SEGMENTATION OF SATELLITE IMAGES IN

OPTOELECTRONIC SYSTEM

Andrey S. Ostrovsky, Ernesto Pino-Mota and Paulo C. Romero-Soría

Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla

A.P. 1152, 70000, Puebla, Pue., Mexico

Keywords: Image Segmentation, Image Classification, Synthetic Discriminant Functions, Optical Image Processing.

Abstract: The problem of segmenting the satellite images into homogeneous texture regions that correspond to the

different classes of terrestrial surface is considered. It is shown that this problem may be successfully solved

by using the method of spectral synthetic discriminant functions recently proposed by the authors for

classification of random image fields and realized by means of a rather simple optoelectronic technique. The

experimental results of segmenting the true satellite images are given.

1 INTRODUCTION

One of the central problems in automatic processing

of satellite images is to segment the given image into

homogeneous texture regions corresponding to

different classes of the terrestrial surface such as

different urban zones, mountainous zones, wooded

zones, agricultural zones, aquatic zones, etc. (Wu et

al, 1995). A specific feature of this problem is in the

fact that the images to be classified have

fundamentally random within-class variations so that

they must be viewed as being perfectly random or

stochastic. In this situation, one is better off talking

about the random image field and not the image

itself, i.e., as a deterministic function of space.

Recently we proposed a new method for

classification of such images in which we use the

special discriminant functions being synthesized to

separate linearly the power spectra of random image

fields of different classes (Ostrovsky et al, 2003).

We refer to this method as spectral synthetic

discriminant function (SSDF) method. In this paper,

we show how the SSDF method realized by menas

of a rather simple optoelectronic system may be

used for segmenting the satellite images.

2 SSDF METHOD

We consider a certain image of the nth classs (n =

1,…, N) as the 2-D kth (k = 1,…, K) sample

function

(

)

yxf

nk

, of a stationary and isotropic

random field

(

)

yxf

n

, with a power spectrum

() ()

2

;,

1

lim RF

R

S

nk

R

n

θρρ

∞→

= , (1)

where

() ()

ϕθρ

π

,;,

2

00

rfRF

nk

R

nk

∫∫

=

()

[

]

ϕ

θ

ϕ

ρ

π

ddcos2exp rrri −

−

×

, (2)

is the finite Fourier transform of

()

yxf

nk

, over the

domain of radio R occupied by the image,

()

ϕ

,r and

(

)

θ

ρ

, are the polar coordinates in the spatial and

spatial-frequency domains respectively, and the

angular brackets denote the expected value operation

over the ensemble index k. The SSDFs are defined

as linear combinations of power spectra

()

ρ

n

S , i.e.,

() ()

∑

=

=

N

l

lmlm

Sah

1

ρρ

, Nm ,...,1= , (3)

such that the following identity is determined:

() ()

nmmn

hS

δρρρ

≡

∫

∞

d

0

, (4)

408

S. Ostrovsky A., Pino-Mota E. and C. Romero-Soría P. (2007).

SEGMENTATION OF SATELLITE IMAGES IN OPTOELECTRONIC SYSTEM.

In Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics, pages 408-411

DOI: 10.5220/0001615204080411

Copyright

c

SciTePress

where

nm

δ

is the Kronecker symbol. On substituting

for

()

ρ

m

h from Eq.(3) into Eq. (4) and taking for

granted the hypotesis of linear independence among

the power spectra

()

ρ

n

S for different classes, one

can find the unknown coefficients

ml

a as the

solutions of the system of linear equations

() ()

∑

∫

=

∞

=

N

l

nmlnml

SSa

1

0

d

δρρρ

, Nmn ,...,1, = . (5)

Once the SSDFs have been calculated in accordance

with Eq. (3), a procedure for classifying the

unknown sample image

()

yxf

k

,

0

is to verify

identity (4) for every m when substituting for

(

)

ρ

n

S

the power spectrum

()

ρ

0

S of corresponding image

field

()

ρ

0

f .

