Fuzzy Clustering Methods in Multispectral Satellite

Image Segmentation

Rauf Kh. Sadykhov

, Andrey V. Dorogush

and Leonid P. Podenok

Computer Systems Department, Belarusian State

University of Informatics and Radioelecrtronics

6 P. Brovka st, Minsk, Belarus

Laboratory of System Identiﬁcation, United Institute of

Informatics Problems, National Academy of Sciences of Belarus

6 Surganov st, Minsk, Belarus

Abstract. Segmentation method for subject processing the multispectral satel-

lite images based on fuzzy clustering and preliminary non-linear ﬁltering is rep-

resented. Three fuzzy clustering algorithms, namely Fuzzy C-means, Gustafson-

Kessel, and Gath-Geva have been utilized. The experimental results obtained us-

ing these algorithms with and without preliminary nonlinear ﬁltering to segment

multispectral Landsat images have approved that segmentation based on fuzzy

clustering provides good-looking discrimination of different land cover types. Im-

plementations of Fuzzy C-means, Gustafson-Kessel, and Gath-Geva algorithms

have got linear computational complexity depending on initial cluster amount

and image size for single iteration step. They assume internal parallel imple-

mentation. The preliminary processing of source channels with nonlinear ﬁlter

provides more clear cluster discrimination and has as a consequence more clear

segment outlining.

1 Introduction

It is known that forests and wetland are the main factors preventing the decline in bio-

diversity on the Earth in aggressive conditions of human activity. The main problem is

agricultural expansion and deforestation. Deforestation is the consequence of two main

reasons – agricultural expansion and accidental events. But forestry and agriculture are

inseparable and condemned to work hand in hand. Signiﬁcant part of forest is damaged

by ﬁre, pests, irrational agricultural politics leading to change of ground water level

and as result leads to sickness and wreck. At now it is possible to discriminate forest

areas on early stage of damaging using multispectral images of high spatial resolution

received from satellites. That technology started about 40 years ago to monitor Earth

surface at now is the effective instrument of ecological and agricultural monitoring such

the regions as forests and wetland and preventing any accidents. Multispectral satellite

images are able to bring us information in both visible and invisible spectral bands about

vegetation, water temperature and land cover.

Kh. Sadykhov R., V. Dorogush A. and P. Podenok L. (2007).

Fuzzy Clustering Methods in Multispectral Satellite Image Segmentation.

In Proceedings of the 3rd International Workshop on Artiﬁcial Neural Networks and Intelligent Information Processing, pages 91-98

DOI: 10.5220/0001635200910098

 SciTePress

Multi-dimensional cluster analysis and segmentation are base procedures in the-

matic processing the multispectral images received from remote sensing satellites. There

are lot of clustering and segmentation methods which have different beneﬁts and im-

perfections. The special class of such the methods is represented by fuzzy clustering

ones.

2 Method Description

Three clustering algorithms based on fuzzy methods where developed and utilized as

part of segmentation software. There are fuzzy c-means[1] (FCM) and its variants –

Gustafson-Kessel clustering algorithm [2, 3] and Gath-Geva one [4].

FCM is a method of data clustering which allows one data objects to be a member

of two or more clusters. This method developed by [5] and improved by [6] is based on

minimization of the following objective function:

J =

i=1

j=1

k x

− s

k, (1)

where m is real number ≥ 0, µ

– degree of membership of x

in cluster s

, x

the multi-dimensional data object, s

is the multi-dimensional center of the cluster, and

k · k is any norm expressing the similarity between any measured data and the cluster

center.

Fuzzy clustering is carried out through an iterative optimization of the J

with the

update of membership matrix µ

and the cluster centers s

using folowing algorithm:

1. The data set X = (x

) = (x

, x

. . . , x

)

given. We choose the number of

clusters 1 < c < n, where p – dimension of data set.

2. Initialize the partition matrix µ

using random number genetrator in range [0, 1]:

i=1

= 1, (2)

3. Calculate the cluster centers s

= (s

, s

, . . . , s

)

(i = 1, 2, ..., c):

j=1

, (3)

4. Calculate the error:

E =

i=1

j=1

− x

)

− x

). (4)

If error is small enough, then stop iterations, else go to item 5.

5. Calculate the ”new“ partition matrix µ

m=1

−

(5)

and then go to step 3.

where d

is similarity measure k · k.

