int. j. remote sensing, 1998 , vol. 19, no. 18 , 3595± 3606
An automated region growing algorithm for segmentation of texture regions in SAR images J. LIRA² and L. FRULLA³ ² Instituto de Geofõ sicaÐ UNAM, AP 22 -560 , 14091 Me xico DF, Mexico; e-mail:
[email protected] ³ Satellite Radiometry DivisionÐ CONICET, Julia n Alvarez 1218 , ( 1414 ) Buenos Aires, Argentina; e-mail:
[email protected] (Received 1 6 May
1997;
in revised form 2 0 January 1 9 9 8 )
Synthetic Aperture Radar (SAR) images have a high geomorphologic information content. Due to the particular operation of this sensor the geomorphologic features of the Earth’s surface are enhanced, hence providing valuable detail related to texture of terrain. In this work, speckle reduction in SAR images is considered ® rst by applying selected ® lters to the original image. The e ectiveness of the ® ltering was qualitatively evaluated for the whole image, and quantitatively estimated on selected smooth and rough texture areas. The quantitative evaluation was done by calculation of image parameters such as contrast, edge sharpening and speckle reduction. This analysis indicated that the geometric ® lter performs the best for SAR images. The ® ltered image was input into an automated region growing algorithm that produced segmented texture objects. The texture model and the parameters of the algorithm are based upon the co-occurrence matrix. From this, a new texture distance is introduced. This distance is used to quantify the optimal parameters of the automated algorithm and to determine the e ectiveness of the segmentation. Once the image is segmented the morphology of texture regions is obtained, this comprises the following parameters: area, perimeter and fractal dimension. A texture distance between regions is also calculated in order to estimate the texture separation of these regions. A detailed example is provided to illustrate the methodology proposed in this research. Abstract.
1.
Introduction
The concept of texture is a subjective and qualitative idea developed by the psicovision in human beings. This concept is structured with limited capacity in the psicovision because textures di ering beyond the second statistical moment are not distinguished (Gotlieb and Kreyszig 1990 ) by humans. In a digital image, texture manifests itself as an organized spatial phenomenon of pixel values. A texture object is a particular or speci® c organization of pixels. Therefore, before attempting detection of texture objects the construction of a texture model is required that quanti® es and delimits the idea stored in the psicovision. To detect an object a texture model is needed, and to quantify the e ectiveness of the segmentation, a texture distance is required. This in order to measure the texture separation among the various objects obtained in the detection process. The recognition of a texture object is the result of a detection process implying the segmentation and labelling of the object in one of a category of class textures. In this work the labelling step is qualitative. 0 143 ± 1161 / 98 $12 .0 0
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1998 Taylor & Francis Ltd
3596
J. L ira and L . Frulla
On the other hand, the coherent interaction of the phased electromagnetic pulses with the surface under study gives rise to a granularity aspect in the image known as speckle noise (Lee 1986 ). The reduction of this noise by digital techniques is required before a texture analysis is carried on the radar image. The texture models reported in the literature (Reed and du Buf 1993 ) may be classi® ed in three broad categories: structured-based, feature-based and model-based. In the ® rst category the existence of detectable primitive elements is assumed. Due to the heterogeneity of natural scenes this condition is not generally ful® lled by radar images. In the feature-based methods, regions of constant and predetermined texture characteristics are sought, while in a model-based technique the textures are conceived as the result of an underlying stochastic process. When model parameters are employed as texture features, the model-based techniques may be considered as a subcategory of the feature-based methods. In the present work a model-based texture approach was selected, utilizing the entropy descriptor for the co-occurrence matrix that is evaluated on a window in the image. The segmentation of a speci® c texture object is carried out by means of an automated region growing algorithm. The nature of a region growing algorithm (Zucker 1976 , Morel and Solimini 1995 ) is appropriate for detection (segmentation) of texture objects. A number of results have been reported in the literature. Raafat and Wong ( 1988 ) constructed a texture model and a texture distance based on the gradient magnitude and gradient directionality. In this work the region initiation is achieved by using resolutiondependent texture information measures. The region growing process is then directed by the texture distances between image texture blocks; a good but a rather coarse segmentation is obtained with this procedure. Considering a region growing scheme, Kai and Muller ( 1991 ) segmented multi-spectral satellite imagery generating thematic maps of unidenti® ed spectral features. The growing of the regions was conducted using a local absolute brightness di erence as a threshold provided by the user in combination with edge information derived from the image itself. This proved to be useful in segmenting low contrast satellite data. In this paper, a model-based texture approach was selected. The results of this research on segmentation of texture objects and a new texture distance by means of a region growing algorithm are presented. The parameters involved in this algorithm, the window size and the threshold, are optimized according to the texture model and to the texture distance. This optimization is to obtain the best separation among the segmented objects. Once an optimum segmentation is achieved the morphology of each segmented region is evaluated so the spatial structure of texture objects may be estimated. Hence the objective of this work is twofold: ( 1 ) to design and construct an automated region growing algorithm; and ( 2 ) to measure the morphological characteristics of speci® c segmented texture objects. In the following three sections details about speckle reduction, the texture model, the texture distance, and the region growing algorithm are provided. 2.
