The color of the digital images is one of the most important components of the image processing research area. In many applications such as image segmentation, analysis, compression and transition, it is preferable to reduce the colors as much as possible. In this paper, a color clustering technique which is the combination of a neural network and a fuzzy algorithm is proposed. Initially, the Kohonen Self Organized Featured Map (KSOFM) is applied to the original image. Then, the KSOFM results are fed to the Gustafson-Kessel (GK) fuzzy clustering algorithm as starting values. Finally, the output classes of GK algorithm define the numbers of colors of which the image will be reduced.

1. DEMOCRITUS UNIVERSITY OF THRACE - GREECE
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Color Reduction using the combination of the Kohonen Self-
Organized Feature Map and the Gustafson-Kessel fuzzy
algorithm
Konstantinos Zagoris, Nikos Papamarkos and Ioannis Koustoudis
Image Processing and Multimedia Laboratory
Department of Electrical & Computer Engineering
Democritus University of Thrace
67100 Xanthi, Greece
Email: papamark@ee.duth.gr
http://ipml.ee.duth.gr/~papamark/

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Problem definition
• The main objective of this work is to propose a novel Color
Clustering technique which is the combination of a neural network
and a fuzzy algorithm.
• Quantization of image colors is a very useful tool for segmentation,
compression, presentation and transmission of images.
• Reduction of the image’s colors to a small number (to its dominant
colors) is important mainly for image segmentation (for example,
segmentation of color documents).

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Fig. 1 Original image Fig. 2 RGB color distribution
Fig. 3 Image with only 20 dominant
colors
Fig. 4 Distribution of 20
colors

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Color Reduction techniques
• Several techniques have been proposed for color
quantization which can be classified in the following main
categories:
– First, there is the class of splitting-merging algorithms that
divide the color space into disjoint regions, by consecutive
splitting up the color space.
– Another class of quantization techniques consider the
problem as a clustering approach.
– Finally, there are general color segmentation techniques,
which can be considered as color reduction algorithms.

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Splitting-merging algorithms
• P. Heckbert, "Color image quantization for frame buffer display", Computer & Graphics, vol. 16,
pp. 297-307, 1982.
• S. Wan, S. Wong, and P. Prusinkiewicz, “An Algorithm for Multidimentional Data Clustering”,
ACM Trans. Math. Softw., vol. 14 no. 2, pp. 153-162, June 1988.
• I. Ashdown, "Octree color quantization", from the book: Radiosity-A Programmer's Perspective,
Wiley, New York, 1994.
Algorithms based on clustering
• A.H. Dekker, "Kohonen neural networks for optimal color quantization", Network:
Computation in Neural Systems, vol. 5, pp. 351-367, 1994.
• N. Papamarkos, "Color reduction using local features and a SOFM neural network", Int.
Journal of Imaging Systems and Technology, vol. 10, no 5, pp. 404-409, 1999.
• N. Papamarkos, A. Atsalakis and C. Strouthopoulos, "Adaptive Color Reduction", IEEE Trans.
On Systems, Man, and Cybernetics, IEEE Trans. on Systems, Man, and Cybernetics-Part B,
vol. 32, no. 1, Feb. 2002.
• A. Atsalakis, N. Papamarkos , N. Kroupis , D. Soudris and A. Thanailakis, "A Color
Quantization Technique Based on Image Decomposition And Its Hardware Implementation",
IEE Proceedings Vision, Image and Signal Processing, Vol. 151, Issue 6, pp. 511-524, 2004.

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General Color Segmentation Algorithms
• Comaniciu, D., Meer, P.: Mean shift: a robust approach toward
feature space analysis. IEEE Transactions on Pattern Analysis
and Machine Intelligence 24 (5). (2002) 603–619..
• Nikolaou, N., Papamarkos, N.: Color segmentation of complex
document images. International Conference on Computer
Vision Theory and Applications. Setúbal, Portugal, (2006) 220-
227

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Overview of the Proposed Method

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Fractal Sub-Sampling Procedure
Hilbert ‘s curve
Benefits:
•Smaller number of sampling pixels
•Capture of neighborhood regions
Fig. 1 Fig. 2
Fig. 3 Fig. 4

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Kohonen Self Organized Featured Map (KSOFM)
j k jky arg min x w= −
• The training algorithm of the KSOFM is
based on competitive learning:
• The winner output neuron changes its
connections weights as follows:
( )jk k jkw n x w∆ = −

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Gustafson – Kessel Fuzzy Algorithm
The Gustafson – Kessel fuzzy algorithm is an extension of
the fuzzy c-mean algorithm that produces ellipsoidal classes
by using a covariance matrix:
Figure 1 Figure 2 Figure 3

11. DEMOCRITUS UNIVERSITY OF THRACE - GREECE
Gustafson – Kessel Fuzzy Algorithm
1. Define the number of the classes c, the weighting parameter m and the cluster
volumes ρi.
2. Define the termination tolerance ε>0 and the number of iterations λ. Set a counter α
equal to one ( α = 1).
3. Initialize randomly the partition matrix U=[uik]. In this work, the partition matrix is
initialized not randomly but from the connections weights wjk of the KSOFM for each
output class.
4. Compute the centers of the classes according to the following equation:
5. Compute the covariance matrix Fi for each class according to the following equation:
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( )
( )
[ ] [ ]
n
m
ik k
k 1
i n
m
ik
k 1
u x
v , i 1,c and k 1,n
u
=
=
= ∈ ∈
∑
∑
( )
( )
n
m T
ik k i k i
k 1
i n
m
ik
k 1
u (x v )(x v )
F , i [1,c]
u
=
=
− −
= ∈
∑
∑

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6. Compute the matrix Ai for each class according to the following equation:
7. Compute the distance dik of every sample xk from the center of each class vi according
to the following equation:
8. Update the partition matrix U=[uik] for each sample xk according to the following
equation:
9. if or stop, else set and go to step 4.
( ) 1h
i i i iA det F F , i [1,c]−
= ρ ∈
( ) ( )T2
ik k i i k id x v A x v= − −
[ ] [ ]ik 2
m 1c
ik
j 1 ij
1
u , i 1,c and k 1,n
d
d
−
=
= ∈ ∈
 
 ÷ ÷
 
∑
( ) ( 1)
max U Uα α−
− < ε α ≥ λ 1α = α +

13. DEMOCRITUS UNIVERSITY OF THRACE - GREECE
The parameters of the algorithms during the testing
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KSOFM Fuzzy C-Mean KSOFM - GK
Initially Learning Rate:
ninitially = 10-2 m = 1.2
Initially Learning Rate:
ninitially = 10-2
Final Learning Rate:
nfinal = 10-4 Epochs = 2000
Final Learning Rate:
nfinal = 10-4
Step of the Learning Rate:
nstep = 10-5
Termination Tolerance:
= 5ε ∙10-5
Step of the Learning Rate:
nstep = 10-5
KSOFM Termination
Tolerance: = 5ε ∙10-5
m = 1.2
GK termination Tolerance:
= 5ε ∙10-4
Iterations: = 100λ

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Original Image
22410 colors
KSOFM
4 colors
FCM
4 colors

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KSOFM – GK
4 colors
Median Cut
4 colors
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Original Image
99760 colors
KSOFM
7 colors
FCM
7 colors

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KSOFM – GK
7 colors
Median Cut
7 colors
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Original Image
33784 colors
KSOFM
5 colors
FCM
5 colors

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KSOFM – GK
5 colors
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Median Cut
5 colors

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Original Image
31655 colors
KSOFM
4 colors
FCM
4 colors

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KSOFM – GK
4 colors
Median Cut
4 colors

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Original Image
69656 colors
KSOFM
8 colors
FCM
8 colors

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KSOFM – GK
8 colors
Median Cut
8 colors

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Advatages
• The experimental results have shown that the proposed
technique has the ability to retain the dominant colors
even if the final image consists of a very small number of
unique colors.
• It can merge areas of the image having similar colors. In
this point of view, it can be considered as a powerful
color image segmentation procedure
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25. DEMOCRITUS UNIVERSITY OF THRACE - GREECE
Disadvatage
High Computation Cost which comes from the determination of the
Mahalanobis distance.
For an AMD Athlon 64 3000+ (2GHz) based PC with 1GByte RAM, the
processing time for a 512x384 image with 119143 colors for all the algorithms
are:
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KSOFM Fuzzy C-Mean KSOFM - GK
2.43 seconds 8.32 seconds 43.27 seconds
The number of colors of which the image is reduced is six (6).

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Conclusions
• A new Color Clustering technique is proposed which is based on a
combination of a KSOFM neural network and the Gustafson-Kessel
fuzzy algorithm.
• The main advantages is that it can merge areas of the image with
similar colors and has the ability to retain the image’s dominant
colors.
• Future directions should include the ability to detect the optimal
number of final colors and reduce the high computational cost.