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Color image segmentation using local histogram and self-organization of Kohonen feature map

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Color Image Segmentation Using Local Histogram and

Self-organization of Kohonen Feature Map

You-Shen Lo and Soo-Chang Pei

Department

of

Electrical Engineering

National Taiwan University

Taipei, Taiwan,

R. 0. C.

E-mail:pei@cc.

ee.

ntu. edu. tw

Abstract

Segmentation is an important step for image anal- ysis, but a good segment algorithm which can handle color image with texture area and has less computa- tion time is rare. W e propose to use the local window image histogram, which is easy to compute and could quickly collect the information of neighbors, together with the Se2f-Organization of Kohonen Feature Map ( SOFM ) neural network, which can eficiently cluster data and has parallel hardware structure, as a segmen- tation kernel. Under the Euclidean distance function with input data normalization and the simplified Ma- halanobis distance function, this algorithm will have very good Segmentation results for natural images ei- ther full with texture or mixed with smooth scenes. 1

Introduction

Segmentation is an important pre-processing step for many inspections or detections in image analysis. Generally speaking, segmentation could be classified

into three major classes [l] : (1) characteristic feature

thresholding or clustering, (2) edge detection, and (3) region extraction.

The feature thresholding or clustering methods

[2, 31 usually project all the image data into the color

feature space to find the histogram, then try to thresh- old the histogram iteratively on the spatial domain and the histogram plane to segment the images [2].

More often, the researchers get used to take the color

spaces as the feature spaces [2, 31

.

Color feature

thresholding approaches assume each object in the im- age occupies its own color cluster in the color space. On the other hand, pixels with the same color may spread out around the the whole image, purely us- ing thresholding method, sometimes, can not clearly segment out the objects that we want. Actually, im-

ages bear more or less a few portions of texture area.

Therefore, many researchers try to use some compli-

cated features, like mean, energy, inertia, entropy and contrast etc. to segment images [4]. These features are derived from the spatial gray level dependence matrix (SGLDM). Though these features will involve more spatial information, they also introduce more compu- tational loading.

Self-organization of Kohonen Feature Map (

SOFM ) is a very powerful tool for data clustering.

It has shown successfully on image quantization [5, 61.

Since segmentation is a process of clustering, there-

fore, it is also suitable to apply SOFM computation. In this paper, we use SOFM neural network as a training tool and adopt the index-counts of the local histograms as the clustering features. First, we use SOFM trainer to do color quantization on a true nat- ural color image to get an indexed image. Second, we build index-count vectors of each local histogram from the indexed image. Then, we use the index-count vec- tors ( or features ) as the second step of SOFM training data. Finally, after the training, we map back the bor- ders between each cluster from the index-count space to the original image. And we get a well-segmented result.

In section 2, we describe the local histogram based segmentation algorithm. In section 3, we show the simulation results and have discussions on distance

functions, numbers

of

classes and window sizes. And

finally, we make some conclusions.

2

Local Histogram Based Segmenta-

t ion Algorithm

The proposed local histogram based segmentation algorithm is a two-step training algorithm. First, we apply SOFM trainer to do the color quantization for

input true color images. It is a data reduction pro-

cess. Too much data and information will cause the computation loading too heavy. And the color quanti- zation is a fast and efficient data reduction process for

232

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true color images. Our previous paper [5] uses SOFM method to do color quantization and gets the indexed images. This method will reduce the redandant in-

formation and also keep the borders’ information for

segmentation.

Second, any image may have its own histogram. The histogram reveals part of characteristics of that image. But dividing the feature spaces into a few clus- ters by thresholding, still there are some portions of image hardly to find their correct clusters. Due to the vague separation on global histogram, we use the lo- cal histograms as our dynamic segment features. The indexed image is a kind of image with fewer color in- dexes and its color table. Therefore, we can calculate the index histogram of that indexed image. Instead of calculating the global histogram of the index im-

age, we calculated the local histograms at a n, x n,

moving window centered at pixel (i, j) and sliding over

the whole index image. We call one of the entries of the local histogram as an index-count, which is the counting number of one specified index in the moving window at pixel ( i , j ) in that index image. Since the pixel

(i,

j ) is around with n, x n,

-

1 neighboring pix-

els, the local histogram calculation

,

dealing with n,

x n, window of pixels, will include in all the neigh-

boring ( spatial ) information. We have three ma- jor reasons to support the index-counts as the train features: First, the index-count vectors are omnidi- rectional, therefore, features are not biased for any direction. We do not have to worry about the direc- tion problem. Second, local index-counts are around

pixel (i,j)

,

so they could collect local and neighbor-

ing information. Third, local index-counts are easily calculated and very low complexity.

Then, we apply SOFM training algorithm to the local histogram index-count vectors of the first step output indexed image. For two pixels, if their index- counts are similar, they should belong to the same class. According to the characteristics of index-counts, the SOFM trainer would classify the indexed image into several pre-defined classes; that is, we use the index-counts of local histograms as the features to classify the image into the predefined clusters. And the borders of the clusters form the segmented pieces

of the image. Then we get our final segmented image

results. See Figure 1 for the flowchart of the algorithm. We have tried serveral distance function for train-

ing; such as : the Euclidean distance function, the in-

ner product distance function, the min-max distance function, the Mahalanobis distance function and the simplified Mahalanobis distance function. Each train- ing case may have input data with normalization or

not. The equations are shown as below. The Eu-

clidean distance function :

J

min dist(x,mi) =

C(rj

-

r n i , j ) 2

.

(1)

2

j=1

The inner product distance function :

J

m p dist(x, m i ) = ~j

.

m i j

.

(2)

j=1

The min-max distance function :

J

max 2 dist(x,mi) = C m i n ( z j , r n i , j )

.