Speckle reduction in SAR im ages
The antenna of a Synthetic Aperture Radar (SAR) system produces a wavetrain of coherent phased electromagnetic pulses that interact with the Earth’s surface. In the instantaneous ® eld of view irradiated by these pulses, there is a certain set of objects that perform as scatters when their size is comparable to the wavelength of the radar. Those objects backscatter the incoming radiation in di erent directions and phases, generating a constructive and destructive undulatory phenomenon. This
An algorithm for segmentation of texture regions
3597
interference phenomenon is known as speckle coherence e ect, appearing in the image as a random granularity formed by pixels of varying brightness. In this sense the speckle noise appears with a well-de® ned structure: very narrow spikes with positive and negative intensities superimposed on the general pro® le of the image. Hence, based on the family of speckle ® lters (Frost et al. 1982 , Kuan et al. 1985 , Lee et al. 1994 ), the noise structure is adequate for the application of a geometric ® lter (Crimmins 1985 ). The construction of this ® lter is upon a Hit or Miss (Pratt 1991 ) morphological transformation. Thus, this ® lter was applied to the SAR image and compared to the Median and the Lee multiplicative ® lters (Lee et al. 1994 ). The comparison included the change in contrast (cf ), retention of mean value ( m), change of standard deviation (s), and a speckle factor given by s/ m. On the grounds of a previous work (Escalante-Ramirez and Lira 1996 ), a qualitative comparison was also done. This included the modi® cation of a selected pro® le (® gure 2 (a)), preservation of edges and texture details, overall sharpness and general image quality (® gure 2 (b )). This evaluation was done on two selected windows that included smooth and textured regions. In brief, based on ® gure 2 and table 2 , the mean value, the edges, the texture details and image sharpness should be maintained as much as possible. On the other hand, the contrast, the standard deviation, and the speckle factor should be reduced and converge as fast as possible. The image quality should improve as appreciated from ® gures 1 and 2 . The modi® cation of these parameters (quantitative and qualitative) through several iterations of the ® lters was observed. The geometric ® lter is the fastest convergent ® lter (Pastrana 1996 ) in relation to the above parameters: the overall change from the ® rst iteration to the second was less than 10 %. The above permits us to conclude that the geometric ® lter applied with one iteration is the most suitable speckle reduction procedure for SAR images.
3.
Texture model
The texture image and the speckle noise are assumed to be the result of a stochastic process, resulting in two hierarchical random ® elds (Nguyen and Cohen 1993 ). At the higher level is the texture image and at the lower level is the speckle process. The speckle process is assumed stationary resulting from the average of independent realizations of single-look intensity observations (Derin et al. 1990 ). Therefore, let z = {z (i, j )} de® ned over the domain D = {(i, j ), 1 < i # N , 1 < j < M } be a speci® c speckled textural image. The image z is a realization of a bidimensional random ® eld Z = {Z (i, j )} , hierarchically de® ned in terms of an underlying random ® eld X = {X (i, j )} . This characterizes the partition of the domain D into regions of di erent texture type. The random variable X (i, j ) may take value in one of a set of labels representing a set of texture regions. In each of these regions a texture object is assumed to be the result of a homogeneous random ® eld. Then, the region growing based segmentation may be stated as follows: given the speckled textural image z = {z (i, j )} , estimate the partition xà = {xà (i, j )} that best corresponds to a similarity criterion applied to z . This criterion is derived from the texture model itself. The texture model is based on the co-occurrence matrix de® ned as follows: let d be a compact and convex set established in the image space as and odd-sized rectangular window and let b be a vector position operator relating the relative spatial location of a pair of pixels in the window. The co-occurrence matrix C is the estimated probability of having a pair of pixel values (lp , lq ) in the relative position
J. L ira and L . Frulla
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given by b; the elements of this matrix are then given by c (lp , lq , b , d )=
O { r |r, r + b × s (d ), g (r )= lp , g (r + b )= lq } O { r |r + b × d }
(1 )
where g (r ) is the radar image, s(d ) is a translation isometry over the window, O is the order of the set, and r = (i, j ) is the vector position of a pixel in the image. The dimension of the co-occurrence matrix is equal to the allowable pixel values: 256 for most radar images. The in¯ uence of this quantization level on texture evaluation was studied by inspection of the image histogram and by evaluation of the co-occurrence matrix for 64 and 256 levels. Considering this, the quantization level is reduced to 64 since no signi® cant loss of information is observed, resulting in a manageable co-occurrence matrix with less computational load. In addition to this, since the correlation between neighbouring pixels falls o rapidly (Li 1988 ), the magnitude of b is taken to consider only eight connected pixels. To characterize the texture information content of the co-occurrence matrix the entropy criterion (Haralick 1979 , Gotlieb and Kreyszig 1990 , Reed and du Buf 1993 ) was utilized E =Õ
p
63
63
= 0 q= 0
c pq
log c pq
(2 )
where c pq are the elements of the co-occurrence matrix for a given b and d . The radar image is referred to a regular grid where eight principal directions are de® ned according to the Freeman code: 0 ß , 45 ß , ¼ , 315 ß . However, the elements of the co-occurrence matrix are symmetric for opposite directions. Hence, four directions of b were selected: 0 ß , 45 ß , 90 ß and 135 ß , and an average value is obtained over these directions. 4.
