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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS 1
Gabor Feature Based Unsupervised Change
Detection of Multitemporal SAR Images
Based on Two-Level Clustering
1
2
3
Heng-Chao Li, Senior Member, IEEE, Turgay Celik, Nathan Longbotham, Member, IEEE,and
William J. Emery, Fellow, IEEE
4
5
Abstract—In this letter, we propose a simple yet effective unsu-6
pervised change detection approach for multitemporal synthetic7
aperture radar images from the perspective of clustering. This8
approach jointly exploits the robust Gabor wavelet representation9
and the advanced cascade clustering. First, a log-ratio image10
is generated from the multitemporal images. Then, to integrate11
contextual information in the feature extraction process, Gabor12
wavelets are employed to yield the representation of the log-ratio13
image at multiple scales and orientations, whose maximum mag-14
nitude over all orientations in each scale is concatenated to form15
the Gabor feature vector. Next, a cascade clustering algorithm is16
designed in this discriminative feature space by successively com-17
bining the first-level fuzzy c-means clustering with the second-level18
nearest neighbor rule. Finally, the two-level combination of the19
changed and unchanged results generates the final change map.20
Experimental results are presented to demonstrate the effective-21
ness of the proposed approach.22
Index Terms—Fuzzy c-means (FCM), gabor wavelets, multitem-23
poral synthetic aperture radar (SAR) images, two-level clustering,24
unsupervised change detection.25
I. INTRODUCTION26
27 THE ever-increasing availability of Earth observation satel-28
lites equipped with advanced synthetic aperture radar29
(SAR) sensors allows for repeat coverage of the earth’s surface30
at shorter intervals with the independence of atmospheric and31
sunlight conditions. In this context, SAR images are an ideal32
information source for performing change detection, which33
tends to identify changes that occur on the ground by jointly34
Manuscript received April 21, 2015; revised August 13, 2015; accepted
September 21, 2015. This work was supported in part by the National Natural
Science Foundation of China under Grant 61371165, by the Chengdu Science
and Technology Bureau project under Grant 2014-HM01-00279-SF, and by
the Program for New Century Excellent Talents in University under Grant
NCET-11-0711.
H.-C. Li is with the Sichuan Provincial Key Laboratory of Information Cod-
ing & Transmission, Southwest Jiaotong University, Chengdu 610031, China,
and also with the Department of Aerospace Engineering Sciences, University
of Colorado, Boulder, CO 80309 USA (e-mail: lihengchao_78@163.com).
T. Celik is with the School of Computer Science, University of the
Witwatersrand, Johannesburg 2000, South Africa (e-mail: Turgay.Celik@wits.
ac.za).
N. Longbotham is with DigitalGlobe, Inc., Longmont, CO 80503 USA
(e-mail: nathan.longbotham@colorado.edu).
W. J. Emery is with the Department of Aerospace Engineering Sciences,
University of Colorado, Boulder, CO 80309 USA (e-mail: emery@colorado.
edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/LGRS.2015.2484220
processing two (or more) images acquired over the same ge- 35
ographical area at different times. Increasing human activi- 36
ties, together with frequently occurring natural disasters, make 37
change detection applicable to many scenarios, such as urban 38
planning, deforestation, and the monitoring and assessment 39
of natural hazards. Consequently, there has been a growing 40
interest in research on SAR change detection. 41
Unsupervised change detection is to directly analyze the mul- 42
titemporal source images or their derivatives to discriminate the 43
unchanged and changed classes without requiring any ground 44
reference. Limited to the availability of labeled data in practice, 45
it has been extensively studied from several perspectives: statis- 46
tical (dis)similarity measure [1], [2], meta-herustic optimization 47
[3], thresholding [4]–[6], clustering [7]–[10], active contours 48
[11], [12], and Markov fusion [13], etc. Among them, the 49
clustering methods are a simple yet effective family, being 50
popular and well accepted in the SAR community. As far as 51
clustering is concerned, it is a process of grouping a given 52
collection of unlabeled patterns (e.g., observations or feature 53
vectors) into meaningful clusters. In [7], a binary k-means 54
clustering is employed on the principal component analysis 55
(PCA)-extracted feature vectors for all pixels of the difference 56
image to compute the final change detection results. Still using 57
k-means, the multiscale feature vectors, formed by locally 58
sampling the data from the multiresolution representation of the 59
difference image, are proposed as the patterns to yield two dis- 60
joint classes [8]: changed and unchanged. To improve the detec- 61
tion performance, a kernel k-means based approach to change 62
detection is introduced in [9] by representing the difference 63
image in the feature space through the use of kernel functions. 64
In addition, from the viewpoint of soft clustering, an improved 65
fuzzy c-means (FCM) clustering algorithm by modifying the 66
membership of each pixel with a novel Markov random field 67
(MRF) based spatial prior is proposed to classify the changed 68
and unchanged regions in the log-ratio difference image [10]. 69
Though promising results have been reported in the litera- 70
ture, there is still considerable room to improve the clustering- 71
based approach for change detection. As we know, in the 72
clustering task, one challenge is how to extract a more accurate 73
and discriminative representation of the data, the other is the 74
design of an efficient clustering algorithm. Starting from these 75
two points, a Gabor feature based unsupervised change detec- 76
tion of multitemporal SAR images with two-level clustering 77
is proposed in this letter, called the GaborTLC. Our main 78
contributions are twofold: 1) The Gabor wavelets [14]–[16] 79
are adopted as the feature extractor for change detection. The 80
resulting Gabor features also can automatically integrate the 81
contextual information, and are more robust and discriminative 82
1545-598X © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
IEEE
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2IEEE GEOSCIENCE AND REMOTE SENSING LETTERS
Fig. 1. Framework of the proposed change detection approach.
