Sharif University of Technology
Scientia Iranica
Transactions A: Civil Engineering
www.sciencedirect.com
Improving change detection methods of SAR images using fractals
H. Aghababaee
a,∗,
J. Amini
a,
Y.C. Tzeng
b,1aDepartment of Surveying and Geomatic Engineering, University of Tehran, Tehran, Iran bDepartment of Electronic Engineering, National United University, Maio-Li, Taiwan Received 2 August 2011; revised 10 September 2012; accepted 1 October 2012
KEYWORDS Change detection; FCM; Fractal dimension; Neural network; SAR images; SVM.
Abstract Land use/cover change detection is very important in the application of remote sensing. In the case of Synthetic Aperture Radar (SAR) acquisitions for change detection, the standard detector or change measure is based on the ratio of images. However, this measure is sensitive to the speckle effect. In this paper, we improve change detection methods using a new change measure. The measure uses a grey level gradient or intensity information and the fractal dimension. The proposed measure is partitioned into two distinct regions, namely, changed and unchanged, using some change detection methods like Support Vector Machines (SVM), Fuzzy C -Means clustering (FCM) and artificial neural networks with a back propagation training algorithm. Experiments over the study area show that the results of implementing change detection methods are improved by using the proposed measure, in comparison to the classical log-ratio image. Also, results prove that the measure is very robust to the speckle effect.
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1. Introduction
In remote sensing applications, change detection is the process of identifying the differences in the state of land cover or land use by analyzing a pair of images acquired in the same geographical area at different times [1,2]. Land use/cover change detection in remotely sensed data may be done in either a supervised or an unsupervised way [3–5]. In supervised techniques, a set of training patterns is required for training the classifier. On the other hand, there is no need for training data in unsupervised techniques. The supervised manner requires the availability of a multi-temporal ground truth to derive a suitable training set for the learning process of the detectors. Although the supervised approach exhibits some advantages over the unsupervised one, the generation of an appropriate multi-temporal ground truth is usually a difficult and expensive
∗Corresponding author. Tel.: +98 2188334409.
E-mail addresses:aghababaee@ut.ac.ir(H. Aghababaee),jamini@ut.ac.ir
(J. Amini),john@nuu.edu.tw(Y.C. Tzeng). 1 Tel.: +886 37381526.
task. Consequently, the use of effective unsupervised change detection methods is fundamental to many applications for which ground truth is not available. The unsupervised approach is attractive for change detection tasks due to its self organizing, generalizable and fault tolerant characteristics [6]. In some cases, change detection can be viewed as a particular case of the multi-temporal image classification problem. Post and pre classification comparisons are the two main approaches in this view. In the first case, the images of two dates are independently classified and co-registered, and an algorithm is used to identify those pixels whose predicted labels change between dates. In the second case, a single classification is performed on the combined image data sets for the two dates [7].
Synthetic Aperture Radar (SAR) is active microwave coher-ent imaging radar, so it can acquire remote sensing data under all weather and all day, which can make up for the shortage of optics and infrared remote sensing. With the development of SAR image technology, platform, band, multi-polarization SAR image resources supply an advantage for SAR images. However, a downside in SAR images is the presence of speckle noise. Theoretically, SAR signals can be characterized as a chaotic phenomenon, because the scattering signals within a resolution cell are summed up coherently. Accordingly, SAR sig-nal can be represented by a spatial chaotic model and charac-terized by its fractal dimension [8,9]. Therefore, speckle, which
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doi:10.1016/j.scient.2012.11.006
Open access under CC BY-NC-ND license.
a
b
Figure 1: (a) Coherent scattering of many elementary scatters in a footprint; (b) sum of individual scattering contribution inside one resolution.
is resulted from coherent energy imaging, can also be properly characterized by its fractal dimension [8].
An interest in using fractals in satellite images has been sparked since 1989 [10,11]. From then to now, fractal models have been used in a variety of image processing and pattern recognition applications. For example, several researchers have applied fractal techniques to describe image textures, data fusion, edge detection and classification [12–15].
