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International Journal of Remote Sensing

ISSN: 0143-1161 (Print) 1366-5901 (Online) Journal homepage: https://www.tandfonline.com/loi/tres20

Change detection using distance-based algorithmsbetween synthetic aperture radar polarimetricdecompositions

Amir Najafi, Mahdi Hasanlou & Vahid Akbari

To cite this article: Amir Najafi, Mahdi Hasanlou & Vahid Akbari (2019): Change detectionusing distance-based algorithms between synthetic aperture radar polarimetric decompositions,International Journal of Remote Sensing

To link to this article: https://doi.org/10.1080/01431161.2019.1587202

Published online: 07 Mar 2019.

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Change detection using distance-based algorithms betweensynthetic aperture radar polarimetric decompositionsAmir Najafi a, Mahdi Hasanlou a and Vahid Akbari b

aSchool of Surveying and Geospatial Engineering, College of Engineering, University of Tehran, Tehran,Iran; bDepartment of Physics and Technology, UiT The Arctic University of Norway, Tromsø, Norway

ABSTRACTThe present study introduces distance based change detection (CD)algorithms in polarimetric synthetic aperture radar (PolSAR) data.PolSAR images, due to interactions between electromagnetic wavesand target and because of the high spatial resolution, can be usedto study changes in the Earth’s surface. The purpose of this paper isto use features extracted from the fully-polarimetry imaging radarthat involved Yamaguchi four-component and H/A/α decomposi-tion based on the distance between the vectors of features for CD.We first extract features from polarimetric decompositions of multi-looked covariance (or coherency) matrix data. We then use twowell-known distance measures namely Canberra and Euclideandistances for measuring the similarity between the vectors of polari-metric decompositions at different times. Assessment of incorpo-rated methods is performed using different criteria, such as overallaccuracy, area under the receiver operating characteristic curve,and false alarms rate. The results of the experiments show thatCanberra distance has better performance with high overall accu-racy and low false alarm rate than Euclidean distance and othercompared algorithms to detect changes.

ARTICLE HISTORYReceived 16 June 2018Accepted 30 December 2018

1. Introduction

Change detection (CD) in remote sensing is processed to analyze and identify changes inthe same geographic area at different times (Hasanlou and Seydi 2018a; Radke et al.2005). Synthetic aperture radar (SAR) sensors, operating independently of weatherconditions and daylight, are widely used for CD (Hu and Ban 2014; Akbari et al. 2016).In addition, these images include an inherent speckle noise that must be suppressedbefore any further processing (Gong et al. 2016). Polarimetric synthetic aperture radar(PolSAR) data are one of the important generations of remotely sensed images that areused in various applications. These images have the combination of the backscatteringlinear receiver and transmit polarization in four channels that involved: HH (Horizontaltransmit and Horizontal receive), HV (Horizontal transmit and Vertical receive), VH(Vertical transmit and Horizontal receive), and VV (Vertical transmit and Vertical receive),from which different scattering mechanisms (surface, double-bounce, and volume

CONTACT Mahdi Hasanlou hasanlou@ut.ac.ir School of Surveying and Geospatial Engineering, College ofEngineering, University of Tehran, 11155-4563, 1439957131, Tehran, Iran

INTERNATIONAL JOURNAL OF REMOTE SENSINGhttps://doi.org/10.1080/01431161.2019.1587202

© 2019 Informa UK Limited, trading as Taylor & Francis Group

scattering) can be extracted (Akbari et al. 2016). By investigating this characteristic,various information can be extracted from the physical nature of the land covercharacteristics in different polarizations (Lee and Pottier 2009). In this regard, incorpor-ating decomposition of PolSAR images may be beneficial and improve the results of theCD (Huang et al. 2017). CD in remote sensing is generally performed in three main steps:(1) preprocessing images including co-registration and speckle noise reduction; (2)computing a difference image (DI); and (3) making a decision based on analysis of thedifference image computed in the step two and preparing change and no-change classes(Akbari 2013).