than the intensity-based representations. 2) A two-level cluster-83
ing scheme is designed to effectively identify the changed and84
unchanged classes by successively implementing FCM with the85
nearest neighbor (NN) rule. This cascade framework opens up86
the prospect of improvement in change-detection performance,87
while these basic algorithms used in different levels make the88
whole method relatively simple.89
The remainder of this letter is organized as follows. SectionII90
is devoted to the development of the proposed change detection91
approach. Experimental results are reported in Section III,92
followed by concluding remarks in Section IV.93
II. PROPOSED CHANGE DETECTION APPROACH94
A. Problem Formulation and Overview of Our Approach95
Suppose that Y1={y1(i, j)|1≤i≤M, 1≤j≤N}and96
Y2={y2(i, j)|1≤i≤M, 1≤j≤N}are two coregistered97
SAR images with a size of M×N, acquired over the same98
geographical area but at two different times, t1and t2, respec-99
tively. The objective of change detection is to yield a change100
map, representing changes that occurred on the ground between101
the acquisition dates of two SAR images Y1and Y2. As such,102
we can formulate the change detection problem as an unsuper-103
vised binary classification problem, with L={wc,w
u}being104
the set of classes corresponding to changed and unchanged105
pixels between Y1and Y2. It is equivalent to partitioning a106
given difference image YDinto two groups Ωwcand Ωwu,107
such that 1) Ωwc=∅,Ωwu=∅;2)ΩwcΩwu=YD; and 3)108
ΩwcΩwu=∅. To this end, a top-down cascade clustering109
technique is presented, whose framework is illustrated in Fig. 1,110
mainly consisting of the following three steps:111
112
•Step 1—Log-ratio Image Generation: This step aims at113
providing the object of study for the following clustering114
analysis using Y1and Y2. To reduce the influence of115
speckle and simultaneously to enhance the low-intensity 116
pixels, the log-ratio operator is utilized to generate YD117
(i.e., log-ratio image), given by YD=|log(Y2/Y1)|=118
|log Y2−log Y1|[5]. 119
•Step 2—Gabor Feature Extraction: The goal is to 120
properly extract the features on which clustering will 121
be performed so as to provide as much discriminative 122
information as possible concerning the change-detection 123
task of our interest. To this end, we adopt the Gabor 124
wavelet transform to extract the local spatial contextual 125
features of the difference image. 126
•Step 3—Two-level Clustering: This step refers to the 127
design of a good clustering scheme for the Gabor feature 128
vectors obtained in Step 2. The proposed method is a 129
cascade divisive clustering algorithm, including the first- 130
level FCM clustering and the second-level NN rule. The 131
two-level combination of the changed and unchanged 132
results yields the final change map. 133
The detailed descriptions of Step 2 and Step 3 are provided in 134
Section II-A and B. 135
B. Gabor Feature Extraction 136
After the pioneering work of extending 1-D Gabor wavelets 137
to the 2-D case in [14], [15], Gabor wavelets have been 138
extensively applied to image analysis due to their biological 139
relevance and computational properties. A 2-D Gabor wavelet 140
kernel is the product of an elliptical Gaussian envelope and a 141
complex plane wave, given by [16] 142
ψµ,ν (z)= kµ,ν 2
σ2exp −kµ,ν 2z2
2σ2
×exp (ikµ,ν z)−exp −σ2
2 (1)
where µ,ν, respectively, denote the orientation and scale of the 143
Gabor kernels, •is the norm operator, kµ,ν =kvexp(iφµ)144
with φµ=πµ/8and kν=kmax/fν,kmax is the maximum 145
frequency and fis the spacing factor between kernels in the 146
frequency domain. 147
The Gabor wavelet representation of the log-ratio image is 148
obtained by convolving YDwith a family of Gabor kernels 149
{ψµ,ν (z):µ∈{0,...,U−1},ν∈{0,...,V −1}},definedas 150
Oµ,ν (z)=YD(z)∗ψµ,ν (z)(2)
where z=(i, j )represents the pixel location, and ∗is the 151
convolution operator. Oµ,ν(z)is the convolution result corre- 152
sponding to the Gabor kernel at orientation µand scale ν.153
Uand Vdenote the total number of orientations and that of 154
scales, respectively. The response of (2), i.e., Oµ,ν (z),isa155
complex-valued quantity, having the real and imaginary parts, 156
respectively, given by Re(Oµ,ν (z)) and Im(Oµ,ν (z)). Then, 157
Oµ,ν (z)can be written as 158
Oµ,ν (z)=Aµ,ν (z)exp(iθµ,ν (z)) (3)
with Aµ,ν (z)=Re(Oµ,ν (z))2+Im(Oµ,ν (z))2and θµ,ν (z)= 159
arctan(Im(Oµ,ν(z))/Re(Oµ,ν (z))). As is well known, the real 160
part of a Gabor wavelet kernel is regarded as a smooth filter and 161
its imaginary part is used for edge detection. The magnitude 162
Aµ,ν (z), which integrates the complementary information pro- 163
vided by Re(Oµ,ν (z)) and Im(Oµ,ν (z)), is generally selected 164
IEEE
Proof
LI et al.: GABOR FEATURE BASED UNSUPERVISED CHANGE DETECTION OF MULTITEMPORAL SAR IMAGES 3
Fig. 2. Tree topology of the proposed two-level clustering for change detection.