The main problems of change detection in SAR images are: (1) Generating a change measure or the change indicator. (2) Thresholding the change measure to produce a binary
change map.
The overall performance of the detection system will depend on both the quality of the change measure and the quality of thresholding. For addressing the aforementioned problems, a new measure is proposed by combining the fractal dimension and the intensity information of the original SAR images. Fractal dimension is computed by using wavelet multi-resolution analysis based on the concept of fractional Brownian motion. To obtain a change map, the measure is partitioned into the changed and unchanged regions using some change detection methods, like Support Vector Machines (SVM), Fuzzy C-Means clustering (FCM) and artificial neural networks with a back propagation training algorithm. The main contribution of the paper is an information theory-based measure which uses original SAR image information and its fractal dimensions simultaneously in supervised and unsupervised change detection. For interesting approaches in the field of change detection on SAR images, the reader can refer to the works of Martinis et al. [16], Xiong et al. [17], Bovolo and Bruzzone [18] and Wan and Jiao [19].
The rest of the paper is organized as follows: The next section presents the improvement in change detection methods using fractals. Section 3 describes the data sets used in the experiments and its results, and, finally, Section 4 includes discussion and the conclusion of this paper.
2. Material and method
SAR satellite systems are active systems that receive a complex combination of scattering of many scatterers in a footprint (Figure 1(a)). In many instances, thousands of pulses are summed for each footprint, resulting in a tremendous increase of the target signal compared to that from a single pulse. The sum of individual scattering contributions inside a footprint can be formulated by Eq.(1):
Aeiϕ
=
n
k=1
Akeiϕk
.
(1)In Eq.(1), the sum looks like a random walk in a complex plane (see Figure 1(b)), where each step of length Ak is
in a completely random direction. A random walk process is equivalent to a Brownian motion, which is the special case of fractional Brownian motion (fBm) with Hurst index 0.5 [8]. Based on this concept, many researchers have already proven that the SAR signal is chaotic and follows fBm [20–22]. According to [8,9], SAR images resulting from these signals can be characterized by the fractal dimension in a Spatial Chaotic Model (SCM). There are various methods for computing fractal dimension. One of them is based on the concepts of fractional Brownian motion (fBm) and wavelet multi-resolution analysis. Fractional Brownian motion is a Gaussian zero-mean nonstationary stochastic process
(
BH(
t))
, indexed by a singlescalar parameter, 0
<
H<
1, and defined as [23]:BH
(
0) =
0,
BH(
t) −
BH(
s)
=
1 Γ(
H+
0.
5)
0 −∞
(
t−
s)
H−0.5−
(
s)
H−0.5
dB(
s)
+
∞ 0(
t−
s)
H−0.5dB(
s)
,
(2)where H is the Hurst coefficient, t and s represent time, andΓ is the Gamma operator. Fractal dimension
(
Fd)
and the Hurstcoefficient are related to each other, as seen in Eq.(3):
Fd
=
E+
1−
H,
(3)where E is the Euclidian dimension. The Euclidian dimension for the image is 2
(
E=
2)
, and Eq.(3)can be written by Fd=
3
−
H. By computing the Hurst index(
H)
, the fractal dimension is determined. For computing the Hurst index, we should compute the power spectrum of fBm. The power spectrum of fBm can be written as [24]:S
(w1, w2) ∝
1|
w
21
+
w
22|
H+1.
(4)In Eq.(4),
w1
,w2
are the two axes in the frequency domain. To compute the power spectrum of fBm from SAR images, the following equation can be used [24]:S
(w1, w2) = |
FFT(
image)|
2.