Many researches have demonstrated the potential of SAR images in CD. The purposeof this paper is to use the produced and extracted features from PolSAR and then todetect change areas by combing some distance metrics and producing some of thefeatures. Hence, the literature on CD with PolSAR data is sparser. Baroni et al. used thePrincipal Component Analysis (PCA) on HH, VV and HV channels of multi-temporalPolSAR collected during the National Aeronautics and Space Administration (NASA)Multi-Sensor Aircraft Campaign (MAC). This algorithm takes a lot of time to implement(Baronti et al. 1994). Yakoub Bazi et al. presented a novel automatic CD approach thatused the single-channel single-polarization SAR images. To this end, the authors usedthe Log-Ratio operator for comparison between multi-temporal images and made thechange map based on the modified Kittler–Illingworth (K&I) (Kittler and Illingworth 1986)threshold and generalized Gaussian model for modeling the distributions of changedand no-changed classes (Bazi, Bruzzone, and Melgani 2005). Marino et al. developeda target detector based on Polarimetric Fork (PF) of the single targets (Huynen para-meters or α angle). The detector was implemented for multiple reflections (odd andeven bounces) and oriented dipoles. The detector was also compared witha Polarimetric Whitening Filter (PWF). The presented algorithm developed suitablevalidation and performance for embedded targets (Marino, Cloude, and Woodhouse2010). Tang et al. extracted the Yamaguchi four-component decomposition from quadpolarimetric RADARSAT-2 images and generated the change map by the Log-Ratio ofdouble bounce features from this dataset at different times. The K&I algorithm is finallyused to separate change and no-change classes (Tang et al. 2012). Liu et al. incorporatedsegmentation of images with the K&I minimum-error thresholding algorithm and dis-tance measurement for measuring the distance between texture features at differenttimes and finally detected changes in PolSAR images (Liu et al. 2012). Marino et al.presented a new polarimetric change detector based on the partial targets in the firstacquisition as a reference target and for detecting the second acquisition. Angle differ-ence was defined as thresholding, which was achieved from the eigenvector model forthe coherency matrix. This detector was implemented on a variety of datasets. Thisdetector was compared the Maximum Likelihood (ML) ratio. The results of this detectorare suitable because, in the presented detector, the overall amplitude of the back-scattering is neglected (Marino, Cloude, and Lopez-Sanchez 2013). Quan et al. incorpo-rated the Freeman-Durden decomposition to extract the polarization scatteringcharacteristics of different objects. Then, the refined Lee filter was applied to reducethe speckle noise. Finally, an improved distance measurement of CD was proposed formulti-temporal PolSAR data (Quan et al. 2015). Qi et al. used the three-componentalgorithms that include decomposition of PolSAR images in multi-temporal format and

2 A. NAJAFI ET AL.

hierarchically segmented these images to define land parcels. They finally appliedchange vector analysis on a coherency matrix to detect the changed pixels and usedpost classification procedures on these images to identify land cover types and changemap (Qi et al. 2015). Ratha et al. produced change maps based on the measurement ofthe geodesic distance using the observed Kennaugh matrix of the span and intensityfeatures from the decomposition of PolSAR images (Ratha et al. 2017). As shown in theliterature, current algorithms for CD with PolSAR data take a lot of time to be imple-mented. Moreover, in the literature, the researchers used the single feature to CD but inthis paper, we used the combination of features for CD (combination of Yamaguchi four-component decomposition and H/A/α decomposition as the cube form of features).

The main objective of this paper is to apply two well-known distance measures, namelyCanberra distance (CAD) and Euclidean distance (ED), as metric test statistics to measure thedistance between polarimetric target decompositions (PTDs). The distancemeasures are usedto contrast two vectors of polarimetric decompositions at different times and produce a scalarvalue, to which a threshold can be applied. In fact, we use the different PTD methods(Yamaguchi four-component and H/A/α decompositions) as input for measuring the similarityusing the CAD and ED methods. In other words, the significance of the proposed methodrelated to this integration. We compare the CD results obtained from our proposed methodwith the Hotelling-Lawley Trace (HLT) proposed by Akbari et al. (2016). We test the perfor-mance of distance measures for CD based on polarimetric decompositions extracted frommulti-looked airborne Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR) images.

2. Theory

This section consists of three parts. The first part explains the structure of PolSAR data.The second part describes the theory of polarimetric target decomposition, and the thirdpart is a review of the Otsu image segmentation algorithm.