Fuzzy c-means, Gustafson-Kessel, and Gath-Geva clustering algorithms are distin-

guished in the deﬁnition of distance function between the objects to be classiﬁed: Fuzzy

C-means:

= (s

− x

)

− x

), (6)

Simple euclidean distance provides hyper-spherical form of clusters.

Gustafson-Kessel:

= (s

− x

)

(det(F

)

−1

)(s

− x

), (7)

Gath-Geva:

det(F

)

exp(

− x

)

−1

)(s

− x

)), (8)

where F

is covariance matrix, that provides ellipsoidal form of clusters and more com-

prehensive partitioning the multi-dimensional data, α

is calculated in following man-

ner:

j=1

. (9)

Covariance matrix is used to form non-spherical clusters which are more suitable for

multi-dimensional data partitioning. That also leads to visible difference in algorithm

convergence, effectivity and performance of processing the multispectral images.

Distance function for Gustafson-Kessel and Gath-Geva algorithms uses covariance

matrix to take into account different metrics (scales) in different dimensions. The large

images to be processed might be the reason of weak covariance matrix conditional-

ity that results in heavy losses of aptitude for discrimination for Gustafson-Kessel and

overﬂows for Gath-Geva when ﬁxed digit capacity arithmetics based on atomic numer-

ical types is used. To keep of that problems standard normalization methods and arbi-

trary (multi-precision) arithmetics are the sufﬁcient efforts. When d

becomes small

the overﬂow may occure. To prevent that case the distant function is conﬁned from

below by some smallest value d

min

Due to source signal noise the some spatial segment granularity occurs. To reduce

that granularity the weak nonlinear ﬁltering using algorithm [7] was applied to source

channels. That algorithm may be used both for edges extraction and for nonlinear ﬁlter-

ing. It does not lower the sharpness of transitions of channel brightness the boundaries

of cover types remain clear. As a result the boundaries of spatial segments after cluster-

ing process also remain legible. Algorithm works with values of brightness and pixels’

coordinates simultaneously. To form the homogeneous areas or search the edges on the

gray-scale image a round mask is used. Usually the mask’s radius is 3.4 pixels which

Fig.1. Channels 2-5 of multispectral Landsat image to be processed with fuzzy clustering algo-

rithm.

gives mask of 37 pixels size. The mask is placed at each point of the image and the

brightness of each pixel of the mask is compared with the brightness of the mask cen-

tral pixel.

c(r, r

) =

(

1, I(r) − I(r

) ≤ t

0, I(r) − I(r

) > t,

(10)

where I(r

) – the brightness value of the mask’s center, I(r) – the brightness value of

the mask pixel, t speciﬁc threshold.

The result of the comparisons is sum:

n(r

) =

c(r, r

). (11)

where n is the quantity of pixels in the USAN (Univalue Segment Assimilating Nu-

cleus). Then that sum should be minimized, so the algorithm is called SUSAN (Small-

est USAN). Parameter t means the maximum of ignored noise. Then n is compared

with it’s thresholding value g, which is 3n

max

/4, where n

max

– maximum value which

could be assigned to n.

3 Experimental Results

To test the fuzzy clustering algorithms the multispectral Landsat images have been used.

Fig. 1 shows channels 2-5 which were chosen for processing. Landsat channels shown

on ﬁg.1 have different dispersion and were equalized using netpbm utilities to make

them visible more clearly. The channel data to be fed into clustering software remain

untouched because of clustering algorithm takes in to account real distribution of chan-

nel signal level on one’s own.

Raw output data of developed segmentation software is 2-d vector ﬁeld over R

where N is a number of clusters. Each component of that ﬁeld is strictly increasing

function of probability for pixel to be member of one of N clusters.