(5)Figure 2illustrates the wavelet decomposition of an image at two different resolutions. If the frequency domain signal is filtered with a wavelet filter, the resulting spectrum at the specific resolution
(
j)
is [25]:S2j
(w1, w2) =
S(w1, w2)|
Ψ32j
(
2−j
(w1, w2))|
2,
(6)whereΨ3
(w1, w2) = ψ(w1)ψ(w2)
andψ(w1)
orψ(w2)
is aone-dimensional wavelet associated with the scaling function
ϕ(w1)
orϕ(w2)
. Based onψ(w1or2)
andϕ(w1or2)
, the threetwo-dimensional wavelets can be defined as follows:
Ψ1
(w1, w2) = φ(w1)ψ(w2),
(7a)Ψ2
(w1, w2) = ψ(w1)φ(w2),
(7b)Ψ3
(w1, w2) = ψ(w1)ψ(w2).
(7c)It should be noted that in this paper, the Daubechies-6 wavelet and scaling function are used. According to [25], the discrete version of Eq.(6)can be written in the form of Eq.(8):
S2j
(w1, w2) =
2j ∞
k=−∞ ∞
l=−∞ S2j(w1
+
2j2kπ, w2
+
2j2kπ).
(8)Figure 2: Decomposition of two-dimensional frequency.
The energy of the detail function at a specific resolution
(
j)
can be calculated by integration in the support ofΨj3
(w1or2)
of the chosen wavelet filter:σ
2 2j=
2−2j 4π
2 2jπ
−2jπ 2jπ
−2jπ S2j(w1, w2)
dw1
dw2,
(9)where
σ
is the energy of the detail signal at specific resolution. By integrating Eq.(9)at two different resolutions (j and j+
1), the following relationship is obtained:σ
22j
=
22H
σ
22j+1
.
(10)The above result does not depend on specific resolutions. A linear least square fit performed on Eq.(10)yields [26]:
H
=
1(
J+
1)
log 4·
log J−1
j=−1σ2
j+1 J−1
j=−1σ2
j,
(11)where J is the number of different resolutions of the image. Thus, according to Eq.(3), we can find the fractal dimension based on parameter H. Because the fractal dimension repre-sents information regarding spatial variations, its estimation should be realized by moving a specific window size over the entire image. In this paper, a window with size of 11
×
11 pix-els is used to compute the local fractal dimension. The center pixel of the window at each position of the image is replaced by the estimated local fractal dimension with the earlier method.Figure 3(a) shows an ALOS-PALSAR image and its correspond-ing fractal image is shown inFigure 3(b), which is obtained by a moving window.
To find the change map of two SAR images, I1, I2, which have
been registered with respect to each other, after computing fractal images, we propose a heuristic parameter, D, as a change measure computed by the normalized log-ratio of two SAR images and the normalized difference of two fractal images:
D
=
|
FI2−
FI1|
2+
Log
I2 I1
2,
(12)where FI1, FI2are two fractal images corresponding to the SAR
images. Fractal images give information regarding the texture of the image, which means the proposed measure
(
D)
is sensitive to texture changes. At this stage, the measure is segmented into the changed and the unchanged regions by employing the change detection method. In the following subsection, there is a brief description of change detection methods used to partition the change measure.2.1. Support vector machines (SVM)
SVM can be use as a binary classification method to segment the change measure into two distinct regions. According to [27–30], in the following, there is a brief description of support vector machines.
A two-class classification problem can be stated in the following way. A data training with N training samples can be represented by the pair
(
yi,
xi),
i=
1,
2, . . . ,
N, with yi: labelclass; xi
∈
Rn: feature vector; and n: dimension of vector space.The SVM method consists in finding the optimum separating hyperplane with equation f
(
x) = w ·
x+
b, where(w,
b)
are the parameters of the hyperplane, so that:(a) Samples with label
+
1 and−
1 are located on each side of the hyperplane.(b) The distance of the closest vectors to the hyper plane in each of the two classes is maximum.
These are called support vectors and the distance is the optimal margin (Figure 4left). The vectors that are not on the hyperplane, then lead to:
w·
x+
b>
0 orw·
x+
b<
0 and allow the classifier to be defined as f(
x;
w,
b) =
sgn(w ·
x+
b)
. The support vectors lie on two hyperplanes, parallel to the optimal hyperplane, with equations:w ·
x+
b= ±
1. Maximization of the margin with support vector hyperplanes equations, leads to the following constrained optimization problem:min
1 2∥
w∥
2
with yi(w ·
xi+
b) ≥
1,
i=
1,
2,
3, . . . ,
N.
(13)If the training samples are not linearly separable (Figure 4
right), a regularization parameter, C , and error variables,
ξ
i,are used in order to deal with misclassified vectors. Then, the optimization problem becomes:
min
1 2∥
w∥
2+
C N
i=1ξ
i
,
yi(w ·
xi+
b) ≥
1−
ξ
i,
ξ
i≥
0 i=
1,
2,
3, . . . ,
N.
(14)This optimization problem can be solved using Lagrange multipliers and then becomes:
max
N
i=1α
i−
1 2 N
i=1 N
j=1α
iα
jyiyjxi·
xj
,
C≥
α
i≥
0,
N
i=1α
iyi=
0 i=
1,
2,
3, . . . ,
N.
(15)α
are the Lagrange multipliers and are non-zero only for the support vector. In some cases (Figure 5), separating the data with a linear hyperplane is impossible. To solve this problem, the data project in a higher dimension space where they are linearly separable. SVM is applied to this space, which leads to the(a) Original image. (b) Fractal image. Figure 3: ALOS-PALSAR image at two different subsets.
Figure 4: Optimal separating hyperplane, optimal margin, and support vectors: (left) linearly separable case; (right) nonlinearly separable case [28].
the projection can be simulated using a kernel method. If x
∈
Rnis projected in higher-dimension space, H, with a nonlinear function,Φ
:
Rn→
H, then(
xi
·
xj)
is replaced withΦ(
xi)·
Φ(
xj)
.In another words, the kernel function for projecting data into a higher dimension is: K
(
xi·
xj) =
Φ(
xi) ·
Φ(
xj)
. There are severalkernel functions for projecting the data into a higher dimension. In this article, the following function (known as the Gaussian radial basis function) is used:
K
(
xi·
xj) =
exp
−
∥
xi−
xj∥
2 2σ
2
.
(16)2.2. Fuzzy C -means clustering (FCM)
In fuzzy clustering, we need to determine the portioning of the sample data for each input variable into a number of clusters. These clusters have fuzzy boundaries. Each object is bound to each cluster to a certain degree,
µ ∈ [
0,
1]
, also known as membership [31]. Fuzzy c-means clustering is a probabilistic clustering. The basic idea of fuzzy c-means is very similar tok-means algorithm. It assumes that the number of cluster c is
known a priori, and tries to minimize the objective function. FCM attempts to find fuzzy partitioning of a given pattern-set by minimizing the objective function [32].
Jm
(
X;
U,
V) =
c
i=1 n
k=1(µ
ik)
mDik.
(17)The main property of fuzzy is that it obeys the constraint:
Jm
(
X;
U,
V) =
c
i=1 n
k=1(µ
ik)
mDik.
(18)In Eq. (17),
µ
ik is the membership value of object ktowards concept i
,
U is the fuzzy partition matrix of X,
X=
[
x1,x2, . . . ,xn]
is the input data set, V= [
v1, v2, . . . , v
c]
is thevector collecting all cluster centers and term Dikis assumed to
be the square of the Euclidean distance between the individual,
Figure 5: Non-linear hyperplane [30].
xk, and the center,
v
i; Dik= |
xk−
v
i|
2. In this equation, m isa parameter, called a fuzzifier, which controls the fuzziness of the algorithm, and
µ
ik andv
i are defined as in the followingequation:
v
i=
n
k=1(µ
ik)
mxk n
k=1(µ
ik)
m, µ
ik=
c
j=1
Dik Djk1
/m−1
−1.