2.1. Polarimetric SAR

A fully-polarimetric imaging radar measures the amplitude and phase of backscatteredsignals that consist of four linear receiver and transmit polarizations (HH, HV, VH, andVV). These signals are used to form a 2 × 2 complex scattering matrix at each resolutioncell on the ground (Lee and Pottier 2009). The measured PolSAR data can be mathema-tically written as a scattering matrix Equation (1):

S ¼ Shh ShvSvh Svv

� �(1)

where Shv is a complex-valued measurement. Based on two important basic sets,lexicographic and Pauli, the following scattering vectors, kl and kp, in each case areobtained under the assumption of the reciprocity theorem, Shv ¼ Svh for a monostaticobservation Equation (2):

kl ¼Shhffiffiffi2

pShv

Svv

24

35 ; kp ¼ 1ffiffiffi

2p

Shhþ SvvShh� Svv2 Svh

24

35 (2)

INTERNATIONAL JOURNAL OF REMOTE SENSING 3

Shv is a coherent average of the HV and VH channel measurements andffiffiffi2

parises from

the requirement to conserve the total scattered power, after coherent averaging of thecross polarization channels (Lee et al. 1998). The polarimetric covariance and coherencymatrix can be formed by computing the spatial average of the outer-product of thelexicographic and Pauli scattering vectors, respectively, Equation (3):

C ¼ hkl klHi (3)

T¼ hkp kpHi (4)

Here, (⋅)H means the Hermitian transposition operator and h�i denotes a spatial ensem-ble average. Coherency or covariance matrices are used as input to polarimetric targetdecompositions (Lee and Pottier 2009).

2.2. Polarimetric SAR decompositions

PTD is an advanced technique for extractingmore detailed and quantitative physical informa-tion to characterize the scattering mechanism of different ground targets. Many PTD techni-ques (Cloude and Pottier 1997; Freeman and Durden 1998; Touzi 2007; Yamaguchi et al. 2005)have been proposed for the interpretation of target scattering mechanisms using the coher-ency and covariance matrices. In this study, the two most well-known polarimetric decom-positions, namely Yamaguchi four-component and H/A/α decompositions, are used toinvestigate the effect of different decomposition features for the PolSAR CD.

Yamaguchi et al. proposed an extension of the four-component model that involvesnon-reflection symmetric cases (Yamaguchi et al. 2005). This approach consists of fourcomponents: helix, surface, double bounce, and volume scattering. The helix scatteringincludes terrain reflection asymmetry that can be introduced by man-made structures orurban feature orientation. The covariance matrix (CY ) of Yamaguchi is expressed as thecombination of these four components in Equation (5):

hCYi ¼ Ps Cs þ Pd Cdþ Pv Cv þ Ph Ch (5)

where Ps, Pd, Pv and Ph are the coefficients of single, double bounce, volume and helixscattering, respectively, and Cs, Cd, Cv and Ch represent the covariance matrices of thesefour scattering mechanisms.

The H/A/α decomposition is based on eigenvectors and eigenvalues of the coherencymatrix decomposition (Cloude and Pottier 1997). Eigenvector analysis provides informationabout different types of scattering processes, while eigenvalue analysis provides informationabout their relative magnitudes. Entropy (H) determines the degree of randomness of thedistribution and is defined in the range of [0,1], where H = 0 indicates a single scatteringmechanism and H = 1 indicates the random target scattering process and represents thecompletely depolarizing system. Anisotropy (A) parameter is an entropy complement, and itsvalue indicates the relative importance of the second and third values. It is a useful parameterto improve the ability to detect various types of dispersion process. The alpha angle (α) is themain parameter for identifying the dominant scattering mechanism. The value can be easilyassociated with the physics behind the scattering process involved. The range of this para-meter is between [0°,90°]; α = 0° denotes odd bounce scattering, the values of 45° refer to

4 A. NAJAFI ET AL.

dipole scattering, and the α = 90°corresponds to double-bounce scattering (Lee and Pottier2009).

Equation (4), based on the eigenvectors of the coherency matrix, is written as follows,Equation (6) where U is the matrix of eigenvectors (note that U�1 ¼ UH for Hermitiansymmetric matrices) and Λ is a diagonal matrix of the corresponding eigenvalues. Theeigenvectors u share the same polarimetric bases as the input Pauli feature vectors. TheH/A/α decomposition computes the following quantities from the set of eigenvectorsand eigenvalues (the eigenvalues are assumed to be in the order of λ1 � λ2 � λ3 � 0),Equations (6)–(10):

T ¼ UΛU�1 ¼X3i¼ 1

λiuiuH

i (6)

Pi ¼ λiP3i¼ 1

λi

0 � Pi � 1 (7)

H ¼ �X3i¼ 1

Pi log3 Pi 0 � H � 1 (8)

A ¼ λ2 � λ3λ2 þ λ3

0 � A � 1 (9)

α ