2.Mutitemporal Image Change Detection Using Undecimated Discrete Wavelet Transform and Active Contours

7/29/2019 2.Mutitemporal Image Change Detection Using Undecimated Discrete Wavelet Transform and Active Contours

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706 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 2, FEBRUARY 2011

Multitemporal Image Change Detection UsingUndecimated Discrete Wavelet Transform

and Active ContoursTurgay Celik and Kai-Kuang Ma, Senior Member, IEEE

AbstractIn this paper, an unsupervised change detectionmethod for satellite images is proposed. Owing to its robustnessagainst noise, the undecimated discrete wavelet transform is ex-ploited to obtain a multiresolution representation of the differenceimage, which is obtained from two satellite images acquired fromthe same geographical area but at different time instances. Aregion-based active contour model is then applied to the multires-olution representation of the difference image for segmenting thedifference image into the changed and unchanged regions.

The proposed change detection method has been conducted on twotypes of image data sets, i.e., the synthetic aperture radar imagesand the optical images. The change detection results are comparedwith several state-of-the-art techniques. The extensive simulationresults clearly show that the proposed change detection methodconsistently yields superior performance.

Index TermsActive contours, change detection, difference im-age, environmental monitoring, level sets, multitemporal images,optical images, remote sensing, satellite images, surveillance, syn-thetic aperture radar (SAR), undecimated discrete wavelet trans-form (UDWT).

I. INTRODUCTION

CLIMATE change has been widely recognized as one of the

alarming environmental concerns. The global warming

has brought unpredictable changes in the weather patterns. This

leads to land changes (for example, due to a falling or rising

water level) that require a constant surveillance process. For

that, it is quite desirable to have an automatic or unsupervised

change detection method that is able to make a direct com-

parison of a pair of remote sensing images acquired from the

same geographical area but at different time instances in order

to identify and measure the changed areas.

Manuscript received October 3, 2009; revised February 1, 2010 andMarch 6, 2010; accepted April 12, 2010. Date of publication October 7, 2010;date of current version January 21, 2011.

T. Celik is with the Department of Chemistry, Faculty of Science, NationalUniversity of Singapore, Singapore 117543, and also with the Computer Visionand Pattern Discovery Group, Bioinformatics Institute, Agency for Science,Technology and Research, Singapore 138671 (e-mail: [email protected];[email protected]).

K.-K. Ma is with the School of Electrical and Electronic Engineer-ing, Nanyang Technological University, Singapore 639798 (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2010.2066979

Remote sensing imagery generally requires certain pre-

processing corrections due to undesirable sensor characteristics

and other disturbing effects before performing any data analysis

on it. Typical corrections include noise reduction, radiometric

calibration, sensor calibration, atmospheric correction, solar

correction, topographic correction, and geometric correction

[1][3]. In this paper, we assume that the changes yielded

between the two images under comparison are only caused bythe physical changes on the geographical area, and those typical

corrections as mentioned previously either play no issue or have

been carried out on the images before applying any change

detection method.

Unsupervised change detection techniques can be cate-

gorized into two major classes according to the data do-

main to which they apply: 1) spatial-domain approach and

2) transform-domain approach. The spatial-domain techniques

[4][6] directly extract certain statistical quantities from the

input images while the transform-domain techniques [7][9]

apply a certain transformation, such as the undecimated discrete

wavelet transform (UDWT) [7], [9] or the dual-tree complex

wavelet transform (DT-CWT) [8], on the input images first,followed by conducting a statistical analysis to mitigate the

noise interference on the change detection accuracy.

In [4], two unsupervised techniques based on the Bayesian

inferencing for analyzing the difference image are proposed.

One exploits an adaptive decision threshold for minimizing the

overall change detection error under the assumption that the

pixels of the difference image are spatially independent.

The other, which is based on the Markov random fields (MRFs),

analyzes the difference image by considering the spatial contex-

tual information included in the neighborhood of each pixel. In

[5], the observed multitemporal images are modeled as MRFs

in order to generate a change image by using the maximuma posteriori probability decision criterion and the simulated

annealing energy minimization method. These algorithms are

applied in the spatial domain and provide impressive change

detection results at the expense of high computational complex-

ity; thus, they are not suitable for real-time change detection

applications.

Recently, a computationally efficient and yet effective

method for conducting unsupervised change detection is pro-

posed in [6], where the difference image is analyzed by us-

ing the principal component analysis (PCA) and the k-meansclustering algorithm. The PCA is employed for the purpose of

conducting dimension reduction and feature extraction, which

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CELIK AND MA: MULTITEMPORAL IMAGE CHANGE DETECTION USING 707

is a canonical technique to find the useful data representations

in a space with a much reduced dimensionality. The eigenvector

space is created by applying the PCA on nonoverlapping square

blocks collected from the entire difference image. The number

of eigenvectors determines the dimensionality of the feature

vector. The feature vector at each pixel position is computed

by projecting the local change of the pixel values onto theeigenvector space. The binary k-means clustering (i.e., k = 2)is then employed on the PCA-extracted feature vectors to com-

pute the final change detection result. The algorithm produces

promising results with a low computational cost. Note that the

PCA can only separate pairwise linear dependencies between

data points and thus may fail in situations where the dependen-

cies between the data points are highly nonlinear. Therefore,

the PCA is prone to produce false detections due to noise

interference.

Transform techniques can be exploited to analyze the differ-

ence image and to reduce the effect of noise contamination even

through a multiresolution structure. In [8], the DT-CWT is used

to individually decompose each input image into one low-pass

subband and six directional high-pass subbands at each scale of

the decomposition. The DT-CWT coefficient differences which

resulted from the subbands of the two satellite images are

analyzed in order to decide whether each pixel position belongs

to the changed or unchanged class for each subband. The

binary change detection map is thus formed for each subband,

and all the produced subband maps are then merged by using

both the interscale fusion and the intrascale fusion to yield the

final change detection map. This method is free of parameter

selection, except that the number of decomposition scales used

in the DT-CWT decomposition is required to be imposed

in advance. The attractive change detection performance androbustness against noise contamination are accomplished at

the expense of high computational cost. In [7], the log-ratio

image is first obtained by taking the logarithm of the pixel

ratio of the two satellite images, followed by the multiresolution

analysis by using the UDWT for generating different resolu-

tions of the representation of the difference image. The final

change detection result is obtained according to an adaptive

scale-driven fusion algorithm. The method achieves a highly

accurate change detection result but has a major concern on

the selection of an appropriate detection threshold for each

resolution.

Recently, another UDWT-based multiresolution representa-tion is exploited to decompose the difference image of the

multitemporal images [9]. A feature vector at each pixel is then

formed by locally sampling the data from the multiresolution

representation of the difference image. The final change detec-

tion map is obtained by clustering the multiscale feature vectors

using binary k-means algorithm to obtain two disjoint classes:changed and unchanged. Overall, this method performs quite

well, particularly on detecting adequate changes even under

strong noise interference. However, due to the spatial support

of the local sampling structure employed in the feature vector

computation, the boundary accuracy of the changed regions is

sacrificed.

The multiresolution analysis of the difference image, to-gether with the level set implementation of the scalar

MumfordShah segmentation [10], is employed in [11] to

perform the unsupervised change detection. The multireso-

lution representation of the difference image is achieved by

iteratively down sampling the difference image by a factor

of two in both directions [11]. First, the difference image is

segmented into changed and unchanged regions at the coarse

resolution using the scalar MumfordShah segmentation. Thesegmentation result from the coarse resolution is upscaled by

a factor of two in both directions and then used as the initial

segmentation estimate for the change detection at the next finer

resolution. This aforementioned process is repeated on the next

finer resolution levels until the final segmentation result reaches

to the same spatial support of the difference image. This method

achieves comparable change detection results compared with

several state-of-the-art change detection methods [11]; how-

ever, it mainly depends on the initial segmentation achieved

at the coarse resolution. The segmentation error yielded at the

coarser resolutions will be propagated inevitably to its finer

resolution and results in performance degradations. Because of

the down-sampling process used in the multiresolution repre-

sentation, this method is unable to detect the changes whose

spatial supports are lost through the multiresolution repre-

sentation of the difference image due to the down-sampling

operation.

In order to alleviate the aforementioned concerns, an un-

supervised change detection method should possess the fol-

lowing features: 1) high robustness against noise; 2) accurate

boundary of changed regions; 3) free of a priori assumptions

in modeling the data distribution of the difference image;

and 4) low computational complexity. In this paper, an unsu-

pervised change detection method for multitemporal satellite

images is proposed by exploiting an active contour methodon the multiresolution representation of the difference image.

The multiresolution representation is achieved by using the

UDWT to benefit from its inherited robustness against the noise

interference on the representation. The UDWT is exploited,

instead of the discrete wavelet transform (DWT), because of

the following characteristics: 1) There is no down-sampling

operation involved, and thus, it is free from an aliasing prob-

lem; and 2) it is shift invariant. The active contour method

is employed on the multiresolution representation to segment

the difference image into the changed and unchanged regions

with accurate region boundaries. The active contour model used

in this paper was first introduced in [10] which is free frommaking any a priori assumption on the statistical modeling

of the input data. It is robust to noise interference and holds

good regularization properties. The model has been extended

for the vector-valued images (as the one proposed in [12]) and

used in this paper for segmenting the multiresolution repre-

sentation of the difference image into changed and unchanged

regions. Furthermore, a level set implementation of the active

contour model [10], [12] makes it possible to perform the seg-

mentation process with a moderate computational complexity

[10], [12].

This paper is organized as follows. Section II gives a brief

review of the UDWT-based multiresolution image analysis and

describes its use on the difference image to generate the vector-valued difference image for conducting change detection.



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Fig. 1. One-level filter bank implementation of the UDWT. (a) Forwardtransform. (b) Inverse transform.

Section III provides a necessary background on the level sets

and briefly describes the general framework of the region-

based geometric active contour method. The ChanVese active

contour model for the vector-valued difference image is then

described. Section IV describes the proposed unsupervised

change detection algorithm. Section V describes the test data

sets, the quantitative measures employed for conducting thechange detection performance evaluation, the implementation

details of the different change detection techniques used in our

experiments, and the experiments. Section VI concludes this

paper.

II. MULTIRESOLUTION ANALYSIS USING UDWT

The multiresolution representation of the image X is ob-

tained by applying the forward and then inverse UDWTs with

further processing on the wavelet subbands to create XMR ={X0,X1, . . . ,Xs, . . . ,XS}, where the subscript s indicates the

resolution index and S is the maximum number of the resolu-tion levels targeted to achieve. The resolution 0 corresponds to

the input image itself, i.e., X0 = X. The images with a lowervalue of resolution index s are more affected by noise; however,they are inherited with a large amount of details of the image

content. On the other hand, the image with a higher value of

resolution index s contains much reduced noise interferenceand less image content details.

The s-level UDWT decomposition of image X creates foursubbands at each level of decomposition; in symbols, for the kthlevel, they are labeled asXk,ll,Xk,lh,Xk,hl, andXk,hh, where

k = 1, 2, . . . , s. The basebandXk,ll is generated by conducting

low-pass filtering (l) along the rows, followed by performingthe same operation along the columns. The remaining subbandsXk,lh, Xk,hl, and Xk,hh are the decomposed high-frequency

subbands that are produced by performing low-pass (l) (orhigh-pass (h)) along the rows and then high-pass (h) (orlow-pass (l)) filtering along the columns. To obtain the nextlevel of subband decomposition, only the baseband generated

at level k will be decomposed into four subbands for levelk + 1. For example, as shown in Fig. 1(a), the subband Xk,llis further decomposed to produce Xk+1,ll, Xk+1,lh, Xk+1,hl,

and Xk+1,hh. This process will be recursively repeated to the

current baseband until the targeted final level (i.e., k = s) isreached.

In summary, the UDWT decomposition is realized by recur-sively applying the aforementioned procedure to the baseband

Xk,ll, whereX0,ll = X, i.e.,

Xk+1,ll(i, j)=

Nk,l1m=0

Nk,l1n=0

lk(m)lk(n)Xk,ll(i+m, j +n),

Xk+1,lh(i, j)=

Nk,l1

m=0

Nk,h1

n=0

lk(m)hk(n)Xk,ll(i+m, j +n),

Xk+1,hl(i, j)=

Nk,h1m=0

Nk,l1n=0

hk(m)lk(n)Xk,ll(i+m, j +n),

Xk+1,hh(i, j)=

Nk,h1m=0

Nk,h1n=0

hk(m)hk(n)Xk,ll(i+m, j +n)

where Nk,l and Nk,h are the lengths of the low-pass filter lkand the high-pass filter hk, respectively. At each decompo-sition level, the impulse response of the low-pass and high-

pass filters are upsampled by a factor of two. Thus, the filter

coefficients lk+1 and hk+1 for computing the subbands atlevel k + 1 are obtained by applying an interpolation operationto the filter coefficients (i.e., lk and hk) at level k. That is,2k1 zeros are inserted between the filter coefficients usedto compute the subbands at the lower resolution level [13],

i.e., lk(n) = h(n/2k), if n/2k is an integer and 0 otherwise.

For example, we have l1 = [. . . , l(1), 0, l(0), 0, l(1), . . .], andh1 = [. . . , h(1), 0, h(0), 0, h(1), . . .].

The inverse UDWT (IUDWT) for the reconstruction of the

input imageX is obtained by applying the previously described

steps in the reverse order. That is, the subbands Xk+1,ll,

Xk+1,lh, Xk+1,hl, and Xk+1,hh at level k + 1 are used to

reconstruct the approximation subband Xk,ll at the level k by

applying a low-pass filter lk and a high-pass filter hk along therows and the columns of the subbands alternatively as shown in

Fig. 1(b), i.e.,

Xk,ll(i, j) =

Nkl

1m=0

Nkl

1n=0

lk(m)lk(n)Xk+1,ll(i+m, j +n)

+

Nkl

1m=0

Nkh

1n=0

lk(m)hk(n)Xk+1,lh(i+m, j +n)

+

Nkh

1

m=0

Nkl

1

n=0

hk(m)lk(n)Xk+1,hl(i + m, j + n)

+

Nkh

1m=0

Nkh

1n=0

hk(m)hk(n)Xk+1,hh(i+m, j +n)

where Nkl

and Nkh

are the lengths of the low-pass filter lk and

the high-pass filter hk at level k, respectively. The reconstruc-tion was iteratively applied starting from the last level (s) of thedecomposition, where Xs,ll = Xs,ll.

The filter bank needs only to verify the perfect reconstruction

condition [13], i.e.,

l(n) = (1)

n1

h(1 n)l(n) = (1)n1h(1 n)



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which means that the reconstructed signal X = X0,ll is exactly

the same as the decomposed signal X = X0,ll, i.e., X = X.The IUDWT is then applied to the s-level UDWT decom-

posed input image to reconstruct a realizationXs of the input

imageX. In the reconstruction, the baseband, together with the

subbands containing the vertical and horizontal details at each

level, is kept, and the subbands with very high details are set tozero, i.e.,Xk,hh(i, j) = 0, where k = 1, 2, . . . , s.

III. CHA NVES E ACTIVE CONTOUR MODEL

FO R BINARY SEGMENTATION

The ChanVese algorithm [10] is a region-based segmenta-

tion algorithm which is based on the ideas of contour evolution,

the MumfordShah functional [14], and the level sets of Osher

and Sethian [15]. This algorithm has several advantages [10]:

1) Since the gradient-based information is replaced by a crite-

rion which is related to region homogeneity, it can detect the

region contours with and without strong gradient information;

2) it is able to detect interior contours; 3) the initial curve

does not necessarily have to start around the objects to be

detected and can be placed anywhere in the image instead;

4) it partitions the image into two regions, the detected objects

as the foreground and the rest as the background; and 5) it does

not need to have noise removal preprocessing in advance.

The ChanVese segmentation algorithm can be applied to the

scalar-valued images [10] as well as to the vector-valued images

[12], which is adopted in this paper.

A. ChanVese Model for Scalar-Valued Images

Let R2

be a bounded open subset and X : R be adifference image which consists of two homogenous regions

1 and 2; i.e., = 1 2. The ChanVese algorithmfinds a contour C that partitions the difference image into

two regions, 1 and 2, that describe an optimal piecewise

constant approximation of the image.

The contour C is determined by minimizing the segmenta-

tion energy [10]

E(C, c1, c2) = 1

1

(X(x, y) c1)2 dxdy

+ 2 2

(X(x, y) c2)2 dxdy + Length(C) (1)

where c1 and c2 represent the average intensities in the regions1 and 2, respectively, and 1, 2 > 0 and > 0 are theweighting parameters for the fitting terms and regularization

term, respectively.

The ChanVese algorithm does not use any control points

or interpolation to represent the contour C; instead, it exploits

the level sets of Osher and Sethian [15]. The contour C is

represented as the zero level set of function over domain ,which satisfies the following conditions:

< 0 in1 = 0 onC > 0 in2.

Using the Heaviside function H, which is defined by

H(z) =

1, ifz 00, ifz < 0

and its distributional derivative (z) = dH(z)/dz, one canrewrite the energy function (1) as follows:

E(, c1, c2) =

1 (X(x, y) c1)

2 (1 H((x, y)))

+ 2 (X(x, y) c2)2 H((x, y))

+ ((x, y)) |H((x, y))|

dxdy.

The energy functional E(, c1, c2) can be minimized with re-spect to the constants c1 and c2, for a fixed , according to [10]

c1 = (X), for 0c2 = (X), for < 0

where (X) computes the average of the pixel intensity valuesofX for a given region of interest. Using the gradient descent

method, the EulerLagrange equation for can be establishedby minimizing the energy functional E(, c1, c2) with respectto , for fixed c1 and c2, which is governed by the meancurvature and the error terms (see [10] for more details).

B. Extending the Model to the Vector-Valued Images

Let Xs be the sth channel of a vector-valued image on (where s = 0, 1, . . . , S ) and C be the evolving curve. Letc1 = [c

01, c

11, . . . , c

S1 ] and

c2 = [c02, c

12, . . . , c

S2 ] be the unknown

constant vectors.

The extension of the ChanVese model to the vector-valuedimage is [12]

E(C, c1 , c2) =1

S

Ss=0

s1

1

(Xs(x, y) cs1)2 dxdy

+1

S

Ss=0

s2

2

(Xs(x, y) cs2)2 dxdy

+ Length(C) (2)

where s1, s2 > 0 and > 0 are the weighting parameters

and the active contour C becomes the boundary between the

two regions 1 and 2 [12]. The model looks for the bestapproximation of vectors c1 and c2 [12]. However, note thatthis model can only detect the edges presented in at least one of

the channels but not necessarily in all channels.

As presented in [12], the level set form of (2) is

E(C,c1 ,c2) =

((x, y)) |H((x, y))|

+1

S

Ss=0

s1(Xs(x, y)cs1)2(1H((x, y)))

+1

S

S

s=0

s2(Xs(x, y)cs2)2H((x, y))dxdy

(3)



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where the parameter is the weight for adjusting the contri-bution based on the length of the curve C and the coefficient

vector = (01, . . . ,

S1 ,

02, . . . ,

S2 ) denotes the weights for

the error terms. In order to filter the high-frequency noise, a

large and/or a small are necessary for the model. On

the other hand, in order to detect the objects boundary more

accurately, larger coefficients

are necessary.The energy functional E(C, c1 , c2 ) can be minimized with

respect to the constants cs1 and cs2, for s = 0, 1, . . . , S , for a

fixed , according to

cs1 =1

Xs(x, y)H((x, y)) dxdy

cs2 =1

Xs(x, y) (1 H((x, y))) dxdy

where =

H((x, y))dx dy is a normalization term.

The minimization of E(C, c1 , c2) with respect to , forfixed vectors c1 and c2 , yields the following EulerLagrangeequation for (parameterizing the descent direction by usingan artificial time variable t) [12]

t=

div

||

1

S

Ss=0

s1 (Xs cs1)2

+1

S

Ss=0

s2 (Xs cs2)2

in, with the boundary condition [12]

()

||

n = 0

on boundary , where n denotes the unit normal vector atthe boundary of and is the distributional derivative of theregularized Heaviside function H [12].

IV. PROPOSED CHANGE DETECTION ALGORITHM

Let us formulate the change detection problem by consider-

ing two images, X1 = {x1(i, j)|1 i H, 1 j W} andX2 = {x2(i, j)|1 i H, 1 j W}, with a size of H W pixels acquired at the same geographical area but at two

different time instances, respectively. Let us further assumethat such images have been registered with respect to each

other [2]. The main objective of the change detection is to

generate a binary change detection map CM = {cm(i, j)|1 i H, 1 j W}, where cm(i, j) {0, 1}, based on thedifference image X = {x(i, j)|1 i H, 1 j W} com-puted from two input images, X1 and X2. The pixel value at

the spatial location (i, j) of the change detection map is labeledas 0 where the corresponding pixel position is identified as

changed (hence, 1 for unchanged).

The proposed change detection method consists of three

stages (as shown in Fig. 2). They are detailed as follows. The

difference image can be computed differently according to the

physical nature of the input image. For the optical images, Xcan be computed pixelwise as the absolute-valued difference

Fig. 2. Proposed unsupervised change detection algorithm.

of the intensity values of the two images under comparison

[4], i.e.,

x(i, j) = |x2(i, j) x1(i, j)| .

On the other hand, when the input satellite images are the

synthetic aperture radar (SAR) images, X can be computed

likewise by using the logarithm operation to enhance the low-

intensity pixels [7], i.e.,

x(i, j) =

log x2(i, j)x1(i, j) (4)

where log stands for the logarithm with the natural base. In this

paper, each pixel value of the difference image X is further

normalized according to

x(i, j) =x(i, j) min(X)

max(X) min(X) 255 (5)

to ensure that they are in the range of [0, 255], i.e., x(i, j) [0, 255], where the functions min() and max() find the min-imum and maximum values of the input difference image X,

respectively.

The second step of the proposed method aims at building

a multiresolution representation of the difference image X,

denoted as

XMR = {X0, . . . ,Xs, . . . ,XS}

where the superscript s, for s = 0, 1, . . . , S , indicates the res-olution level. The value of S provides a tradeoff betweenthe spatial detail preservation and the noise reduction. To be

specific, a higher value of S will yield more noise reductionthrough low-pass filtering but at the expense of sacrificing the

image details. Conversely, a lower value of S will be stronglyaffected by the noise while preserving more image details. To

demonstrate, a multiresolution representation of the difference

image with S = 5 is shown in Fig. 3.The multiresolution representation XMR of the difference

image X is used to generate the change detection map accord-

ing to the ChanVese segmentation algorithm for the vector-

valued image. The proposed method iteratively finds the finalchange detection map based on all the images in XMR. For this,



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Fig. 3. Multiresolution representation of the difference image X with fivemultiresolution levels (i.e., S = 5). (a) Difference image X (or X0). (b) X1.(c)X2. (d)X3. (e)X4. (f)X5.

a proper initialization of the proposed method is needed, i.e.,

the weighting parameters , the smoothness parameter , and

the number of multiresolution levels S. The stopping criterionfor the iterative algorithm is formulated as follows. If the zero-

level set of remains unchanged in the consecutive iterations,then the algorithm is declared converged. Alternatively, the

convergence can also be monitored by calculating the energy of

(3); however, this approach is not used in this paper.

In (3), the parameters s1 and s2 determine the degree of

contributions from Xs, where s = 0, 1, . . . , S , in the finalresult. In [12], the regularization parameters

are used to

filter the high-frequency noise from different channels. In ourcase, we constantly set s1 = 1 and

s2 = 1 to weight each

realization of the multiresolution equally. The parameter controls the smoothness of the contour and, thus, the sharpness

of the boundaries of the segmented regions. The setting of is somewhat empirical as it weights the contribution of the

smoothness term against the contribution of the data-driven

term. However, the simulation results do not seem to be very

sensitive to the value of which only needs to be adjustedwithin the permissible operational range for a given type of

input satellite images. Because of the normalization operation

employed on the difference image according to (5), the type

of the input satellite images does not affect the value settingof . The value of is set as = 5 104 2552 for theinput images as suggested by Chan and Vese [10]. The number

of multiresolution levels is set to three (i.e., S = 3) and usedin all our simulation experiments. The Haar wavelet filters are

employed in the UDWT implementation.

The initialization of the algorithm is achieved with a set of

circles uniformly distributed over the entire image as shown

in Fig. 4(a). It can be observed from Fig. 4 that the proposed

method is able to iteratively fine tune the initial contour toward

the final change detection map. The contour evolution is robust

to different initializations. However, initializing with an array of

circles uniformly distributed over the entire image effectively

speeds up the convergence compared to the conventional wayby initializing with a single large closed curve. Some interme-

Fig. 4. Contour evolution of the proposed change detection method onXMRas shown in Fig. 3 through different numbers of iterations. (a) Initialization.(b) Iteration 100. (c) Iteration 200. (d) Iteration 300. (e) Iteration 400.

(f) Iteration 500.

diate results of the contour evolution are shown in Fig. 4(b)(f)

at different numbers of iterations.

V. EXPERIMENTAL RESULTS

A. Data Sets

In order to assess the effectiveness of exploiting the UDWT-

based multiresolution representation of the difference image

for change detection, we experimented on few multitemporal

satellite image data sets acquired from a geographical area of

Alaska and of the city of San Francisco in California.The first data set is available from [16], which contains a

very high resolution (7713 7749 pixels) set of SAR imagescollected on the city of San Francisco, California. Two of them

are chosen for our simulation experiments which were acquired

on August 10, 2003 and May 16, 2004 by the ESA ERS-2

satellite. The instruments pixel resolution is 25 m [17]. A

small area with 512 512 pixels is selected from two veryhigh resolution images and presented in Fig. 5(a) and (b),

respectively. The ground truth of the change detection map

which is shown in Fig. 5(c) was manually created based on the

input images shown in Fig. 5(a) and (b).

The second data set is available from [18], which con-tains a high resolution (1305 1520 pixels) set of multi-spectral images collected on a geographical area of Alaska.

Two of them are chosen for our simulation experiments

which were acquired by Landsat-5 Thematic Mapper (TM) on

July 22, 1985 and July 13, 2005, respectively. A small area with

1024 1024 pixels is selected from two high resolution imagesand presented in Fig. 5(d) and (e), respectively. The Landsat-5

TM provides optical imageries using seven spectral bands,

Bands 17. The instruments pixel resolution is 30 m for all

bands except in Band 6 which has a 120-m resolution. The

visible Band 1 is selected for our simulation experiments. The

ground truth of the change detection map which is shown in

Fig. 5(f) was created by the manual analysis of the input imagesbased on Fig. 5(d) and (e).



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Fig. 5. Datasets used in theexperiments. (a) ESAERS-2SAR image acquiredon August 10, 2003. (b) ESA ERS-2 SAR image acquired on May 16, 2004.(c) Manually created ground truth of the change detection map yielded based

on (a) and (b). (d) Landsat-5 TM Band 1 optical image acquired on July 22,1985. (e) Landsat-5 TM Band 1 optical image acquired on July 13, 2005.(f) Manually created ground truth of the change detection map yielded basedon (d) and (e).

The histograms of the difference images computed from the

two SAR images [i.e., Fig. 5(a) and (b)] and the two optical

images [i.e., Fig. 5(d) and (e)] are shown in Fig. 6(a) and

(b), respectively. As can be seen from Fig. 6(a), the separation

between the changed and unchanged classes is not very clear.

This makes it difficult to partition the difference image into two

such classes. On the other hand, one can observe two peaks in

Fig. 6(b), and they are far apart from each other. This makes it

much easier to separate the difference image into two classes forconducting the change detection by simply using an appropriate

threshold value.

B. Quantitative Measures

For performing the evaluation, both the quantitative and

qualitative measurements are conducted. For the former, once

the binary change detection map has been obtained by using a

change detection method, the following defined quantities are

computed for comparing the computed change detection map

against the ground truth change detection map.

1) False Alarm (FA): The number of actually unchangedpixels that were incorrectly determined as changed ones.

The false alarm rate PFA is computed in percentage asPFA = FA/N1 100%, where N1 is the total numberof unchanged pixels counted in the ground truth change

detection map.

2) Miss Detection (MD): The number of actually changed

pixels that were missed out on their detections and

mistakenly determined as unchanged ones. The missed

detection rate PMD is counted in percentage as PMD =MD/N0 100%, where N0 is the total number ofchanged pixels counted in the ground truth change de-

tection map.

3) Total Error (TE): The total number of incorrect deci-sions made, which is the sum of the false alarms and

Fig. 6. Histograms of the difference images which resulted from two testimages obtained from two different data sets. (a) SAR image data set.(b) Optical image data set.

the missed detections. Hence, the total error rate PTE inpercentage is computed as PTE = (F A + MD)/(N0 +N1) 100%.

C. Implementation of Change Detection Methods

There are two methods presented in [4] to produce the change

detection map based on the analysis of the difference im-

age: 1) the Expectation-Maximization (EM)-based thresholding

method and 2) the MRF-based thresholding method. The for-

mer is free from using any parameters while the latter depends

on a regularization parameter that influences the spatial-contextual information for the change detection process. In this

paper, = 1.67 is empirically determined for the experiments.We implement the change detection techniques of Bovolo

and Bruzzone [7] using the same set of parameters as presented

in [7], which consists of three major steps: 1) obtaining a multi-

resolution representation of the log-ratio image as described in

[7]; 2) identifying the number of reliable scales; and 3) produc-ing the final change detection map according to a scale-driven



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TABLE IFALSE ALARMS, MIS S DETECTIONS, AN D TOTAL ERRORS (IN NUMBER

OF PIXELS AND IN PERCENTAGE) WHICH RESULTED FROM THEPROPOSED CHANGE DETECTION METHOD WITH DIFFERENT

VALUES OF S EXPERIMENTED ON THE SAR TESTIMAGES SHOWN IN FIG . 5(a) and (b)

fusion strategy. According to the scale-driven fusion strategy,

three fusion techniques are proposed in [7]: 1) the fusion at

the decision level by an optimal scale selection (FDL-OSS);

2) the fusion at the decision level on all reliable scales (FDL-

ARS); and 3) the fusion at the feature level on all reliable

scales (FFL-ARS). It is reported in [7] that the FFL-ARS

approach outperforms the other two methods. Because of this,

we only compare the performance of the FFL-ARS approach

[7]. The change detection using the FFL-ARS approach [7]

requires manual settings for the thresholds which are used for

thresholding the reconstructed images from the approximation

subbands of the UDWT decomposition of the log-ratio image,

from the number of scales used in the UDWT decompositions,

and from the local window size that is used for finding the

reliable scales for each pixel. All parameters are exhaustively

searched for the input SAR images shown in Fig. 5(a) and

(b) and for the optical images shown in Fig. 5(d) and (e) by

minimizing the total errors yielded by taking the difference

of the change detection results of the FFL-ARS approach andthe ground truth change detection maps shown in Fig. 5(c)

and (f). The optimum value of the maximum number of the

decomposition levels used in the UDWT decomposition of the

log-ratio image is found to be six.

We implement the change detection methods presented in

[6], [8], and [9], and the parameters required for the imple-

mentations are settled at the minimum error yielded between

the resultant change detection map (from the methods in [6],

[8], and [9], respectively) and the ground truth change de-

tection map.

D. Effect of the Maximum Number of Scales

The proposed method exploits a multiresolution representa-

tion of the difference image X; hence, the maximum number

of resolution levels S used will affect the change detectionperformance result. The proposed change detection method

with different values of S is experimented on the input SARimages and optical images shown in Fig. 5.

The input SAR images shown in Fig. 5(a) and (b) are noisy,

and the change detection performance of the proposed method

improves when the value ofSgets larger. This can be seen fromthe quantitative results tabulated in Table I as well as the qual-

itative results as shown in Fig. 7. When S = 0, the proposed

method performs only on the difference image itself, which canbe viewed as the performance of the scalar-valued ChanVese

Fig. 7. Change detection results by using the proposed change detectionmethod with different values ofS experimented on the SAR test images shownin Fig. 5(a) and (b). (a) S = 0. (b) S = 1. (c) S = 2. (d) S = 3. (e) S = 4.

(f) S = 5.

TABLE IIFALSE ALARMS, MIS S DETECTIONS, AN D TOTAL ERRORS (IN NUMBER

OF PIXELS AND IN PERCENTAGE) WHICH RESULTED FROM THEPROPOSED CHANGE DETECTION METHOD WITH DIFFERENT

VALUES OF S EXPERIMENTED ON THE OPTICAL TES TIMAGES SHOWN IN FIG . 5(d) and (e)

model. It is clear that the performance inproves for S > 0. Thatis, the performance of the scalar-valued ChanVese model is

improved by using the vector-valued ChanVese model on a set

of images obtained from the multiresolution representation of

the difference image, at the expense of a higher computational

cost. The performance of the proposed system starts to degrade

when the difference image is oversmoothed which results in

high degradations on the image details. According to Table I,

S = 3 yields the best performance.