(19)This objective function should be optimized by an alterna-tive optimization algorithm, which is an iteraalterna-tive algorithm. The
iteration process continues for a predefined number of it or the stopping criterion is satisfied.
2.3. Artificial neural network with a back propagation training algorithm
There are many different types of neural network. Learning algorithms of the network play an important role in the process of change detection. The back-propagation learning algorithm is used to train the weights in the network and update the weights of a multi-layered network which undergoes supervised training. The back propagation algorithm uses the supervised learning approach, due to the fact that the target output vectors are defined earlier in the system. The learning process begins with the presentation of an input pattern to the network in which the total input is found using the standard summation of products as defined in Eq.(20)[33]:
(a) In 2006. (b) In 2008.
Figure 6: Images set of the test site in the south east of Tehran.
(a) Log-ratio. (b) Proposed change measure. (c) Ground truth map. Figure 7: The log-ratio image, the change measure and the ground truth map of the test site.
where
w
ijis the weight associated with the connection betweenneuron i and j
,
oi is the output of neuron i in the output layer,µ
is the learning rate,δ
jis the output error from the last cycle,α
is momentum and n is the number of cycles. The delta rule algorithm will adjust the weights leading to the output units. It is affected by variation of theµ
learning rate andα
momentum. Each factor can be changed independently of the others to obtain the best results. In this paper, a multi-layer feed-forward network with 4 hidden layers and 5 neurons is used.3. Data description and experimental results
In order to carry out the experimental analysis aimed at assessing the effectiveness of using the proposed change measure, we considered ALOS-PALSAR data sets corresponding to geographical areas of the south east of Tehran (Iran). These images were acquired using HH polarization mode and 10 m spatial resolution, in 2006 and 2008. Figure 6 shows these images.
The study area images include buildings, roads and distinct agricultural crops. Land use and land cover were changed due to urban growth, seasonal effects and agriculture practices. The proposed measure has been compared to the classical log-ratio detector to evaluate its performance. In Figure 7, the proposed change measure and also log-ratio image of the test site are given. Since the original ALOS-PALSAR images are pre-processed without speckle reduction, the quality of a change measure can also indicate its resistance to the speckle. As can be seen, the quality of the log-ratio detector is very poor because of the speckle. On the other hand, as demonstrated, the quality of the proposed measure seems to be satisfactory. As shown in
Figure 7(c), there are 256 changed and unchanged pixels on the ground truth map, where white and black pixels correspond to the changed and unchanged areas, respectively. Each black and white box contains 16 pixels.
Table 1: The confusion matrix for the change map obtained by applying SVM to the log-ratio image.
True class
Changed Unchanged Total Estimated class
Changed 118 18 136
Unchanged 10 110 120
Total 128 128 256
The change map of the test site is obtained by applying the change detection methods that have been introduced in the previous section to the proposed change measure and also the log-ratio image.Figure 8 shows the results of applying SVM to the log-ratio image and the change measure. Since SVM is a supervised method, 30 pixels are chosen for its training. As can be seen fromFigure 8, detected changes from the measure are more concentrated than in the log-ratio image. The change map from the log-ratio image produces more false alarms, while it seems that the result of the measure has more resistance to the speckle effect and it traces the changes without suffering from the speckle effect, because speckle, which is resulted from coherent energy imaging, is modeled properly in the proposed fractal measure and its effect is minimized. Compare to the log-ratio image, use of the change measure yields a better performance in distinguishing between changed and unchanged areas. For quantitative comparison, the confusion matrixes of the change maps in Tables 1–3 are given. The comparison of kappa coefficients and overall accuracies prove the efficiency of using the change measure instead of the classical log-ratio image.
In the next experiment, FCM has been applied to the log-ratio image and also the change measure. Unlike to the SVM, FCM is an unsupervised clustering method and is more sensitive to the noise. According toFigure 9, it is obvious that the result of the log-ratio image has given too much false detection,
(a) Log-ratio image. (b) The measure. Figure 8: Change map of test site by applying SVM.
