. B. Rosen, “FuzzyARTMAP: a neural network architecture for incremental supervised learning of analogmultidimensional maps,” IEEE Trans. Neural Networks 3, 5 (1992) 698–713.

4. G. A. Carpenter, S. Grossberg and J. H. Reynolds, “ARTMAP: supervised real timelearning and classification of non stationary data by a self organizing neural network,”Neural Networks 4 (1991) 565–588.

5. A. Kandel, Fuzzy Techniques in Pattern Recognition, Wiley, NY, 1982.6. T. Kasuba, “Simplified fuzzy ARTMAP,” AI Expert, November (1993) 18–25.7. B. Kosko, Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to

Machine Intelligence, Prentice Hall, Englewood Cliffs, NJ, 1992.8. S. K. Pal and D. K. D. Majumdar, Fuzzy Mathematical Approach in Pattern Recog-

nition, Wiley Eastern Ltd., New Delhi, India, 1986.9. S. Rajasekaran and G. A. V. Pai, “Application of simplified fuzzy ARTMAP to struc-tural engineering problems,” All India Seminar on Application of NN in Science,Engineering and Management, Bhubaneswar, June 1997.

10. S. Rajasekaran, G. A. V. Pai and J. P. George, “Simplified fuzzy ARTMAP for de-termination of deflection in slabs of different geometry,” Nat. Conf. NN and FuzzySystems, Chennai, 1997, pp. 107–116.

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S. Rajasekaran isProfessor Emeritus of

AICTE at the Depart-ment of Civil Engi-neering, PSG Collegeof Technology, Coim-batore, India. He ob-tained his Ph.D. in civilengineering from theUniversity of Alberta,

Edmonton, Canada in 1971 and D.Sc. (civilengineering) from the Bharathiar Univer-sity, India in October 1999. He was a visit-ing Professor at the University of Alberta,Canada, University of Sydney, Australia, andthe Alexander von Humboldt Guest Profes-sor at the University of Stuttgart, Germany.He is a recipient of the ISTE National Awardfor his outstanding research work in engineer-ing and technology in the year 1991, Tamil-nadu Scientist Award by TNSCST, Govern-ment of Tamilnadu in 1966 and NAGADIaward for his book “Finite Element Anal-ysis in Engineering Design” by the Associ-ation of Consulting Civil Engineers(ACCE)in 1996 and the Vocational Excellence awardby the Coimbatore West Rotary in Decem-ber 1999 and ISTE Anna University NationalAward for the outstanding Academic for theyear 1999–2000. Rajasekaran is the princi-pal investigator of many projects sponsoredby AICTE, ARDB, BARC, DST, ISRO andMHRD. He is a Fellow of the Institution ofEngineers, The Institute of Valuers and aMember of American Society of Civil Engi-neers and Computer Society of India and In-dian Society of Technical Education. He haspublished more than 230 research papers innational and international journals and con-ferences, besides fifteen books. He is listedin the American Biographical Research Insti-tute and the eminent personalities of India.His specific interests include finite element

analysis, boundary integral element method,nonlinear analysis, neural networks, geneticalgorithms and fuzzy systems.

G. A. VijayalakshmiPai is a Lecturer (Se-

nior Grade) in com-puter applications inthe Department of Com-puter Applications, PSGCollege of Technology,Coimbatore. She com-pleted her Masters De-gree and Master of Phi-

losophy in applied mathematics, specializingin computer science, in 1984 and 1989, re-spectively, both degrees awarded by the Fac-ulty of Engineering, Bharathiar University.She obtained her Ph.D. in computer sciencefrom the Department of Civil Engineering,PSG College of Technology in 1999.Her research interests include neural net-

works, fuzzy logic, genetic algorithms andlogic for artificial intelligence.

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IMAGE RECOGNITION USING SIMPLIFIED FUZZY ARTMAP AUGMENTED