as the stable and discriminative feature value [16], [17]. How-165
ever, if we extract the magnitude responses in all scales and166
orientations, and directly concatenate them to form a feature167
vector, the dimension of the resultant feature is quite high. To168
overcome this problem, we are interested in the response with169
maximum magnitude over all the possible orientations from the170
orientation sensitivity characteristic of Gabor wavelets, i.e.,171
xν=max
µ∈[0,U−1] Aµ,ν (z).(4)
For each pixel and considered the scale value, the compact
172
Gabor feature vector xis derived as x=[x0,x
1,...,x
ν,...,173
xV−1]. As such, the Gabor features X=[x1,...,xMN]Tare174
extracted for the log-ratio image.175
C. Two-Level Clustering176
Once the Gabor features have been extracted, theoretically177
any clustering method can be utilized to cluster the log-ratio178
image into two disjoint groups based on X. But to effectively179
identify the changed class from the unchanged class, one180
prefers to a good clustering algorithm, which should achieve181
better within-class compactness and between-class separation.182
Due to the overlap of the changed and unchanged classes, a183
single partitional clustering algorithm, such as k-means, FCM,184
or their variants, has limited applicability and effectiveness in185
making a reliable decision. To address this issue, we propose a186
two-level clustering method in this subsection, for which two187
simple clustering algorithms are organized in a cascade way188
to implement a coarse-to-fine procedure with the purpose of189
improving accuracy while guaranteeing efficiency.190
Its tree topology is shown in Fig. 2. Specifically, it starts from191
the root of the tree standing for a unique class including all the192
samples. In the first level, for its simplicity and applicability,193
the FCM algorithm is utilized to divide the root node into three194
child nodes, respectively, denoting the changed, unchanged,195
and intermediate classes (i.e., w1
c,w1
u,andwi). Now, the pixels196
belonging to w1
cand w1
uhave the high probability to be changed197
and unchanged. In other words, w1
cand w1
uhave the higher198
within-class similarity and the lower between-class similarity,199
and thus can be regarded as the pure changed and unchanged200
classes. In the second level, the internal node wiis further sepa-201
ratedintotwoleavesw2
cand w2
uusing the nearest neighbor rule202
by comparing the distances of the corresponding Gabor feature203
vectors to the centroids of w1
cand w1
u. Finally, we combine two-204
level subclusters to form the change map. The following is a205
detailed description of the proposed cascade clustering.206
207
•Input: Given the Gabor features Xcorresponding to YD
208
with M×Npixels.209
•Level 1: Perform the FCM algorithm on Xto partition YD210
into cclusters by minimizing the objective function 211
Jm(U,V)=
c
i=1
MN
j=1
um
ij xj−vi2(5)
s.t. uij ∈[0,1],
c
i=1
uij =1 ∀j, 0
<
MN
j=1
uij <MN ∀i(6)
where m∈[1,+∞)is the degree of fuzziness, U=212
[uij ]c×MN is a partition matrix with uij being the mem- 213
bership grade of jth pixel in cluster i,andV=[v1,v
2,v
3]214
is the vector of the centroid of cluster. Jmof (5) can be 215
iteratively optimized by alternately updating uij and vi216
until convergence [18], i.e., 217218
1) Set parameters c=3,m=2,t=0, and initialize the 219
partition matrix U(0) .220
2) Calculate the centroid of ith cluster by using 221
v(t+1)
i=MN
j=1 u(t)
ij m
xj
MN
j=1 u(t)
ij m.(7)
3) Update the membership grade uij by using 222
u(t+1)
ij =
xj−v(t+1)
i
−2/(m−1)
c
r=1
xj−v(t+1)
r
−2/(m−1) .(8)
4) Set t:= t+1, go to 2), and continue until convergence. 223
5) Assign the pixels to a class of {w1
c,w
i,w
1
u}from 224
label Yl∈Ωp
d=
w1
c,p=arg max
i=1,2,3MΩi
w1
u,p=arg min
i=1,2,3MΩi
wi,otherwise
(9)
where Ωi=1,2,3denote three distinct clusters identified 225
by discriminating the highest grade of membership for 226
each pixel from U,andMΩi=(1/|Ωi|)l∈ΩiYl
Dis 227
the average value (i.e., mean) of YDin cluster Ωi.228
•Level 2: Recalculate the centroids of w1
cand w1
uby 229
vw1
c=j∈Ωw1
c
(uij )mxj
j∈Ωw1
c
(uij )m,i→w1
c(10)
vw1
u=j∈Ωw1
u
(uij )mxj
j∈Ωw1
u
(uij )m,i→w1
u,(11)
then utilize the nearest neighbor rule to further separate 230
wiinto two classes, i.e., 231
labelYl∈Ωwi
D=w2
c,
xl−vw1
c
2≤
xl−vw1
u
2
w2
u,
xl−vw1
c
2>
xl−vw1
u
2.(12)
•Output: As a result, one can achieve the final change map 232
with 233
Ωwc=Ω
w1
cΩw2
c,Ωwu=Ω
w1
uΩw2
u.(13)
IEEE
Proof
4IEEE GEOSCIENCE AND REMOTE SENSING LETTERS
Fig. 3. Effect of parameter σon detection accuracy for difference data sets: (a) Bern and (b) San Francisco.