(3) j=1

The Mahalanobis distance function :

min dist(x, mi) = (x

-

mi)TC;’(x

-

mi)

.

(4)

2

The simplified Mahalanobis distance function :

J

9 (5)

(Zj

-

r n i , j ) 2

min 1 dist(x,mi) = C i , j j=1

where x is the input local index-count vector, mi is

the i’th neuron’s value and the c t j is the each entry

of the covariance matrix of all input data.

When the distance measure for training is the Eu-

clidean distance function, we should use the minimum criterion for two-vector difference. If we use inner product distance function as the distance measure, we should use the maximum criterion for two-vector inner

product, the same as the min-max distance function.

Other distance functions all apply the minimum cri- terion.

3

Simulation Results and Discussions

We test the ”lake” color image for segmentation,

and the segmented results are on Figure 2. Figure 2

(a) is the segment result for lake whose window size is

7

x 7 and the distance function is Euclidean distance

for 4 clustering classes. Also, the input data have been

normalized at every training step. We could clearly

see from the segmented image of lake that the ho-

mogeneous portions ( with and without texture ) are clearly segmented out. There is no objective evalua- tion function for segmentation, but we could see from the segmented pictures that the segmented results are fairly good. Hence, our proposed algorithm is very powerful for image segmentation.

When considering the spatial interaction due to the

window sizes, we show the segmented result of 15 x

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15 window size for comparison. Figure 2(b) is the

result with the same condition as Figure 2(a) except

for the window size. With larger window size, the segmentation results degenerate in some area and can not match the borders of the objects. Too small the window size may have more detail segment and better alignment but causes more ragged edges.

As for different distance functions, we have tried Euclidean distance function, inner product distance function, min-max distance function, Mahalanobis distance function and simplified Mahalanobis distance function. Each training case may have input data with

normalization or not. This may have great influence

on training results. The segmented results applied the Euclidean distance function and with input data nor- malization are better than those cases without nor- malization.

When increasing the cluster classes from 4 to 8,

the segmentation results have more ragged detail area. The darker leaves and lighter leaves are easily sep- arated out. Figure 2(c) shows the result. The more classes the image data could be assigned, the more de- tailed segments we can see. Hence, if we desire more details of the image, we could increase the number of classes. This is suitable for segmentation-based image compression.

The results which applied simplified Mahalanobis distance function are better than the Mahalanobis dis- tance function, and their results are shown on Figure There is no significant difference when the number

of color index is 16 or 32. Therefore, we do not show

any result of this part.

The final disscusion is about the training features. Compared to many features derived from SGLDM [4], which many papers use [4], we use the index-counts of

local histogram as the training features. The SGLDM

is a 2-dimensional distribution based on the number of

occurrences from one gray level to another. And those features, like mean, variance, correlation, energy, en- tropy, contrast and homogeneity, are calculated from the SGLDM. The first layer of SGLDM calculation is

as simple as our index-count calculation

of

local his-

togram. But the second layer of the above features are derived from the complicated calculation and with

many multiplications. Even there is a fast algorithm

to find those features in the second step [4], it still

takes time. Therefore, our training features will be a

simple calculation. 2(d).

4

Conclusions

The significant concept of our local index histogram based segmentation algorithm is that the color quan-

tization is the first rough segmenting process on the color space and the index-counts of local histogram training is the second stage fine process for segmenta- tion. The first stage of operation reduces the amount

of data for the second stage training. And, at the

second stage, instead of using SGLDM [4] parameter

as the training feature, we find that the index-counts

of local histogram is a nice.feature for segmentation. Index-counts are omnidirectional, full of spatial and local information and easy to compute. Hence, our algorithm not only considers the neighboring informa- tion of the image for segment, but also greatly reduces

the computation burden. Meanwhile, SOFM is a fast

training method and has parallel hardware structures. Therefore, it can segment images very fast and well no matter the images are mixed with smooth or texture areas.

References

[l] N. R. Pal and

S.

K. Pal, ”A review on image

segmentation techniques ”

,

Pattern Recognition,

vol. 26, no. 9, pp. 1277-1294, 1993.

[2] M. Celenk, ”Analysis of color images of natural

scenes”, Journal of Electronic Imaging, vol. 4, no.

[3]

S.

Tominaga, ”Color classification of natural color

images”, Color Research and Application, vol. 17,

no. 4, Aug. 1992.

[4] Z. Wang, A. Guerriero, M. De Sario, ”Compari-

son of several approaches for the segmentation of

texture images”, Pattern Recognition Letters, vol.

[5]

S.

Pei and Y. Lo, ” Color image compression and

limited display using self-organixation Kohonen map

”,

IEEE Trans. on Circuit and System for

Video Technology, vol. 8, no. 2, pp.191-205, Apr. 1998.

[6] N.

M.

Nasrabadi and

Y.

Feng, ”Vector quan-

tization of images based upon Kohonen self-

organizing feature maps”

,Proc.

IEEE ICNN, pp.

4, pp. 382-396, 1995.

17, pp. 509-521, 1996.

1101-1108, 1988.

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Create an indexed image from the true color image

a

-

Calculate the Train the index-count Map back the borders

--

index-counts of

-.

vectors of the

-

-

between two different local histogram clusters to original image the local histogram

c.

Figure 2: Segmented results : (a)window size 7 x 7

,

4 classes

,

Euclidean distance function with data normaliza- tion. (b) window size 15 x 15

,

4 classes

,

Euclidean distance function with data normalization. (c) window size 7 x 7, 8 classes, Euclidean distance function with data normalization. (d) window size 7 x 7

,

4 classes

,

simplified Mahalanobis distance function.

數據

Figure 2:  Segmented results  :  (a)window size  7  x  7  ,  4  classes  ,  Euclidean distance function with data normaliza-  tion

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