The test results using the optical images shown in Fig. 5(d)and (e) are tabulated in Table II and shown in Fig. 8. Unlike

the test results based on the SAR images, the test results on

the optical images show that the performance of the proposed

method is less sensitive for different values of S. This ismainly due to the fact that the difference image computed from

the optical images can be easily separated into two distinct

regions, as shown from the histogram of the difference image

in Fig. 6(b), which has two peaks that can be easily separated

from each other.

The test results show that the change detection performance

obtained by exploiting different values of S offers varioustradeoffs between the spatial-detail preservation and the noise

reduction. In particular, images with a lower value of S aremore subject to noise interference while preserving more details



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Fig. 8. Change detection results by using the proposed change detectionmethod with different values of S experimented on the optical test imagesshown in Fig. 5(d) and (e). (a) S = 0. (b) S = 1. (c) S = 2. (d) S = 3.(e) S = 4. (f) S = 5.

TABLE IIIFALSE ALARMS, MIS S DETECTIONS, AN D TOTAL ERRORS

(IN NUMBER OF PIXELS AND IN PERCENTAGE) RESULTING FROMDIFFERENT CHANGE DETECTION METHODS EXPERIMENTED

ON THE SAR TEST IMAGES SHOWN IN FIG . 5(a) and (b)

of the image content. On the contrary, images with a higher

value ofSare less susceptible to noise interference but sacrificemore degradations on the image details.

E. Change Detection Performance Tests on Data Sets

The quantitative and qualitative change detection results

obtained from different methods for the SAR images shown

in Fig. 5(a) and (b) are tabulated in Table III and shown in

Fig. 9(a)(f), respectively. The proposed method only yields

a 1.29% total erroneous decision rate (i.e., a 98.71% correctdetection rate).

Based on Fig. 9, one can observe that the change detection

results obtained from the EM-based method [4] and the MRF-

based method [4] are far from satisfactory. This is mainly due

to the fact that the Gaussian model assumed in [4] fails to pro-

vide accurate data modeling for the difference image in these

methods. The performance improvement of Celik and Ma [8] is

apparent compared with that of Bruzzone and Prieto [4]. This is

mainly due to the transformation from the image domain to the

DT-CWT domain, resulting in the data distribution of wavelet

coefficients better modeled by the Gaussian model. On the

other hand, the change detection results provided by Celik [6],

Bovolo and Bruzzone [7], Celik [9], and these methods are allquite accurate. This is mainly due to the fact that these methods

Fig. 9. Change detection maps which resulted by using different methodsexperimented on the SAR test images shown in Fig. 5(a) and (b). (a) Groundtruth change detection map. (b) EM-based method [4]. (c) MRF-based method[4]. (d) Method of Celik [6]. (e) Method of Bovolo and Bruzzone [7].(f) Method of Celik and Ma [8]. (g) Method of Celik [9]. (h) Proposed method.

do not depend on any data modeling approach. That is, the

discrimination between the changed and unchanged regions of

the difference image is achieved by using the difference imageitself without incorporating any assumption. The performance

degradation of the change detection results from [6] and [9]

with respect to the proposed method is mainly caused by the

block processing employed in [6] and [9]. Such a process results

in incorrect detection around the region boundaries between the

changed and unchanged regions. It is worthwhile to mention

that the result provided by Bovolo and Bruzzone [7] is achieved

by finding an optimum threshold set with respect to the mini-

mum error between the change detection map of Bovolo and

Bruzzone [7] and the ground truth change detection map shown

in Fig. 5(c). In reality, such a process is infeasible since the

ground truth change detection map is generally not available.Consequently, the performance will be degraded because of the

nonoptimal threshold used.

The change detection results on the optical image data set

are tabulated in Table IV and shown in Fig. 10. The method

of Bovolo and Bruzzone [7] is designed for the SAR images;

thus, the change detection performance on the optical images is

not reported in [7]. Meanwhile, the proposed method delivers

a very similar performance as that in [4], [6], and [9]. As

can be seen from the histogram in Fig. 6(b), the data dis-

tribution of the difference image computed from the optical

images consists of two peaks which can be easily modeled as

a mixture of two Gaussians. This validates the data modeling

of Bruzzone and Prieto [4] and Celik and Ma [8] which resultsin attractive performance. The proposed method yields the best



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TABLE IVFALSE ALARMS, MIS S DETECTIONS, AN D TOTAL ERRORS (IN NUMBER

OF PIXELS AND IN PERCENTAGE) RESULTING FROM DIFFERENTCHANGE DETECTION METHODS EXPERIMENTED ON THE

OPTICAL TES T IMAGES SHOWN IN FIG. 5(d) and (e)

Fig. 10. Change detection results by using different methods experimentedon the optical test images shown in Fig. 5(d) and (e). (a) Ground truthchange detection map. (b) EM-based method [4]. (c) MRF-based method [4].(d) Method of Celik [6]. (e) Method of Celik and Ma [8]. (f) Method of Celik[9]. (g) Proposed method.

performance, i.e., only a 0.34% total erroneous decision rate

(i.e., a 99.66% correct detection rate). Furthermore, since the

proposed method does not make any assumption on the datamodeling, it becomes more applicable for general purpose

change detection applications.