As can be seen from Eq. (3), in oder to

determine the SSDFs, is necessary to know each

power spectrum given by Eq. (1); this presupposes

averaging over the infinite ensemble of infinitely

extensive sample images. Actually, we always have

available a finite number of finitely extensive

sample images, a fact that leads to the statistical

formulation of the problem.

The quantity that can be directly measured in an

experiment is the sample power spectrum integrated

in the azimuthal direction, i.e.,

() ()

θθρ

π

ρ

π

d;,

2

1

;

2

2

0

RF

R

RS

nknk

∫

=

. (6)

In the stage of SSDF synthesis, when we commonly

dispose a sufficiently large number of sample

images, the consistent estimate of power spectrum

()

ρ

n

S can be obtained by averaging the sample

spectra (6) over the ensemble index k:

()

∑

=

∧

=

K

k

nk

n

RS

K

S

1

;

1

ρ

. (7)

In the stage of classification, usually just one sample

image is available, so that identity (4) has to be

substituted for the equation

()()

nmk

n

nk

N

l

ml

uSRSa =

∧

=

∞

∑

∫

ρρρ

d;

1

0

, (8)

where

nmk

u is the kth sample value of some random

variable

nm

u . To maximize the reliability of correct

classification it is obvious to require that

(

)

nmmlnm

au

δ

= (9)

and

Var

(

)

ml

a

mlnm

au min→ . (10)

This can be readily achieved by applying the well

known least-square technique. Once the SSDFs have

been calculated in this way, the decision on the class

to which the sample image

()

yxf

k

,

0

belongs can be

made according to index m of the largest value

mk

u

0

.

3 OPTICAL REALIZATION

As apears from the previous section, the

fundamental problem with practical realization of

the SSDF method is calculating the sample power

spectrum given by Eq. (6). For this purpose the

coherent optical Fourier processor shown in Fig. 1

may be employed.

Figure 1: Optical Fourier processor.

As is well known (Goodman, 1986), if in the

object plane of this processor a transparency with

amplitude transmittance

()

yxf , within a finite

domain D of radio R is placed, then the intensity

distribution of light field registered by the CCD

detector array in the back focal plane of the Fourier

transforming lens is given by

SEGMENTATION OF SATELLITE IMAGES IN OPTOELECTRONIC SYSTEM

409

() ()

∫∫

=

)(

,,

D

yxfqpI

()

[]

2

dd2exp yxyqxpi +−×

π

, (11)

where

fxp

λ

/

′

= , fyq

λ

/

′

= ,

λ

is the wavelength

of illumination, and f is the focal length of the lens.

Using the polar coordinates for input and output

planes of the Fourier processor, Eq. (11) may be

rewritten as follows:

() ()

ϕθρ

π

,,

2

00

rfI

R

∫∫

=

()

[]

2

dd2exp

ϕθϕρπ

rrri −−× . (12)

Comparing the latter equation with Eq. (2) and (5),

we come to conclusion that the sample power

spectrum

()

RS

nk

;

ρ

may be easily calculated in any

PC-compatible system connected with CCD array.

4 EXPERIMENTAL RESULTS

We performed a physical simulation experiment on

segmentation of true satellite (Landsat) images into

homogeneous regions that correspond to four

different classes of terrestrial surface, to wit, “sea”,

“mountains”, “crops” and “settlement”. An example

of such an image is shown in Fig. 2. Each class of

texture images to be classified was considered a

spatially stationary and isotropic random field.

Figure 2: True satellite image used in the experiment.

The experimental setup is sketched schematically

in Fig. 3. The images to be processed in this setup

were previously converted into numerical files using

a standard scanning technique. To provide the

capture of the digitalized images into the optical

Fourier processor, the liquid crystal spatial light

modulator HoloEye-LC2002 (800

× 600 pixels)

controlled by PC was used. The detection of the

light distribution in the output plane of the Fourier

processor was realized by means of the CCD camera

SONY-SSC-M374 (768

×

494 pixels).

Figure 3: Experimental setup.

In our experiment, at the stage of SSDF

synthesis, we used 50 images of 10

× 10 mm for

each of four classes. At the stage of segmentation we

used the composed full-scale image of 100

×

100

mm and realized its 2-D scanning by an aperture of

5

×

5 mm with a discrete step of 5 mm. At every step

of image scanning the corresponding texture image

was classified in accordance with the SSDF method.