(a) Log-ratio image. (b) The measure. Figure 9: Change map of test site by applying FCM.
Table 2: The confusion matrix for the change map obtained by applying SVM to the change measure.
True class
Changed Unchanged Total
Estimated class
Changed 122 1 123
Unchanged 6 127 133
Total 128 128 256
Table 3: Quantitative comparison of the change maps obtained by applying SVM.
SVM Kappa coefficient % Overall accuracy %
Log-ratio 78.13 89.06
The measure 94.53 97.26
Table 4: The confusion matrix for the change map obtained by applying FCM to the log-ratio image.
True class
Changed Unchanged Total
Estimated class
Changed 120 33 153
Unchanged 8 95 103
Total 128 128 256
which makes it almost unusable. On the contrary, speckle noise has less effect on the result of the measure. According to
Tables 4–6, the accuracy (kappa coefficient) of FCM is improved from 67.97% for the log-ratio image to 73.44% for the change measure.
Finally, a feed forward Artificial Neural Network (ANN) as a supervised method, using a back propagation training algorithm introduced in Section 2.3, is used for partitioning of the log-ratio image and the change measure. It should be noted that the feed forward neural network is categorized as
Table 5: The confusion matrix for the change map obtained by applying FCM to the change measure.
True class
Changed Unchanged Total
Estimated class
Changed 94 0 94
Unchanged 34 128 162
Total 128 128 256
Table 6: Quantitative comparison of the change maps obtained by applying FCM.
FCM Kappa coefficient % Overall accuracy %
Log-ratio 67.97 83.98
The measure 73.44 86.72
a supervised approach. In this experiment, its training data is selected the same as SVM training data (30 pixels).Figure 10
shows the results of applying feed forward ANN on the log-ratio image and the change measure. It seems that the neural network is very sensitive to the noise effect. As can be seen, the result of applying it to the log-ratio image is unsatisfactory with a very low accuracy, whereas the result of ANN applied to the measure image is quite acceptable and has not suffered from speckle noise. In this case, the kappa coefficient is 78.13% (Tables 7–9) and it is much lower in comparison to the 94.53% accuracy related to SVM. The weak performance of ANN here is mainly because of inadequate training data and it seems that it is necessary to use more appropriate pixels in the training process. While ANN is sensitive to the training data, SVM does not have to deal with this problem and it gives satisfactory results with a few training data. SVM uses this data as support vectors and tries to separate them by using non-linear hyperplanes.
(a) Log-ratio image. (b) The measure. Figure 10: Change map of test site by applying ANN.
Table 7: The confusion matrix for the change map obtained by applying ANN to the log-ratio image.
True class
Changed Unchanged Total
Estimated class
Changed 126 67 193
Unchanged 2 61 63
Total 128 128 256
Table 8: The confusion matrix for the change map obtained by applying ANN to the change measure.
True class
Changed Unchanged Total
Estimated class
Changed 100 0 100
Unchanged 28 128 156
Total 128 128 256
Table 9: Quantitative comparison of the change maps obtained by applying ANN.
FCM Kappa coefficient % Overall accuracy %
Log-ratio 46.09 73.05
The measure 78.13 89.06
Through quantitative and qualitative comparison of change maps obtained by applying each mentioned method, it is obvious that the results of SVM are the most accurate of all. In the last experiment of this study, the efficiency of using the change measure is taken into consideration. In this regard, an adaptive enhanced Lee filter has been applied to the SAR image used for despeckling. After despeckling, SVM was applied to the filtered log-ratio image (Figure 11).Tables 10and 11
represent the performance accuracy of this approach. According toTables 3and11, the kappa coefficient for the change map, obtained by applying SVM to the log-ratio image, without and with noise reduction, is 78.13% and 82.81%, respectively. However, the kappa for the resulting image of applying SVM to the change measure is 94.53%. According to [8], SAR signals as a chaotic phenomenon can be represented by a spatial chaotic model and characterized by its fractal dimension. Therefore, speckle, which is a result of coherent energy imaging, can also be properly characterized by its fractal dimension.