F. Effect of Wavelet Filters

To study the change detection performance which resulted by

employing different lengths of wavelet filters, the Daubechies

wavelet filters with different lengths are tested on the opti-

cal images, and the change detection results are tabulated in

Table V. In Table V, the index i in dbi indicates half of the filterlength; for example, the actual filter lengths of filters db1 and

db4 are two and eight, respectively. The experimental simula-

tion results show that the proposed method delivers almost thesame performance regardless of the length of the Daubechies

TABLE VFALSE ALARMS, MIS S DETECTIONS, AN D TOTAL ERRORS (IN NUMBER

OF PIXELS AND IN PERCENTAGE) RESULTING FROM THE PROPOSEDCHANGE DETECTION METHOD WIT H DIFFERENT DAUBECHIES (DB )

WAVELET FILTERS EXPERIMENTED ON THE OPTICALTEST IMAGES SHOWN IN FIG . 5(d) and (e)

wavelet filter used, although the performance of the proposed

method slightly degrades when the filter length increases. This

is mainly due to the blurring effect which resulted from the use

of filters with a longer length. However, it is clear from Table V

that this performance degradation is negligibly small.

VI. CONCLUSION

In this paper, an unsupervised change detection method

is proposed and applied to multitemporal SAR and optical

images. It combines the multiresolution analysis of the differ-

ence image and an active contour model for the vector-valued

images. The UDWT is exploited to obtain a multiresolution

representation of the difference image. The proposed method

works without incorporating any a priori assumption on the dis-

tribution of the difference image data. This makes it applicablefor a wide range of change detection applications on different

types of input satellite images.

The number of representation scales used in the multiresolu-

tion representation of the difference image is the only parameter

that needs to be selected, without involving any data modeling.

The change detection results obtained by exploiting different

values of representation scales show various tradeoffs yielded

between the spatial-detail preservation and the noise reduction.

It is worth mentioning that the proposed method works quite

well on a large set of images based on three scales of the multi-

resolution representation. Furthermore, the proposed method

performs almost the same for different types of Daubechies

wavelet filters.Because of the region-based active contour segmentation

employed in segmenting the multiresolution representation of

the difference image, the proposed method achieves accurate

decision on the boundary of the changed and unchanged re-

gions. Furthermore, the use of the level set on the active

contours with a novel initialization scheme makes the proposed

method require moderate computational time.

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Available: http://change.gsfc.nasa.gov/alaska.html

Turgay Celik received the Ph.D. degree in elec-trical and electronic engineering from EasternMediterranean University, Gazimagusa, Turkey.

He is currently a Research Fellow with theDepartment of Chemistry, National University ofSingapore, Singapore, and with the Computer Vi-sion and Pattern Discovery Group, BioinformaticsInstitute, Agency for Science, Technology and Re-search, Singapore, Singapore. He has produced ex-tensive publications in various international journalsand conferences. His research interests include bio-

physics, digital signal, image and video processing, pattern recognition, and ar-tificial intelligence. These include fluorescent microscopy, digital image/videocoding, wavelets and filter banks, image/video processing, content-based imageindexing and retrieval, and scene analysis and recognition.

He has been a Reviewer for various international journals and conferences.

Kai-Kuang Ma (S80M84SM95) received theB.E. degree in electronic engineering from ChungYuan Christian University, Chung Li, Taiwan, theM.S. degree in electrical engineering from DukeUniversity, Durham, NC, and the Ph.D. degree inelectrical engineering from North Carolina StateUniversity, Raleigh.

He is currently a Full Professor with the School

of Electrical and Electronic Engineering, NanyangTechnological University, Singapore, Singapore.From 1992 to 1995, he was a Member of the Tech-

nical Staff at the Institute of Microelectronics, Singapore, where he worked ondigital video coding and the MPEG standards. From 1984 to 1992, he was withthe IBM Corporation, Kingston, NY, and with Research Triangle Park, NC,where he was engaged on various DSP and VLSI advanced product develop-ment. He has produced extensive publications in various international journals,conferences, and MPEG standardization meetings. He is the holder of one U.S.patent on a fast motion estimation algorithm. His research interests includedigital signal and image and video processing. These include digital image/video coding and standards, wavelets and filter banks, image/video processing,denoising, superresolution, error resilience and concealment, content-basedimage indexing and retrieval, and scene analysis and recognition.

Dr. Ma is a member of Eta Kappa Nu. He was the Chairman and the Headof Delegation of the Singapore MPEG (19972001). He was the Chairman ofthe IEEE Signal Processing Society Singapore Chapter (20002002). He has

been actively contributing various technical services for numerous internationalconferences, particularly as the Technical Program Cochair of the IEEE Interna-tional Conference on Image Processing 2004 and the International Symposiumon Intelligent Signal Processing and Communication Systems 2007. He iscurrently an (Associate) Editor or Editorial Board Member of six international

journals: the IEEE TRANSACTIONS ON IMAGE PROCESSING (since 2007),the IEEE TRANSACTIONS ON COMMUNICATIONS (since 1997), the IEEETRANSACTIONS ON MULTIMEDIA (since 2002), the International Journal of

Image and Graphics (since 2002), the Journal of Visual Communication andImage Representation (since 2005), and the Research Letters in Signal Process-ing (since 2008). He is an elected member of three technical committees: theImage and Multidimensional Signal Processing Committee of the IEEE SignalProcessing Society, the Multimedia Communications Committee of the IEEECommunications Society, and the Digital Signal Processing Committee of theIEEE Circuits and Systems Society. He is a Distinguished Lecturer in the IEEECircuits and Systems Society (20082009).


2.Mutitemporal Image Change Detection Using Undecimated Discrete Wavelet Transform and Active Contours

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