Calculation of SSDFs and values

mk

u

0

(see Eq. (8))

was realized in a PC-system using specially

designed software. Decision on image class at every

step of scanning was made on the basis of

thresholding the output data. If none or more than

one of

mk

u

0

values had exceeded the threshold, the

corresponding image region was considered to be

unclassified. The result of four-class segmentation

that corresponds to the satellite image in Fig. 2 is

shown in Fig. 4. The regions of the segmented image

labeled by “

0” correspond to unclassified images.

As can be seen, in the main these regions correctly

repeat the true shape of the boundaries between

terrestrial surface images of different classes, but, in

certain cases, they occupy a rather large area of the

image. The latter can be explained by the fact that,

in reality, our satellite image contains textures of

more than four classes mentioned above (e.g.,

regions of the terrestrial surface covered by clouds),

ICINCO 2007 - International Conference on Informatics in Control, Automation and Robotics

410

but more profound study of this problem exceeds the

limits of our consideration.

2 2 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1

0 0 0 0 4 4 4 0 0 0 3 3 0 0 0 1 1 0 1 1

0 4 0 4 0 4 4 4 0 3 3 3 3 0 0 0 0 1 1 1

0 4 4 0 4 0 0 0 0 3 3 3 3 3 0 0 0 1 1 1

4 4 4 4 0 0 0 0 3 3 3 3 3 3 3 0 0 0 1 1

0 4 4 4 0 0 0 0 3 3 3 3 3 3 3 3 0 0 1 1

0 0 3 3 0 0 0 0 3 0 0 0 0 0 3 0 0 1 0 1

0 0 0 0 0 0 0 3 3 3 3 0 3 3 0 0 0 0 0 1

0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 0 0 0 1

0 0 1 0 0 0 0 0 3 3 3 3 3 3 3 0 0 0 0 1

0 0 1 0 0 0 0 0 3 3 3 3 3 3 3 0 0 0 0 1

2 0 0 1 0 0 4 0 3 3 3 3 3 3 0 0 0 0 1 1

2 2 0 0 0 4 4 0 3 3 3 3 3 3 0 0 0 0 1 1

2 2 2 0 0 0 4 4 0 3 3 3 3 3 0 0 0 0 1 1

2 2 2 2 0 0 0 0 0 3 3 3 3 0 0 1 1 0 1 1

2 2 2 2 0 0 1 0 0 0 3 3 0 0 0 1 0 0 1 1

2 2 2 2 2 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1

2 2 2 2 2 2 0 0 1 0 0 0 1 1 0 0 0 0 1 1

2 1 2 2 2 2 2 0 0 0 0 0 1 0 0 1 0 1 1 1

2 2 2 2 2 2 2 0 1 1 1 0 0 0 0 0 0 1 1 1

Figure 4: Labled map of the satellite image shown in Fig.

2. Lables: 1 – “sea”, 2 – “mountains”, 3 – “crops”, 4 –

“settlement”, 0 – “unclassified image”.

5 CONCLUSIONS

As has been shown the problem of segmentating the

satellite images into homogeneous regions that

correspond to different classes of the terrestrial

surface may be successfully solved by using the

SSDF method for classification of random image

fields realized by means of rather simple

optoelectronic technique.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the support of

Mexican National Council of Science and

Technology – CONACYT, under project SEP-2004-

C01-46510.

REFERENCES

Wu, H.-S., Qian, J., Barba, J., 1995. A classified algorithm

for segmentation of multispectral images, Journal of

Imaging Science and technology, Vol. 39.

Ostrovsky, A.S., Pino-Mota, E., Palma-Cuatianquiz, J.,

2003. Optical classification of random image fields

using spectral synthetic discriminant functions. Optics

and Laser in Engineering, Vol. 40/1-2.

Goodman, J.W., 1986. Introduction to Fourier optics,

McGraw. New York, 2

nd

edition.

SEGMENTATION OF SATELLITE IMAGES IN OPTOELECTRONIC SYSTEM

411