Image Processing for Remote Sensing - Chapter 5 pdf

In the literature, many different techniques for change detection in images acquired bypassive sensors have been presented [1–8], and many applications of these techniqueshave been repor

Unsupervised Change Detection in Multi-Temporal SAR Images

Lorenzo Bruzzone and Francesca Bovolo

CONTENTS

5.1 Introduction 107

5.2 Change Detection in Multi-Temporal Remote-Sensing Images: Literature Survey 110

5.2.1 General Overview 110

5.2.2 Change Detection in SAR Images 113

5.2.2.1 Preprocessing 113

5.2.2.2 Multi-Temporal Image Comparison 114

5.2.2.3 Analysis of the Ratio and Log-Ratio Image 115

5.3 Advanced Approaches to Change Detection in SAR Images: A Detail-Preserving Scale-Driven Technique 117

5.3.1 Multi-Resolution Decomposition of the Log-Ratio Image 119

5.3.2 Adaptive Scale Identification 121

5.3.3 Scale-Driven Fusion 122

5.4 Experimental Results and Comparisons 124

5.4.1 Data Set Description 124

5.4.2 Results 126

5.5 Conclusions 130

Acknowledgments 131

References 131

The recent natural disasters (e.g., tsunami, hurricanes, eruptions, earthquakes, etc.) and the increasing amount of anthropogenic changes (e.g., due to wars, pollution, etc.) gave prominence to the topics related to environment monitoring and damage assessment The study of environmental variations due to the time evolution of the above phenomena is of fundamental interest from a political point of view In this context, the development of effective change-detection techniques capable of automatically identifying land-cover

107

variations occurring on the ground by analyzing multi-temporal remote-sensing imagesassumes an important relevance for both the scientific community and the end-users.The change-detection process considers images acquired at different times over the samegeographical area of interest These images acquired from repeat-pass satellite sensors are

an effective input for addressing change-detection problems Several different observation satellite missions are currently operative, with different kinds of sensorsmounted on board (e.g., MODIS and ASTER on board NASA’s TERRA satellite, MERISand ASAR on board ESA’s ENVISAT satellite, Hyperion on board EO-1 NASA’s satellite,SAR sensors on board RADARSAT-1 and RADARSAT-2 CSA’s satellites, Ikonos and Quick-bird satellites that acquire very high resolution pancromatic and multi-spectral (MS) images,etc.) Each sensor has specific properties with respect to the image acquisition mode (e.g.,passive or active), geometrical, spectral, and radiometric resolutions, etc In the development

Earth-of automatic change-detection techniques, it is mandatory to take into account the ties of the sensors to properly extract information from the considered data

proper-Let us discuss the main characteristics of different kinds of sensors in detail (Table 5.1summarizes some advantages and disadvantages of different sensors for change-detectionapplications according to their characteristics)

Images acquired from passive sensors are obtained by measuring the land-coverreflectance on the basis of the energy emitted from the sun and reflected from theground1 Usually, the measured signal can be modeled as the desired reflectance (meas-ured as a radiance) altered from an additive Gaussian noise This noise model enablesrelatively easy processing of the signal when designing data analysis techniques Passivesensors can acquire two different kinds of images [panchromatic (PAN) images and MSimages] by defining different trade-offs between geometrical and spectral resolutionsaccording to the radiometric resolution of the adopted detectors PAN images are char-acterized by poor spectral resolution but very high geometrical resolution, whereas MSimages have medium geometrical resolution but high spectral resolution From theperspective of change detection, PAN images should be used when the expected size ofthe changed area is too small for adopting MS data For example, in the case of theanalysis of changes in urban areas, where detailed urban studies should be carried out,change detection in PAN images requires the definition of techniques capable of captur-ing the richness of information present both in the spatial-context relations betweenneighboring pixels and in the geometrical shapes of objects MS data should be used

1

Also, the emission of Earth affects the measurements in the infrared portion of the spectrum.

TABLE 5.1

Advantages and Disadvantages of Different Kinds of Sensors for Change-Detection Applications

Multispectral (passive) 3 Characterization of the spectral

3 Complexity of data preprocessing

3 Presence of multiplicative speckle noise

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when a medium geometrical resolution (i.e., 10–30 m) is sufficient for characterizing thesize of the changed areas and a detailed modeling of the spectral signature of the land-covers is necessary for identifying the change investigated Change-detection methods

in MS images should be able to properly exploit the available MS information in thechange detection process A critical problem related to the use of passive sensors in changedetection consists in the sensitivity of the image-acquisition phase to atmospheric condi-tions This problem has two possible effects: (1) atmospheric conditions may not beconducive to measure land-cover spectral signatures, which depends on the presence ofclouds; and (2) variations in illumination and atmospheric conditions at different acqui-sition times may be a potential source of errors, which should be taken into account toavoid the identification of false changes (or the missed detection of true changes).The working principle of active synthetic aperture radar (SAR) sensors is completelydifferent from that of the passive ones and allows overcoming some of the drawbacks thataffect optical images The signal measured by active sensors is the Earth backscattering of

an electromagnetic pulse emitted from the sensor itself SAR instruments acquire differentkinds of signals that result in different images: medium or high-resolution images, single-frequency or multi-frequency, and single-polarimetric or fully polarimetric images As foroptical data, the proper geometrical resolution should be chosen according to the size ofthe expected investigated changes The SAR signal has different geometrical resolutionsand a different penetration capability depending on the signal wavelength, which isusually included between band X and band P (i.e., between 2 and 100 cm) In otherwords, shorter wavelengths should be used for measuring vegetation changes andlonger and more penetrating wavelengths for studying changes that have occurred on orunder the terrain All the wavelengths adopted for SAR sensors neither suffer fromatmospheric and sunlight conditions nor from the presence of clouds; thus multi-temporalradar backscattering does not change with atmospheric conditions The main problemrelated to the use of active sensors is the coherent nature of the SAR signal, which results

in a multiplicative speckle noise that makes acquired data intrinsically complex to beanalyzed A proper handling of speckle requires both an intensive preprocessing phaseand the development of effective data analysis techniques

The different properties and statistical behaviors of signals acquired by active andpassive sensors require the definition of different change-detection techniques capable

of properly exploiting the specific data peculiarities

In the literature, many different techniques for change detection in images acquired bypassive sensors have been presented [1–8], and many applications of these techniqueshave been reported This is because of both the amount of information present in MSimages and the relative simplicity of data analysis, which results from the additive noisemodel adopted for MS data (the radiance of natural classes can be approximated with aGaussian distribution) Less attention has been devoted to change detection in SARimages This is explained by the intrinsic complexity of SAR data, which require both

an intensive preprocessing phase and the development of effective data analysis niques capable of dealing with multiplicative speckle noise Nonetheless, in the past fewyears the remote-sensing community has shown more interest in the use of SAR images inchange-detection problems, due to their independence from atmospheric conditions thatresults in excellent operational properties The recent technological developments insensors and satellites have resulted in the design of more sophisticated systems withincreased geometrical resolution Apart from the active or passive nature of the sensor,the very high geometrical resolution images acquired by these systems (e.g., PAN images)require the development of specific techniques capable of taking advantage of the rich-ness of the geometrical information they contain In particular, both the high correlation

tech-between neighboring pixels and the object shapes should be considered in the design ofdata analysis procedures.

In the above-mentioned context, two main challenging issues of particular interest inthe development of automatic change-detection techniques are: (1) the definition ofadvanced and effective techniques for change detection in SAR images, and (2) thedevelopment of proper methods for the detection of changes in very high geometricalresolution images A solution for these issues lies in the definition of multi-scale andmulti-resolution change-detection techniques, which can properly analyze the differentcomponents of the change signal at their optimal scale2 On the one hand, the multi-scaleanalysis allows one to better handle the noise present in medium-resolution SAR images,resulting in the possibility of obtaining accurate change-detection maps characterized by

a high spatial fidelity On the other hand, multi-scale approaches are intrinsically suitable

to exploit the information present in very high geometrical resolution images according

to effective modeling (at different resolution levels) of the different objects present atthe scene