On presented images one can see some well discriminated land cover types. There

are open water, forests, wetlands, bushes and agriculture areas. Results of segmentation

on 15 clusters using fuzzy C-means without any preliminary ﬁltering show that there

also are fuzzy boundaries of segments on the cluster map going on to sand in some

places. To diminish such the phenomena one can use ﬁlter which will smooth slightly

changing areas rather blur clearly discriminated land cover type edges. Most appropri-

ate ﬁlter having got such the behavior is the non-linear one described in [7]. The ﬁg. 2

demonstrates smoothing properties of that ﬁlter when brightness threshold was choosed

be equal to 7, 15, and 20. Besides the brightness threshold parameter the ﬁlter has spa-

tial one – distance threshold which was set into default value corresponding to radius

equal to about 3.4 and was not changed across experiments. As one can see, smooth-

(a) (b) (c) (d)

Fig.2. Nonlinear ﬁltering samples: (a) original image, (b) brightness threshold = 7, (c) bright-

ness threshold = 15, (d) brightness threshold = 20.

ing property of that ﬁlter increases with brightness threshold grows. At the same time

some part of edges remains sharp. Amount of sharp edges and consequently cluster

granularity depend on brightness threshold. Thus we get additional degree of freedom

in segmentation process control that could dramatically improve the segmentation re-

sults. Nonlinear ﬁltering lowers intraclass covariance but practically doesn’t touches

interclass ones, so cluster discrimination doesn’t suffer. Smoothing the channels before

segmentation allows to eliminate ﬁne granularity of output segment map and to merge

the small cluster with large ones. In reality this means disappearance of some real small

objects, for example, bushes in wetland areas. Nevertheless, sometimes it is necessary

to get generalized segment map. The SUSAN ﬁlter allows to fulﬁl nonlinear processing

variyng the threshold in wide region achieveing the smoothing results from neglible

small up to very strong.

Fig. 3-6 demonstrate examples of segmentation using non-linear ﬁltering with dif-

ferent brightness threshold for Gustafson-Kessel and Gath-Geva clustering algorithms.

The cluster number was choosen taking into account real diversity of land covers for

territory being ivestigated. Actually a lot of experiments with different cluster number

were fulﬁled. As soon as segmentation become to look stable cluster number was stated.

Obtained results have transformed into scalar ﬁeld using simple maximal probabil-

ity solver to get the possibility of visual evaluation and have presented as colour map

of spatial partitions. As a result every pixel became a member of one cluster. All pixels

of same colour are members of same cluster. No any intelligent algorithm was used to

colourize segment map so the same areas on different pictures have different colours.

As one can see the growth of the threshold leads to raising the segment area when

target number of clusters is ﬁxed. However it should be pointed that general structure

of segment arrangement and its structure in relation with land cover types is not signif-

icantly changed.

(a) (b)

Fig.3. Segmentation results using Gustafson-Kessel (a) and Gath-Geva (b) algorithms at 20 clus-

ters without any ﬁltering.

4 Conclusion

Segmentation results of multispectral Landsat images obtained using fuzzy clustering

methods such as Fuzzy C-means, Gustafson-Kessel, and Gath-Geva with and without

preliminary nonlinear ﬁltering testify that segmentation using fuzzy clustering meth-

ods provides good-looking discrimination of land cover types that occurs in uch the

complex cases as wetland, water-meadow, and bush areas. The discrimination quality

of segmented images was tested and approoved by land-improvement specialists using

data of land-based expedition. The non-linear ﬁltering with guided smoothing is the

convenient instrument of preliminary processing for semi-automatic segmentation of

complex land covers.

Implementations of Fuzzy C-means and Gustafson-Kessel algorithms have got lin-

ear computational complexity depending on innitial cluster amount and image size for

single iteration step. All the algorithms assume internal parallel implementation for

MPP computer. The preliminary processing of source channels with nonlinear ﬁlter

provides more clear cluster discrimination and has as a consequence more clear seg-

ment outlining and provides operated generalization of output segment maps.

Really, segmentation software returns the results as 2-d vector ﬁeld v

, which is the

strictly increasing function of probability p

that pixel is a member of i-th cluster. When

using more complex tool then simple maximal probability solver, for example, maximal

(a) (b)

Fig.4. Segmentation results using Gustafson-Kessel (a) and Gath-Geva (b) algorithms at 20 clus-

ters using ﬁltering with threshold = 7.

likehood one, it is possible to signiﬁcantly improve the results of segmentation and to

avoid large part of manual processing the multispectral data.

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(a) (b)

Fig.5. Segmentation results using Gustafson-Kessel (a) and Gath-Geva (b) algorithms at 20 clus-

ters using ﬁltering with threshold = 15.

(a) (b)

Fig.6. Segmentation results using Gustafson-Kessel (a) and Gath-Geva (b) algorithms at 20 clus-

ters using ﬁltering with threshold = 20.