III. EXPERIMENTAL RESULTS AND DISCUSSIONS234
A. Experimental Setup235
In order to demonstrate the effectiveness of the proposed236
approach,1experiments are reported on two real ERS-2 SAR237
data sets: Bern and San Francisco. Results of two other state-238
of-the-art clustering-based techniques for change detection, i.e.,239
PCAKM [7] and MRFFCM [10], are given for comparison240
purpose. Both approaches are implemented using the default241
parameters provided in [7] and [10], respectively, h=4,S=3,242
and R= 30. As far as the proposed approach is concerned, we243
implement the Gabor wavelet transform with U=8,V=5,244
kmax =2π,andf=√2,andleaveσto be tuned. For the245
FCM clustering of Level 1, the partition matrix Uis randomly246
initialized with uniformly distributed values in (0,1) and fur-247
ther normalized to satisfy c
i=1 uij =1 ∀j. It is noted that248
GaborTLC as well as PCAKM and MRFFCM produces the249
same results in different runtimes due to that they all utilize250
contextual information during the detection process though in251
different ways. Additionally, to show the gain of Gabor features252
and two-level clustering, we also implement a variant of the253
proposed approach by replacing the two-level clustering with a254
single FCM clustering, referred to as GaborFCM.255
Besides the visual interpretation, four objective metrics, i.e.,256
false alarm rate (PFA), missed detection (PMD)rate, total error257
(PTE)rate, and Kappa coefficient (κ), are adopted for quan-258
titative evaluation. Specifically, PFA =FA/N
u×100% and259
PMD =MD/Nc×100%,inwhichFAmeasures the number260
of the unchanged pixels that are detected as the changed ones,261
while MD refers to that of the changed pixels that are detected262
as the unchanged ones. The sum of both quantities forms TE263
such that PTE =(FA +MD)/(Nu+Nc)×100% with Nu
264
and Ncdenoting the total number of unchanged and changed265
pixels in the ground-truth change map. As a robust and overall266
measure, κgives the percentage of agreement (correctly classi-267
fied pixels) corrected by the number of agreements that would268
be expected purely by chance.269
B. Influence of Parameter σ270
Before proceeding to the experiments,we first analyze the in-271
fluence of the parameter σof Gabor wavelet transform on the272
performance. To this end, σvaries from 1.0πto 4.5πwith the273
stepsize σ=0.1π. Fig. 3 shows the variety of kappa coeffi-274
1The MATLAB implementation of the proposed approach can be requested
from lihengchao_78@163.com with tag [GaborChangeDetectionTLCluster] in
the subject line.
cient for the Bern and San Francisco data sets with respect to σ.275
It can be seen that both plots rise as σgrows in the beginning, 276
and then remain relatively stable, but progressively worsen with 277
the further increase of σ. By experimental experience, σshould 278
choose not to be too large or too small to achieve the satisfac- 279
tory change detection result. In the following experiments, we 280
prefer σ∈{2.4π, 2.5π,...,3.0π}for two underlying data sets, 281
for each of which the proposed method was implemented to es- 282
timate the average values of four quantitative metrics. A finely 283
tuned parameter will improve the performance of GaborTLC. 284
C. Results and Analysis 285
The Bern data set is made of a pair of SAR images having 286
asizeof301×301 pixels, acquired over an area near the city 287
of Bern, Switzerland, in April and May 1999, respectively. The 288
San Francisco data set with 512 ×512 pixels is extracted from 289
the scene over the city of San Francisco (California) and its bay 290
(originally 7749 ×7713 multitemporal acquisitions in August 291
2003 and May 2004), which is available in [19]. The multitem- 292
poral images of both data sets together with their ground-truth 293
change maps are shown in the first three columns of Fig. 4. 294
Table I summarizes the PFA,PMD,PTE,κvalues of 295
various approaches on the Bern and San Francisco data sets. 296
From Table I, the comparison of quantitative measures between 297
GaborFCM and GaborTLC shows that the latter outperforms 298
the former in detection performance. Specifically, GaborTLC 299
achieves the PTE and κgains of 0.03, 0.34, and 0.12, 1.04 over 300
GaborFCM, respectively, for the Bern and San Francisco data 301
sets, although both have their respective advantages in PFA and 302
PMD. This indicates that the proposed cascade scheme is help- 303
ful to discriminate the intermediate pixels, and works better for 304
the overlap of the changed and unchanged classes than a single 305
FCM clustering. Moreover, to highlight the higher class separa- 306
bility of w1
cand w1
u, the quantity J=trace(SB)/trace(SW)307
[20] is calculated in Gabor feature space, where SB,SWare the 308
between-class and within-class scatter matrices, respectively. A 309
larger value of Jindicates better class separability. For the Bern 310
and San Francisco data sets, the classes of w1
cand w1
uhave 311
the corresponding Jscores equal to 0.0080 and 0.0014, which, 312
as expected, are correspondingly larger than that (i.e., 0.0022, 313
0.0003) for the classes of wcand wuobtained by GaborFCM. 314
Furthermore, by comparison with PCAKM and MRFFCM, 315
it can be observed that the proposed approach performs the 316
best on both experimental data sets with the smallest PTE 317
values of 0.34, 1.07 and the biggest κvalues of 86.16, 83.44 in 318
percentage. PCAKM and MRFFCM are obviously inferior to 319
GaborTLC. For visual interpretation, we take σ=2.8πas an 320
IEEE
Proof
LI et al.: GABOR FEATURE BASED UNSUPERVISED CHANGE DETECTION OF MULTITEMPORAL SAR IMAGES 5
Fig. 4. Visualized results of various change-detection approaches on both experimental data sets. Top row: Bern, and bottom row: San Francisco.Fromleftto
right: Y1,Y2, ground-truth change maps, results by PCAKM, results by MRFFCM, and results by GaborTLC together with its intermediate results.