According to the analysis mentioned above, after a brief survey on change detection and

on unsupervised change detection in SAR images, we present, in this chapter, anovel adaptive multi-scale change detection technique for multi-temporal SAR images.This technique exploits a proper scale-driven analysis to obtain a high sensitivity togeometrical features (i.e., details and borders of changed areas are well preserved) and ahigh robustness to noisy speckle components in homogeneous areas Although explicitlydeveloped and tested for change detection in medium-resolution SAR images, this tech-nique can be easily extended to the analysis of very high geometrical resolution images.The chapter is organized into five sections Section 5.2 defines the change-detectionproblem in multi-temporal remote-sensing images and focuses attention on unsupervisedtechniques for multi-temporal SAR images Section 5.3 presents a multi-scale approach tochange detection in multi-temporal SAR images recently developed by the authors.Section 5.4 gives an example of the application of the proposed multi-scale technique to

a real multi-temporal SAR data set and compares the effectiveness of the presentedmethod with those of standard single-scale change-detection techniques Finally, inSection 5.5, results are discussed and conclusions are drawn

Literature Survey

5.2.1 General Overview

A very important preliminary step in the development of a change-detection system,based on automatic or semi-automatic procedures, consists in the design of a properphase of data collection The phase of data collection aims at defining: (1) the kind ofsatellite to be used (on the basis of the repetition time and on the characteristics of thesensors mounted on-board), (2) the kind of sensor to be considered (on the basis ofthe desired properties of the images and of the system), (3) the end-user requirements(which are of basic importance for the development of a proper change-detection

2 It is worth noting that these kinds of approaches have been successfully exploited in image classification problems [9–12].

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technique), and (4) the kinds of available ancillary data (all the available information thatcan be used for constraining the change-detection procedure).

The outputs of the data-collection phase should be used for defining the automaticchange-detection technique In the literature, many different techniques have been pro-posed We can distinguish between two main categories: supervised and unsupervisedmethods [9,13]

When performing supervised change detection, in addition to the multi-temporalimages, multi-temporal ground-truth information is also needed This information isused for identifying, for each possible land-cover class, spectral signature samples forperforming supervised data classification and also for explicitly identifying what kinds ofland-cover transitions have taken place Three main general approaches to supervisedchange detection can be found in the literature: postclassification comparison, superviseddirect multi-data classification [13], and compound classification [14–16] Postclassificationcomparison computes the change-detection map by comparing the classification mapsobtained by classifying independently two multi-temporal remote-sensing images On theone hand, this procedure avoids data normalization aimed at reducing atmosphericconditions, sensor differences, etc between the two acquisitions; on the other hand, itcritically depends on the accuracies of the classification maps computed at the twoacquisition dates As postclassification comparison does not take into account thedependence existing between two images of the same area acquired at two different times,the global accuracy is close to the product of the accuracies yielded at the two times [13].Supervised direct multi-data classification [13] performs change detection by consideringeach possible transition (according to the available a priori information) as a class and bytraining a classifier to recognize the transitions Although this method exploits thetemporal correlation between images in the classification process, its major drawback

is that training pixels should be related to the same points on the ground at the two timesand should accurately represent the proportions of all the transitions in the whole images.Compound classification overcomes the drawbacks of supervised multi-date classifica-tion technique by removing the constraint that training pixels should be related to thesame area on the ground [14–16] In general, the approach based on supervised classifi-cation is more accurate and detailed than the unsupervised one; nevertheless, the latterapproach is often preferred in real-data applications This is due to the difficulties incollecting proper ground-truth information (necessary for supervised techniques), which

is a complex, time consuming, and expensive process (in many cases this process is notconsistent with the application constraints)

Unsupervised change-detection techniques are based on the comparison of the spectralreflectances of multi-temporal raw images and a subsequent analysis of the comparisonoutput In the literature, the most widely used unsupervised change-detection techniquesare based on a three-step procedure [13,17]: (1) preprocessing, (2) pixel-by-pixel compari-son of two raw images, and (3) image analysis and thresholding (Figure 5.1)

The aim of the preprocessing step is to make the two considered images as comparable aspossible In general, preprocessing operations include: co-registration, radiometric andgeometric corrections, and noise reduction From the practical point of view, co-registration

is a fundamental step as it allows obtaining a pair of images where corresponding pixelsare associated to the same position on the ground3 Radiometric corrections reducedifferences between the two acquisitions due to sunlight and atmospheric conditions.These procedures are applied to optical images, but they are not necessary for SAR

3 It is worth noting that usually it is not possible to obtain a perfect alignment between temporal images This may considerably affect the change-detection process [18] Consequently, if the amount of residual misregistration noise is significant, proper techniques aimed at reducing its effects should be used for change detection [1,4].

images (as SAR data are not affected by atmospheric conditions) Also noise reduction isperformed differently according to the kind of remote-sensing images considered Inoptical images common low-pass filters can be used, whereas in SAR images properdespeckling filters should be applied.