Automated region growing algorithm
The region growing algorithm requires two parameters to initiate a segmentation: a window size and a threshold. Firstly, a number of selected texture objects (regions) are identi® ed (manually or automatically) in the image, and a suitable seed pixel is placed in each of them. In this work a manual placement of seeds was done. Secondly, a window is associated to each seeded pixel where initial texture values are estimated by means of equation ( 2 ). It is assumed that an optimum size window exists that di erentiates the most texture values related to each seeded pixel window. Only oddsized windows are considered. Beginning from 3 Ö 3 pixels, the window size is systematically incremented until an optimum window is obtained according to equation ( 4 ). To decide if a pixel is aggregated into a region a texture di erence between the tested pixel window and the initial one is obtained. If this value does not exceed a certain threshold the tested pixel is incorporated into the region. It is also assumed that an optimum threshold exists that best di erentiates the di erent texture regions signalled by the seeded pixels. To optimize the above parameters a texture distance is required. In the following subsections the optimization of those parameters is introduced. 4 .1 . T exture distance de® nition
This distance is constructed on the grounds of the texture model itself, for this, a joint entropy for pairs of windows is now introduced. Let consider two texture classes: t and s , for which a window of size n Ö n is associated to each seeded pixel.
An algorithm for segmentation of texture regions
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First, a joint co-occurrence matrix for pairs of pixels (lsp , ltq ) that occur in the same relative position in each window is obtained. If two equally smooth (or rough) textures are present in the two windows, the resulting joint matrix shall have a single element, and the joint entropy
st
En=Õ
st
p
c pq
q
st ] log [c pq
(3 )
will be zero, that is the texture distance is null, and reaches a maximum when the texture’s s and t are totally di erent. From equation ( 3 ) a texture distance matrix for pairs of classes is obtained. The texture distance is given by E nst , Ys Þ t . The optimum window size is estimated when the average value E n=
Nc
2 N c (N c Õ
1)
s
Õ
1
Nc
= =+ 1 t
s
st
1
(4 )
En
is maximum, where N c is the number of considered classes. Where E nst = E tsn , if t Þ s , and E stn = 0 , if t = s . It is worthwhile mentioning that a texture class is formed by a set of objects of similar texture value. An object occupies a region or a patch in the image. 4 .2 . Optimum threshold
It is assumed that there is an optimum threshold value for the growing of each region class. The estimation of this threshold is based upon the texture distance among classes and the texture distribution of the window’s pixels that compose the initial window class. Let us consider the group of n Ö n windows centred on each of the pixels of the initial window’s classes. The initial window class is equal to the optimum window size. For each pixel member of this collection of window’s classes a set of n Ö n entropy values is obtained Ea n;
E nÖ
1
n
{E n , ¼
n
}a
(5 )
where a represents the set of texture classes. Each set of distribution entropy values has associated a mean ( mna) and a standard deviation (san ). The average distance (Gong and Howarth 1992 ) between two entropy distributions is de® ned by Ea n
st d =
n
1 nÖ
n
i
Ö
n
=1
|E sn (i )Õ s
t
E n (i ) | t
sn + sn
, Ys Þ
t
(6 )
This expression measures the average similarity or dissimilarity of two texture objects and quanti® es the e ectiveness of the segmentation. Once the optimum window is established, the mean ( man ) and standard deviation (san ) of each initial window class is calculated. Hence a pixel is aggregated into a region if its entropy-related value (E p ) does not di er from this mean by a certain percentage. Therefore an optimum threshold is ® xed as follows ea= 2 san
(7 )
Expression ( 7 ) measures the existence of a textural border for a given class a, and also indicates the percentage of variation about the mean. A tested pixel p is then aggregated into class t if its associated entropy value E p is close enough to the entropy mean of the initial window for this class, thus p
Class t : |E ¾p Õ
m¾n |