TAB L E I
QUANTITATIVEMEAS URES (IN PERCENTAGE)ON
THE BERN AND SAN FRANCISCO DATA SETS
example for GaborTLC, and show the detection results of three321
approaches on the Bern and San Francisco data sets in Fig. 4.322
As shown in Fig. 4, the results obtained by GaborTLC exhibit323
less isolated spots and are better in matching the ground-truth324
change maps compared with that of PCAKM and MRFFCM,325
which is consistent with the above quantitative analysis. In326
addition, from the first-level clustering results of GaborTLC,327
it is illustrated that the pixels (marked as gray) belonging to the328
intermediate class appear more on the boundary between the329
changed and unchanged regions, or locate at some salient parts330
of multitemporal SAR images.331
IV. CONCLUSION332
This letter has proposed a simple yet effective two-level333
clustering approach to change detection of multitemporal SAR334
images based on Gabor features. Experimental results on two335
pairs of real multitemporal SAR images have demonstrated336
that the proposed approach achieves better detection perfor-337
mance than other state-of-the-art clustering-based techniques338
for change detection (e.g., PCAKM and MRFFCM). Future339
work will be devoted to the automatic determination of Gabor340
filter parameters and the efficient design of cascade structure to341
exploit the multiple-change detection.342
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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS 1
Gabor Feature Based Unsupervised Change
Detection of Multitemporal SAR Images
Based on Two-Level Clustering
1
2
3
Heng-Chao Li, Senior Member, IEEE, Turgay Celik, Nathan Longbotham, Member, IEEE,and
William J. Emery, Fellow, IEEE
4
5
Abstract—In this letter, we propose a simple yet effective unsu-6
pervised change detection approach for multitemporal synthetic7
aperture radar images from the perspective of clustering. This8
approach jointly exploits the robust Gabor wavelet representation9
and the advanced cascade clustering. First, a log-ratio image10
is generated from the multitemporal images. Then, to integrate11
contextual information in the feature extraction process, Gabor12
wavelets are employed to yield the representation of the log-ratio13
image at multiple scales and orientations, whose maximum mag-14
nitude over all orientations in each scale is concatenated to form15
the Gabor feature vector. Next, a cascade clustering algorithm is16
designed in this discriminative feature space by successively com-17
bining the first-level fuzzy c-means clustering with the second-level18
nearest neighbor rule. Finally, the two-level combination of the19
changed and unchanged results generates the final change map.20
Experimental results are presented to demonstrate the effective-21
ness of the proposed approach.22
Index Terms—Fuzzy c-means (FCM), gabor wavelets, multitem-23
poral synthetic aperture radar (SAR) images, two-level clustering,24
unsupervised change detection.25
I. INTRODUCTION26
27 THE ever-increasing availability of Earth observation satel-28
lites equipped with advanced synthetic aperture radar29
(SAR) sensors allows for repeat coverage of the earth’s surface30
at shorter intervals with the independence of atmospheric and31
sunlight conditions. In this context, SAR images are an ideal32
information source for performing change detection, which33
tends to identify changes that occur on the ground by jointly34
Manuscript received April 21, 2015; revised August 13, 2015; accepted
September 21, 2015. This work was supported in part by the National Natural
Science Foundation of China under Grant 61371165, by the Chengdu Science
and Technology Bureau project under Grant 2014-HM01-00279-SF, and by
the Program for New Century Excellent Talents in University under Grant
NCET-11-0711.
H.-C. Li is with the Sichuan Provincial Key Laboratory of Information Cod-
ing & Transmission, Southwest Jiaotong University, Chengdu 610031, China,
and also with the Department of Aerospace Engineering Sciences, University
of Colorado, Boulder, CO 80309 USA (e-mail: lihengchao_78@163.com).
T. Celik is with the School of Computer Science, University of the
Witwatersrand, Johannesburg 2000, South Africa (e-mail: Turgay.Celik@wits.
ac.za).
N. Longbotham is with DigitalGlobe, Inc., Longmont, CO 80503 USA
(e-mail: nathan.longbotham@colorado.edu).
W. J. Emery is with the Department of Aerospace Engineering Sciences,
University of Colorado, Boulder, CO 80309 USA (e-mail: emery@colorado.
edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/LGRS.2015.2484220
processing two (or more) images acquired over the same ge- 35
ographical area at different times. Increasing human activi- 36
ties, together with frequently occurring natural disasters, make 37
change detection applicable to many scenarios, such as urban 38
planning, deforestation, and the monitoring and assessment 39
of natural hazards. Consequently, there has been a growing 40
interest in research on SAR change detection. 41
Unsupervised change detection is to directly analyze the mul- 42
titemporal source images or their derivatives to discriminate the 43
unchanged and changed classes without requiring any ground 44
reference. Limited to the availability of labeled data in practice, 45
it has been extensively studied from several perspectives: statis- 46
tical (dis)similarity measure [1], [2], meta-herustic optimization 47
[3], thresholding [4]–[6], clustering [7]–[10], active contours 48
[11], [12], and Markov fusion [13], etc. Among them, the 49
clustering methods are a simple yet effective family, being 50
popular and well accepted in the SAR community. As far as 51
clustering is concerned, it is a process of grouping a given 52
collection of unlabeled patterns (e.g., observations or feature 53
vectors) into meaningful clusters. In [7], a binary k-means 54
clustering is employed on the principal component analysis 55
(PCA)-extracted feature vectors for all pixels of the difference 56
image to compute the final change detection results. Still using 57
k-means, the multiscale feature vectors, formed by locally 58
sampling the data from the multiresolution representation of the 59
difference image, are proposed as the patterns to yield two dis- 60
joint classes [8]: changed and unchanged. To improve the detec- 61
tion performance, a kernel k-means based approach to change 62
detection is introduced in [9] by representing the difference 63
image in the feature space through the use of kernel functions. 64
In addition, from the viewpoint of soft clustering, an improved 65
fuzzy c-means (FCM) clustering algorithm by modifying the 66
membership of each pixel with a novel Markov random field 67
(MRF) based spatial prior is proposed to classify the changed 68
and unchanged regions in the log-ratio difference image [10]. 69
Though promising results have been reported in the litera- 70
ture, there is still considerable room to improve the clustering- 71
based approach for change detection. As we know, in the 72
clustering task, one challenge is how to extract a more accurate 73
and discriminative representation of the data, the other is the 74
design of an efficient clustering algorithm. Starting from these 75
two points, a Gabor feature based unsupervised change detec- 76
tion of multitemporal SAR images with two-level clustering 77
is proposed in this letter, called the GaborTLC. Our main 78
contributions are twofold: 1) The Gabor wavelets [14]–[16] 79
are adopted as the feature extractor for change detection. The 80
resulting Gabor features also can automatically integrate the 81
contextual information, and are more robust and discriminative 82
1545-598X © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
IEEE
Proof
2IEEE GEOSCIENCE AND REMOTE SENSING LETTERS
Fig. 1. Framework of the proposed change detection approach.
than the intensity-based representations. 2) A two-level cluster-83
ing scheme is designed to effectively identify the changed and84
unchanged classes by successively implementing FCM with the85
nearest neighbor (NN) rule. This cascade framework opens up86
the prospect of improvement in change-detection performance,87
while these basic algorithms used in different levels make the88
whole method relatively simple.89
The remainder of this letter is organized as follows. Section II90
is devoted to the development of the proposed change detection91
approach. Experimental results are reported in Section III,92
followed by concluding remarks in Section IV.93
II. PROPOSED CHANGE DETECTION APPROACH94
A. Problem Formulation and Overview of Our Approach95
Suppose that Y1={y1(i, j)|1≤i≤M, 1≤j≤N}and96
Y2={y2(i, j)|1≤i≤M, 1≤j≤N}are two coregistered97
SAR images with a size of M×N, acquired over the same98
geographical area but at two different times, t1and t2, respec-99
tively. The objective of change detection is to yield a change100
map, representing changes that occurred on the ground between101
the acquisition dates of two SAR images Y1and Y2. As such,102
we can formulate the change detection problem as an unsuper-103
vised binary classification problem, with L={wc,w
u}being104
the set of classes corresponding to changed and unchanged105
pixels between Y1and Y2. It is equivalent to partitioning a106
given difference image YDinto two groups Ωwcand Ωwu,107
such that 1) Ωwc=∅,Ωwu=∅;2)ΩwcΩwu=YD; and 3)108
ΩwcΩwu=∅. To this end, a top-down cascade clustering109
technique is presented, whose framework is illustrated in Fig. 1,110
mainly consisting of the following three steps:111
112
•Step 1—Log-ratio Image Generation: This step aims at113
providing the object of study for the following clustering114
analysis using Y1and Y2. To reduce the influence of115
speckle and simultaneously to enhance the low-intensity 116
pixels, the log-ratio operator is utilized to generate YD117
(i.e., log-ratio image), given by YD=|log(Y2/Y1)|=118
|log Y2−log Y1|[5]. 119
•Step 2—Gabor Feature Extraction: The goal is to 120
properly extract the features on which clustering will 121
be performed so as to provide as much discriminative 122
information as possible concerning the change-detection 123
task of our interest. To this end, we adopt the Gabor 124
wavelet transform to extract the local spatial contextual 125
features of the difference image. 126
•Step 3—Two-level Clustering: This step refers to the 127
design of a good clustering scheme for the Gabor feature 128
vectors obtained in Step 2. The proposed method is a 129
cascade divisive clustering algorithm, including the first- 130
level FCM clustering and the second-level NN rule. The 131
two-level combination of the changed and unchanged 132
results yields the final change map. 133
The detailed descriptions of Step 2 and Step 3 are provided in 134
Section II-A and B. 135
B. Gabor Feature Extraction 136
After the pioneering work of extending 1-D Gabor wavelets 137
to the 2-D case in [14], [15], Gabor wavelets have been 138
extensively applied to image analysis due to their biological 139
relevance and computational properties. A 2-D Gabor wavelet 140
kernel is the product of an elliptical Gaussian envelope and a 141
complex plane wave, given by [16] 142
ψµ,ν (z)= kµ,ν 2
σ2exp −kµ,ν 2z2
2σ2
×exp (ikµ,ν z)−exp −σ2
2 (1)
where µ,ν, respectively, denote the orientation and scale of the 143
Gabor kernels, •is the norm operator, kµ,ν =kvexp(iφµ)144
with φµ=πµ/8and kν=kmax/fν,kmax is the maximum 145
frequency and fis the spacing factor between kernels in the 146
frequency domain. 147
The Gabor wavelet representation of the log-ratio image is 148
obtained by convolving YDwith a family of Gabor kernels 149
{ψµ,ν (z):µ∈{0,...,U−1},ν∈{0,...,V −1}},definedas 150
Oµ,ν (z)=YD(z)∗ψµ,ν (z)(2)
where z=(i, j )represents the pixel location, and ∗is the 151
convolution operator. Oµ,ν(z)is the convolution result corre- 152
sponding to the Gabor kernel at orientation µand scale ν.153
Uand Vdenote the total number of orientations and that of 154
scales, respectively. The response of (2), i.e., Oµ,ν (z),isa155
complex-valued quantity, having the real and imaginary parts, 156
respectively, given by Re(Oµ,ν (z)) and Im(Oµ,ν (z)). Then, 157
Oµ,ν (z)can be written as 158
Oµ,ν (z)=Aµ,ν (z)exp(iθµ,ν (z)) (3)
with Aµ,ν (z)=Re(Oµ,ν (z))2+Im(Oµ,ν (z))2and θµ,ν (z)= 159
arctan(Im(Oµ,ν(z))/Re(Oµ,ν (z))). As is well known, the real 160
part of a Gabor wavelet kernel is regarded as a smooth filter and 161
its imaginary part is used for edge detection. The magnitude 162
Aµ,ν (z), which integrates the complementary information pro- 163
vided by Re(Oµ,ν (z)) and Im(Oµ,ν (z)), is generally selected 164
IEEE
Proof
LI et al.: GABOR FEATURE BASED UNSUPERVISED CHANGE DETECTION OF MULTITEMPORAL SAR IMAGES 3
Fig. 2. Tree topology of the proposed two-level clustering for change detection.
as the stable and discriminative feature value [16], [17]. How-165
ever, if we extract the magnitude responses in all scales and166
orientations, and directly concatenate them to form a feature167
vector, the dimension of the resultant feature is quite high. To168
overcome this problem, we are interested in the response with169
maximum magnitude over all the possible orientations from the170
orientation sensitivity characteristic of Gabor wavelets, i.e.,171
xν=max
µ∈[0,U−1] Aµ,ν (z).(4)
For each pixel and considered the scale value, the compact
172
Gabor feature vector xis derived as x=[x0,x
1,...,x
ν,...,173
xV−1]. As such, the Gabor features X=[x1,...,xMN]Tare174
extracted for the log-ratio image.175
C. Two-Level Clustering176
Once the Gabor features have been extracted, theoretically177
any clustering method can be utilized to cluster the log-ratio178
image into two disjoint groups based on X. But to effectively179
identify the changed class from the unchanged class, one180
prefers to a good clustering algorithm, which should achieve181
better within-class compactness and between-class separation.182
Due to the overlap of the changed and unchanged classes, a183
single partitional clustering algorithm, such as k-means, FCM,184
or their variants, has limited applicability and effectiveness in185
making a reliable decision. To address this issue, we propose a186
two-level clustering method in this subsection, for which two187
simple clustering algorithms are organized in a cascade way188
to implement a coarse-to-fine procedure with the purpose of189
improving accuracy while guaranteeing efficiency.190
Its tree topology is shown in Fig. 2. Specifically, it starts from191
the root of the tree standing for a unique class including all the192
samples. In the first level, for its simplicity and applicability,193
the FCM algorithm is utilized to divide the root node into three194
child nodes, respectively, denoting the changed, unchanged,195
and intermediate classes (i.e., w1
c,w1
u,andwi). Now, the pixels196
belonging to w1
cand w1
uhave the high probability to be changed197
and unchanged. In other words, w1
cand w1
uhave the higher198
within-class similarity and the lower between-class similarity,199
and thus can be regarded as the pure changed and unchanged200
classes. In the second level, the internal node wiis further sepa-201
ratedintotwoleavesw2
cand w2
uusing the nearest neighbor rule202
by comparing the distances of the corresponding Gabor feature203
vectors to the centroids of w1
cand w1
u. Finally, we combine two-204
level subclusters to form the change map. The following is a205
detailed description of the proposed cascade clustering.206
207
•Input: Given the Gabor features Xcorresponding to YD
208
with M×Npixels.209
•Level 1: Perform the FCM algorithm on Xto partition YD210
into cclusters by minimizing the objective function 211
Jm(U,V)=
c
i=1
MN
j=1
um
ij xj−vi2(5)
s.t. uij ∈[0,1],
c
i=1
uij =1 ∀j, 0
<
MN
j=1
uij <MN ∀i(6)
where m∈[1,+∞)is the degree of fuzziness, U=212
[uij ]c×MN is a partition matrix with uij being the mem- 213
bership grade of jth pixel in cluster i,andV=[v1,v
2,v
3]214
is the vector of the centroid of cluster. Jmof (5) can be 215
iteratively optimized by alternately updating uij and vi216
until convergence [18], i.e., 217218
1) Set parameters c=3,m=2,t=0, and initialize the 219
partition matrix U(0) .220
2) Calculate the centroid of ith cluster by using 221
v(t+1)
i=MN
j=1 u(t)
ij m
xj
MN
j=1 u(t)
ij m.(7)
3) Update the membership grade uij by using 222
u(t+1)
ij =
xj−v(t+1)
i
−2/(m−1)
c
r=1
xj−v(t+1)
r
−2/(m−1) .(8)
4) Set t:=t+1, go to 2), and continue until convergence. 223
5) Assign the pixels to a class of {w1
c,w
i,w
1
u}from 224
label Yl∈Ωp
d=
w1
c,p=arg max
i=1,2,3MΩi
w1
u,p=arg min
i=1,2,3MΩi
wi,otherwise
(9)
where Ωi=1,2,3denote three distinct clusters identified 225
by discriminating the highest grade of membership for 226
each pixel from U,andMΩi=(1/|Ωi|)l∈ΩiYl
Dis 227
the average value (i.e., mean) of YDin cluster Ωi.228
•Level 2: Recalculate the centroids of w1
cand w1
uby 229
vw1
c=j∈Ωw1
c
(uij )mxj
j∈Ωw1
c
(uij )m,i→w1
c(10)
vw1
u=j∈Ωw1
u
(uij )mxj
j∈Ωw1
u
(uij )m,i→w1
u,(11)
then utilize the nearest neighbor rule to further separate 230
wiinto two classes, i.e., 231
labelYl∈Ωwi
D=w2
c,
xl−vw1
c
2≤
xl−vw1
u
2
w2
u,
xl−vw1
c
2>
xl−vw1
u
2.(12)
•Output: As a result, one can achieve the final change map 232
with 233
Ωwc=Ω
w1
cΩw2
c,Ωwu=Ω
w1
uΩw2
u.(13)
IEEE
Proof
4IEEE GEOSCIENCE AND REMOTE SENSING LETTERS
Fig. 3. Effect of parameter σon detection accuracy for difference data sets: (a) Bern and (b) San Francisco.