The comparison step aims at producing a further image where differences between thetwo acquisitions considered are highlighted Different mathematical operators (see Table5.2 for a summary) can be adopted for performing image comparison; this choice givesrise to different kinds of techniques [13,19–23] One of the most widely used operators isthe difference one The difference can be applied to: (1) a single spectral band (univariateimage differencing) [13,21–23], (2) multiple spectral bands (change vector analysis) [13,24],and (3) vegetation indices (vegetation index differencing) [13,19] or other linear (e.g., tasselledcap transformation [22]) or nonlinear combinations of spectral bands Another widely usedoperator is the ratio operator (image ratioing) [13], which can be successfully used in SARimage processing [17,25,26] A different approach is based on the use of the principalcomponent analysis (PCA) [13,20,23] PCA can be applied separately to the feature space

at single times or jointly to both images In the first case, comparison should be performed

in the transformed feature space before performing change detection; in the second case,the minor components of the transformed feature space contains change information

TABLE 5.2

Summary of the Most Widely Used Comparison Operators (fkis the considered feature at time tkthat can be: (1) a single spectral band Xk, (2) a vector of m spectral bands [Xk, ,Xkm], (3) avegetation index Vk, or (4) a vector of features [Pk, ,Pkm] obtained after PCA XDand XRare the images after comparison with the difference or ratio operators, respectively)

Technique Feature Vector f k at the Time t k Comparison Operator

SAR Image (date t2)

Preprocessing

SAR Image (date t2)

Preprocessing

Comparison

Analysis of the log-ratio image

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Performances of the above-mentioned techniques could be degraded by several factors(like differences in illumination at two dates, differences in atmospheric conditions,and in sensor calibration) that make a direct comparison between raw images acquired

at different times difficult These problems related to unsupervised change detectiondisappear when dealing with SAR images instead of optical data

Once image comparison is performed, the decision threshold can be selected eitherwith a manual trial-and-error procedure (according to the desired trade-off between falseand missed alarms) or with automatic techniques (e.g., by analyzing the statistical distri-bution of the image obtained after comparison, by fixing the desired false alarm prob-ability [27,28], or following a Bayesian minimum-error decision rule [17])

Since the remote-sensing community has devoted more attention to passive sensors [6–8]rather than active SAR sensors, in the following section we focus our attention on change-detection techniques for SAR data Although change-detection techniques based ondifferent architectures have been proposed for SAR images [29–37], we focus on themost widely used techniques, which are based on the three-step procedure describedabove (seeFigure 5.1)

5.2.2 Change Detection in SAR Images

Let us consider two co-registered intensity SAR images, X1 ¼ {X1(i,j), 1  i  I, 1  j  J}and X2 ¼ {X2(i,j), 1  i  I, 1  j  J}, of size I  J, acquired over the same area at differenttimes t1 and t2 Let V ¼ {vc, vu} be the set of classes associated with changed andunchanged pixels Let us assume that no ground-truth information is available forthe design of the change-detection algorithm, i.e., the statistical analysis of change andno-change classes should be performed only on the basis of the raw data The change-detection process aims at generating a change-detection map representing changes on theground between the two considered acquisition dates In other words, one of the possiblelabels in V should be assigned to each pixel (i,j) in the scene

5.2.2.1 Preprocessing

The first step for properly performing change detection based on direct image comparison

is image preprocessing This procedure aims at generating two images that are as similar

as possible unless in changed areas As SAR data are not corrupted by differences inatmospheric and sunlight conditions, preprocessing usually comprises three steps: (1)geometric correction, (2) co-registration, and (3) noise reduction The first procedure aims

at reducing distortions that are strictly related to the active nature of the SAR signal, aslayover, foreshortening, and shadowing due to ground topography The second step isvery important, as it allows aligning temporal images to ensure that correspondingpixels in the spatial domain are associated to the same geographical position on theground Co-registration in SAR images is usually carried out by maximizing cross-correlation between the multi-temporal images [38,39] The major drawback of thisprocess is the need for performing interpolation of backscattering values, which is atime-consuming process Finally, the last step is aimed at reducing the speckle noise.Many different techniques have been developed in the literature for reducing thespeckle One of the most attractive techniques for speckle reduction is multi-looking[25] This procedure, which is used for generating images with the same resolutionalong the azimuth and range directions, allows reduction of the effect of the coherentspeckle components However, a further filtering step is usually applied to the imagesfor making them suitable to the desired analysis Usually, adaptive despeckling proced-ures are applied Among these procedures we mention the following filtering techniques:

Frost [40], Lee [41], Kuan [42], Gamma Map [43,44], and Gamma WMAP [45] (i.e., theGamma MAP filter applied in the wavelet domain) As the description of despecklingfilters is outside the scope of this chapter, we refer the reader to the literature for moredetails.

5.2.2.2 Multi-Temporal Image Comparison

As described in Section 5.1, image pixel-by-pixel comparison can be performed by means

of different mathematical operators In general, the most widely used operators are thedifference and the ratio (or log-ratio) Depending on the selected operator, the imageresulting from the comparison presents different behaviors with respect to the change-detection problem and to the signal statistics To analyze this issue, let us consider twomulti-look intensity images It is possible to show that the measured backscattering ofeach image follows a Gamma distribution [25,26], that is,

p(Xk) ¼ L

LXL
1 k

where Xkis a random variable that represents the value of the pixels in image Xk(k ¼ 1, 2),

mkis the average intensity of a homogeneous region at time tk, and L is the equivalentnumber of looks (ENL) of the considered image Let us also assume that the intensityimages X1 and X2 are statistically independent This assumption, even if not entirelyrealistic, simplifies the analytical derivation of the pixel statistical distribution in theimage after comparison In the following, we analyze the effects of the use of thedifference and ratio (log-ratio) operators on the statistical distributions of the signal

(L
1 þ j)!

j!(L
1
j)! X

L
1
J D

t1 or t2) It is possible to show that the distribution variance of XD increases with thereference intensity level From a practical point of view, this leads to a higher change-detection error for changes that have occurred in high intensity regions of the image than

in low intensity regions Although in some applications the difference operator was usedwith SAR data [46], this behavior is an undesired effect that renders the differenceoperator intrinsically not suited to the statistics of SAR images

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where XRis a random variable that represents the values of the pixels in XRand
XRis thetrue change in the radar cross section The ratio operator shows two main advantagesover the difference operator The first one is that the ratio-image distribution dependsonly on the relative change
XR ¼ m2=m1in the average intensity between the two datesand not on a reference intensity level Thus changes are detected in the same manner both

in high- and low-intensity regions The second advantage is that the ratioing allowsreduction in common multiplicative error components (which are due to both multiplica-tive sensor calibration errors and the multiplicative effects of the interaction of the coherentsignal with the terrain geometry [25,47]), as far as these components are the same forimages acquired with the same geometry It is worth noting that, in the literature, theratio image is usually expressed in a logarithmic scale With this operation the distribu-tion of the two classes of interest (vc and vu) in the ratio image can be made moresymmetrical and the residual multiplicative speckle noise can be transformed to anadditive noise component [17] Thus the log-ratio operator is typically preferred whendealing with SAR images and change detection is performed analyzing the log-ratioimage XLRdefined as:

XLR ¼ log XR¼ logX2

Based on the above considerations, the ratio and log-ratio operators are more used thanthe difference one in SAR change-detection applications [17,26,29,47–49] It is worthnoting that for keeping the changed class on one side of the histogram of the ratio (orlog-ratio) image, a normalized ratio can be computed pixel-by-pixel, i.e.,

This operator allows all changed areas (independently of the increasing or decreasing value

of the backscattering coefficient) to play a similar role in the change-detection problem

5.2.2.3 Analysis of the Ratio and Log-Ratio Image

The most widely used approach to extract change information from the ratio and log-ratioimage is based on histogram thresholding4 In this context, the most difficult task is to

4

For simplicity, in the following, we will refer to the log-ratio image.

properly define the threshold value Typically, changed pixels are identified as those

pixels that modified their backscattering more than + x dB, where x is a real number

depending on the considered scene The value of x is fixed according to the kind of changeand the expected magnitude variation to obtain a desired probability of correct detection

Pd(which is the probability to be over the threshold if a change occurred) or false alarm