4. Conclusion
The main objective of this paper is to improve change detection methods by using a new fractal change measure. The measure uses both fractal dimension and intensity information
Figure 11: Change map of test site by applying SVM to filtered log-ratio image.
Table 10: The confusion matrix for the change map obtained by applying SVM to the filtered log-ratio image.
True class
Changed Unchanged Total
Estimated class
Changed 124 18 142
Unchanged 4 110 114
Total 128 128 256
Table 11: Quantitative comparison of the change map obtained by applying SVM.
SVM Kappa coefficient % Overall accuracy %
Filtered log-ratio 82.81 91.40
simultaneously. SAR signal is a chaotic phenomenon and it can be modeled in a nonlinear dynamic system. Accordingly, SAR image can be described by its fractal dimension. In this paper, change detection, viewed as a particular case of multi-temporal image classification problems and some methods like support vector machines, fuzzy c-means clustering, and artificial neural networks are used for partitioning of the change measure into two distinct regions, namely changed and unchanged. Experimental results proved that the measure has high resistance to the speckle effect in comparison with the classical log-ratio image. Quantitative and qualitative analysis revealed an improvement in the results of the used methods when they were applied to the change measure instead of the log-ratio image.
Among the implemented methods, SVM outperformed all others. The accuracy of SVM when it is applied to the measure
was 94.53% whereas it’s kappa for the log-ratio image was 78.13%. Since original SAR images were pre-processed without speckle reduction, the quality of the results also indicates its resistance to the speckle effect. However, for more analysis, an adaptive enhanced Lee filter was applied to original SAR images for noise reduction or despeckling, and then SVM was applied to the log-ratio image obtained from the despeckled SAR images. In this case, the kappa coefficient improved to 82.81%. However the value of kappa for the change measure is more considerable than its values from the log-ratio image without and with despeckling. From our experiment, we can conclude that the proposed measure provides an appropriate tool for distinguishing between changed and unchanged areas without suffering from the speckle effect.
However, determining of an optimal size of window in computing a fractal image is a question that still remains open. Applying different sizes of window may result in a different fractal dimension. It is more appropriate to use a smaller window in the rough area and a larger window for the smooth area. Also, having the SAR images, additional information, like coherence images, could be used as a third index in the proposed measure. As such, these aspects will be studied as a future development of this work.
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Hossein Aghababaee received a B.S. degree from Isfahan University, Iran,
in 2009 and a M.S. degree in Remote Sensing from Tehran University, Iran, in 2011. His research interests include: remote sensing, change detection, fractal mathematics and image processing in support of damage assessment, in particular, the analysis of damage assessment using fractal methods.
Jalal Amini received a B.S. degree in Surveying Engineering from K.N. Toosi
University, Tehran, Iran, in 1993, an M.S. degree in Photogrammetry from K.N. Toosi University, Tehran, Iran, in 1996, and a Ph.D. degree in Photogramme-try and Remote Sensing from Tehran University, Iran, in 2001. He is currently Associate Professor of Remote Sensing with the Department of Geomatics En-gineering at Tehran University, Iran. His research interests include: automatic object extraction (roads) from aerial and satellite images, mathematic model-ing of space images, morphology, neural networks, fuzzy sets, fractals, DEM, classification, alpha-shapes, floodplain delineation, and microwave remote sensing.
Yu-Chang Tzeng received B.S. and M.S. degrees from the National Taiwan
Institute of Technology, Taiwan, in 1985 and 1987, respectively, and a Ph.D. degree from the University of Texas at Arlington, USA, in 1992, all in Electrical Engineering. He is currently Professor in the Department of Electronic Engineering at the National United University, Taiwan. His research interests include: microwave remote sensing with emphasis on neural network applications, and remote sensing image processing.