III. EXPERIMENTAL RESULTS AND DISCUSSIONS234
A. Experimental Setup235
In order to demonstrate the effectiveness of the proposed236
approach,1experiments are reported on two real ERS-2 SAR237
data sets: Bern and San Francisco. Results of two other state-238
of-the-art clustering-based techniques for change detection, i.e.,239
PCAKM [7] and MRFFCM [10], are given for comparison240
purpose. Both approaches are implemented using the default241
parameters provided in [7] and [10], respectively, h=4,S=3,242
and R= 30. As far as the proposed approach is concerned, we243
implement the Gabor wavelet transform with U=8,V=5,244
kmax =2π,andf=√2,andleaveσto be tuned. For the245
FCM clustering of Level 1, the partition matrix Uis randomly246
initialized with uniformly distributed values in (0,1) and fur-247
ther normalized to satisfy c
i=1 uij =1∀j. It is noted that248
GaborTLC as well as PCAKM and MRFFCM produces the249
same results in different runtimes due to that they all utilize250
contextual information during the detection process though in251
different ways. Additionally, to show the gain of Gabor features252
and two-level clustering, we also implement a variant of the253
proposed approach by replacing the two-level clustering with a254
single FCM clustering, referred to as GaborFCM.255
Besides the visual interpretation, four objective metrics, i.e.,256
false alarm rate (PFA), missed detection (PMD)rate, total error257
(PTE)rate, and Kappa coefficient (κ), are adopted for quan-258
titative evaluation. Specifically, PFA =FA/N
u×100% and259
PMD =MD/Nc×100%,inwhichFAmeasures the number260
of the unchanged pixels that are detected as the changed ones,261
while MD refers to that of the changed pixels that are detected262
as the unchanged ones. The sum of both quantities forms TE263
such that PTE =(FA+MD)/(Nu+Nc)×100% with Nu
264
and Ncdenoting the total number of unchanged and changed265
pixels in the ground-truth change map. As a robust and overall266
measure, κgives the percentage of agreement (correctly classi-267
fied pixels) corrected by the number of agreements that would268
be expected purely by chance.269
B. Influence of Parameter σ270
Before proceeding to the experiments, we first analyze the in-271
fluence of the parameter σof Gabor wavelet transform on the272
performance. To this end, σvaries from 1.0πto 4.5πwith the273
stepsize σ=0.1π. Fig. 3 shows the variety of kappa coeffi-274
1The MATLAB implementation of the proposed approach can be requested
from lihengchao_78@163.com with tag [GaborChangeDetectionTLCluster] in
the subject line.
cient for the Bern and San Francisco data sets with respect to σ.275
It can be seen that both plots rise as σgrows in the beginning, 276
and then remain relatively stable, but progressively worsen with 277
the further increase of σ. By experimental experience, σshould 278
choose not to be too large or too small to achieve the satisfac- 279
tory change detection result. In the following experiments, we 280
prefer σ∈{2.4π, 2.5π,...,3.0π}for two underlying data sets, 281
for each of which the proposed method was implemented to es- 282
timate the average values of four quantitative metrics. A finely 283
tuned parameter will improve the performance of GaborTLC. 284
C. Results and Analysis 285
The Bern data set is made of a pair of SAR images having 286
a size of 301 ×301 pixels, acquired over an area near the city 287
of Bern, Switzerland, in April and May 1999, respectively. The 288
San Francisco data set with 512 ×512 pixels is extracted from 289
the scene over the city of San Francisco (California) and its bay 290
(originally 7749 ×7713 multitemporal acquisitions in August 291
2003 and May 2004), which is available in [19]. The multitem- 292
poral images of both data sets together with their ground-truth 293
change maps are shown in the first three columns of Fig. 4. 294
Table I summarizes the PFA,PMD,PTE,κvalues of 295
various approaches on the Bern and San Francisco data sets. 296
From Table I, the comparison of quantitative measures between 297
GaborFCM and GaborTLC shows that the latter outperforms 298
the former in detection performance. Specifically, GaborTLC 299
achieves the PTE and κgains of 0.03, 0.34, and 0.12, 1.04 over 300
GaborFCM, respectively, for the Bern and San Francisco data 301
sets, although both have their respective advantages in PFA and 302
PMD. This indicates that the proposed cascade scheme is help- 303
ful to discriminate the intermediate pixels, and works better for 304
the overlap of the changed and unchanged classes than a single 305
FCM clustering. Moreover, to highlight the higher class separa- 306
bility of w1
cand w1
u, the quantity J=trace(SB)/trace(SW)307
[20] is calculated in Gabor feature space, where SB,SWare the 308
between-class and within-class scatter matrices, respectively. A 309
larger value of Jindicates better class separability. For the Bern 310
and San Francisco data sets, the classes of w1
cand w1
uhave 311
the corresponding Jscores equal to 0.0080 and 0.0014, which, 312
as expected, are correspondingly larger than that (i.e., 0.0022, 313
0.0003) for the classes of wcand wuobtained by GaborFCM. 314
Furthermore, by comparison with PCAKM and MRFFCM, 315
it can be observed that the proposed approach performs the 316
best on both experimental data sets with the smallest PTE 317
values of 0.34, 1.07 and the biggest κvalues of 86.16, 83.44 in 318
percentage. PCAKM and MRFFCM are obviously inferior to 319
GaborTLC. For visual interpretation, we take σ=2.8πas an 320
IEEE
Proof
LI et al.: GABOR FEATURE BASED UNSUPERVISED CHANGE DETECTION OF MULTITEMPORAL SAR IMAGES 5
Fig. 4. Visualized results of various change-detection approaches on both experimental data sets. Top row: Bern, and bottom row: San Francisco.Fromleftto
right: Y1,Y2, ground-truth change maps, results by PCAKM, results by MRFFCM, and results by GaborTLC together with its intermediate results.
TAB L E I
QUANTITATIVEMEAS URES (IN PERCENTAGE)ON
THE BERN AND SAN FRANCISCO DATA SETS
example for GaborTLC, and show the detection results of three321
approaches on the Bern and San Francisco data sets in Fig. 4.322
As shown in Fig. 4, the results obtained by GaborTLC exhibit323
less isolated spots and are better in matching the ground-truth324
change maps compared with that of PCAKM and MRFFCM,325
which is consistent with the above quantitative analysis. In326
addition, from the first-level clustering results of GaborTLC,327
it is illustrated that the pixels (marked as gray) belonging to the328
intermediate class appear more on the boundary between the329
changed and unchanged regions, or locate at some salient parts330
of multitemporal SAR images.331
IV. CONCLUSION332
This letter has proposed a simple yet effective two-level333
clustering approach to change detection of multitemporal SAR334
images based on Gabor features. Experimental results on two335
pairs of real multitemporal SAR images have demonstrated336
that the proposed approach achieves better detection perfor-337
mance than other state-of-the-art clustering-based techniques338
for change detection (e.g., PCAKM and MRFFCM). Future339
work will be devoted to the automatic determination of Gabor340
filter parameters and the efficient design of cascade structure to341
exploit the multiple-change detection.342
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