Pfa(which is the probability to be over the threshold if no change occurred) It has beenshown that the value of x can be analytically defined as a function of the true change inthe radar backscattering
XR and of the ENL L [25,26], once Pd and Pfa are fixed Thismeans that there exists a value of L such that the given constraints on Pd and Pfa aresatisfied The major drawback of this approach is that, as the desired change intensitydecreases and the detection probability increases, a ratio image with an even higher ENL

is required for constraint satisfaction This is due to the sensitivity of the ratio to thepresence of speckle; thus a complex preprocessing procedure is required for increasingthe ENL A similar approach is presented in Ref [46]; it identifies the decision threshold

on the basis of predefined values on the cumulative histogram of the difference image It

is worth noting that these approaches are not fully automatic and objective from anapplication point of view, as they depend on the user’s sensibility in constraint definitionwith respect to the considered kind of change

Recently, extending the work previously carried out for MS passive images [3,5,23,50], anovel Bayesian framework has been developed for performing automatic unsupervisedchange detection in the log-ratio image derived from SAR data The aim of this frame-work is to use the well-known Bayes decision theory in unsupervised problems forderiving decision thresholds that optimize the separation between changed and un-changed pixels The main problems to be solved for the application of the Bayes decisiontheory consist in the estimation of both the probability density functions p(XLR=vc) andp(XLR=vu) and the a-priori probabilities P(vc) and P(vu) of the classes vcand vu, respect-ively [51], without any ground-truth information (i.e., without any training set) Thestarting point of such kinds of methodologies is the hypothesis that the statistical distri-butions of pixels in the log-ratio image can be modeled as a mixture of two densitiesassociated with the classes of changed and unchanged pixels, i.e.,

p(XLR) ¼ p(XLR=vu)P(vu) þ p(XLR=vc)P(vc) (5:8)Under this hypothesis, two different approaches to estimate class statistical parametershave been proposed in the literature: (1) an implicit approach [17] and (2) an explicitapproach [49] The first approach derives the decision threshold according to an implicitand biased parametric estimation of the statistical model parameters, carried out on thebasis of simple cost functions In this case, the change-detection map is computed in aone-step procedure The second approach separates the image analysis in two steps: (1)estimation of the class statistical parameters and (2) definition of the decision thresholdbased on the estimated statistical parameters Both techniques require the selection of aproper statistical model for the distributions of the change and no-change classes In Ref.[17], it has been shown that the generalized Gaussian distribution is a flexible statisticalmodel that allows handling the complexity of the log-ratio images better than the morecommonly used Gaussian distribution Based on this consideration, in Refs [17] the well-known Kittler and Illingworth (KI) thresholding technique (which is an implicit estimationapproach) [52–55] was reformulated under the generalized Gaussian assumption for thestatistical distributions of classes Despite its simplicity, the KI technique produces satis-factory change-detection results The alternative approach, proposed in Refs [56–58], which

is based on a theoretically more precise explicit procedure for the estimation of statisticalparameters of classes, exploits the combined use of the expectation–maximization (EM)

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algorithm and of the Bayesian decision theory for producing the change-detection map InRef [49], the iterative EM algorithm (reformulated under the hypothesis of generalizedGaussian data distribution) was successfully applied to the analysis of the log-ratio image.Once the statistical parameters are computed, pixel-based or context-based decision rulescan be applied In the former group, we find the Bayes rule for minimum error, the Bayesrule for minimum cost, the Neyman–Pearson criterion, etc [3,5,24,59] In the latter group,

we find the contextual Bayes rule for minimum error formulated in the Markov randomfield (MRF) framework [24,60] In both cases (implicit and explicit parameter estimation),change-detection accuracy increases as the ENL increases This means that, depending onthe data and the application, an intensive despeckling phase may be required to achievegood change-detection accuracies [17] It is worth noting that Equation 5.8 assumes thatonly one kind of change5has occurred in the area under investigation between the twoacquisition dates However, techniques that can automatically identify the number ofchanges and the related threshold values have been recently proposed in the literature(both in the context of implicit [61] and explicit [60] approaches) We refer the reader to theliterature for greater details on these approaches

Depending on the kind of preprocessing applied to the multi-temporal images, thestandard thresholding techniques can achieve different trade-offs between the preserva-tion of detail and accuracy in the representation of homogeneous areas in change-detectionmaps In most of the applications, both properties need to be satisfied; however, they arecontrasting to each other On the one hand, high accuracy in homogeneous areas usuallyrequires an intensive despeckling phase; on the other hand, intensive despecklingdegrades the geometrical details in the SAR images This is due to both the smoothingeffects of the filter and the removal of the informative components of the speckle (which arerelated to the coherent properties of the SAR signal)

To address the above limitations of standard methods, in the next section we present anadaptive scale-driven approach to the analysis of the log-ratio image recently developed

by the authors

A Detail-Preserving Scale-Driven Technique

In this chapter we present a scale-driven approach to unsupervised change detection inSAR images, which is based on a multi-scale analysis of the log-ratio image Thisapproach can be suitably applied to medium- and high-resolution SAR images to producechange-detection maps characterized by high accuracy both in modeling details present

in the scene (e.g., border of changed areas) and in homogeneous regions Multi-temporalSAR images intrinsically contain different areas of changes in the spatial domain that can

be modeled at different spatial resolutions The identification of these areas with highaccuracy requires the development of proper change-detection techniques capable ofhandling information at different scales The rationale of the presented scale-drivenunsupervised change-detection method is to exploit only high-resolution levels in theanalysis of the expected edge (or detail) pixels and to use low-resolution levels also inthe processing of pixels in homogeneous areas, to improve both preservation of geo-metrical detail and accuracy in homogeneous areas in the final change-detection map In

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Or different kinds of changes that can be represented with a single generalized Gaussian distribution.

the following, we present the proposed multi-scale change-detection technique in thecontext of the analysis of multi-temporal SAR images However, we expect thatthe methodology has general validity and can also be applied successfully to changedetection in very high resolution optical and SAR images with small modifications in theimplementation procedures.

The presented scale-driven technique is based on three main steps: (1) multi-scaledecomposition of the log-ratio image, (2) adaptive selection of the reliable scales foreach pixel (i.e., the scales at which the considered pixel can be represented without borderdetails problems) according to an adaptive analysis of its local statistics, and (3) scale-driven combination of the selected scales (Figure 5.2) Scale-driven combination can beperformed by following three different strategies: (1) fusion at the decision level by an

‘‘optimal’’ scale selection, (2) fusion at the decision level of all reliable scales, and (3)fusion at the feature level of all reliable scales

The first step of the proposed method aims at building a multi-scale representation of thechange information in the considered test site The desired scale-dependent representationcan be obtained by applying different decomposition techniques to the data, such as Lapla-cian–Gaussian pyramid decomposition [62], wavelet transform [63,64], recursively up-sampled bicubic filter [65], etc Given the computational cost and the assumption of theadditive noise model required by the above techniques, we chose to apply the multi-resolution decomposition process to the log-ratio image XLR, instead of decomposingthe two original images X1and X2 separately At the same time this allows a reduction

in the computational cost and satisfies the additive noise model hypothesis The selection ofthe most appropriate multi-resolution technique is related to the statistical behaviors of XLRand will be discussed in the next section The multi-resolution decomposition step produces

a set of images XMS ¼ {XLR0 , , XLRn , , XLRN
1}, where the superscript n (n ¼ 0, 1, , N
1)indicates the resolution level As we consider a dyadic decomposition process, the scalecorresponding to each resolution level is given by 2n In our notation, the output atresolution level 0 corresponds to the original image, i.e., XLR0  XLR For n ranging from 0

to N
1, the obtained images are distinguished by different trade-offs between preservation

of spatial detail and speckle reduction In particular, images with a low value of n arestrongly affected by speckle, but they are characterized by a large amount of geometricaldetails, whereas images identified by a high value of n show significant speckle reductionand contain degraded geometrical details (high frequencies are smoothed out)

In the second step, local and global statistics are evaluated for each pixel at differentresolution levels At each level and for each spatial position, by comparing the local and

XLR

Multi-resolution decomposition

Adaptive scale identification

Change-detection map (M)

General scheme of the proposed approach.

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global statistical behaviors it is possible to identify adaptively whether the consideredscale is reliable for the analyzed pixel.

The selected scales are used to drive the last step, which consists of the generation of thechange-detection map according to a scale-driven fusion In this paper, three differentscale-driven combination strategies are proposed and investigated Two perform fusion

at the decision level, while the third performs it at the feature level Fusion at the decisionlevel can either be based on ‘‘optimal’’ scale selection or on the use of all reliable scales;fusion at the feature level is carried out by analyzing all reliable scales

5.3.1 Multi-Resolution Decomposition of the Log-Ratio Image

As mentioned in the previous section, our aim is to handle the information at differentscales (resolution levels) to improve both preservation of geometrical detail and accuracy

in homogeneous areas in the final change-detection map Images included in the set XMSare computed by adopting a multi-resolution decomposition process of the log-ratioimage XLR In the SAR literature [45,66–70], image multi-resolution representation hasbeen applied extensively to image de-noising Here, a decomposition based on the two-dimensional discrete stationary wavelet transform (2D-SWT) has been adopted, as in ourimage analysis framework it has a few advantages (as described in the following) over thestandard discrete wavelet transform (DWT) [71] As the log-ratio operation transforms theSAR signal multiplicative model into an additive noise model, SWT can be applied to XLRwithout any additional processing 2D-SWT applies appropriate level-dependent high-and low-pass filters with impulse response hn() and ln(), (n ¼ 0, 1, , N
1), respect-ively, to the considered signal at each resolution level A one-step wavelet decomposition

is based on both level-dependent high- and low-pass filtering, first along rows and thenalong columns to produce four different images at the next scale After each convolutionstep, unlike DWT, SWT avoids down-sampling the filtered signals Thus, according to thescheme in Figure 5.3, the image XLRis decomposed into four images of the same size asthe original In particular, decomposition produces: (1) a lower resolution version XLR1ofimage XLR, which is called the approximation sub-band, and contains low spatialfrequencies both in the horizontal and the vertical direction at resolution level 1; and (2)three high-frequency images XLRLH1, XLRHL1, and XLRHH1, which correspond to the horizontal,vertical, and diagonal detail sub-bands at resolution level 1, respectively Note that,superscripts LL, LH, HL, and HH specify the order in which high-(H) and low-(L) passfilters have been applied to obtain the considered sub-band

X

LH1LR

X

HL1LR

X

HH1 LR

Multi-resolution decomposition is obtained by recursively applying the describedprocedure to the approximation sub-band XLRn obtained at each scale 2n Thus, theoutputs at a generic resolution level n can be expressed analytically as follows:

by a factor 2 Thus, filter coefficients for computing sub-bands at resolution level nþ1 can

be obtained by applying a dilation operation to the filter coefficients used to computelevel n In particular, 2n
1 zeros are inserted between the filter coefficients used tocompute sub-bands at the lower resolution levels [71] This allows a reduction in thebandwidth of the filters by a factor two between subsequent resolution levels

Filter coefficients of the first decomposition step for n ¼ 0 depend on the selectedwavelet family and on the length of the chosen wavelet filter According to an analysis ofthe literature [68,72], we selected the Daubechies wavelet family and set the filter length to

8 The impulse response of Daubechies of order 4 low-pass filter prototype is given by thefollowing coefficients set: {0.230378, 0.714847, 0.630881,
0.0279838,
0.187035, 0.0308414,0.0328830,
0.0105974}

The finite impulse response of the high-pass filter for the decomposition step isobtained by satisfying the properties of the quadrature mirror filters This is done byreversing the order of the low-pass decomposition filter coefficients and by changing thesign of the even indexed coefficients [73]

To adopt the proposed multi-resolution fusion strategies, one should return to theoriginal image domain This is done by applying the two-dimensional inverse stationarywavelet transform (2D-ISWT) at each computed resolution level independently Forfurther detail about the stationary wavelet transform, the reader is referred to Ref [71]

To obtain the desired image set XMS (where each image contains information at adifferent scale), for each resolution level a one-step inverse stationary wavelet transform

is applied in the reconstruction phase as many times as in the decomposition phase Thereconstruction process can be performed by applying the 2D-ISWT either to the approxi-mation and thresholded detail sub-bands at the considered level (this is usually done inwavelet-based speckle filters [69]) or only to the approximation sub-bands at each reso-lution level6 Since the change-detection phase considers all the different levels, all thegeometrical detail is in XMS even when detail coefficients at a particular scale are

6 It is worth noting that the approximation sub-band contains low frequencies in both horizontal and vertical directions It represents the input image at a coarser scale and contains most informative components, whereas detail sub-bands contain information related to high frequencies (i.e., both geometrical detail information and noise components) each in a preferred direction According to this observation, it is easy to understand how proper thresholding of detail coefficients allows noise reduction [69].

© 2008 by Taylor & Francis Group, LLC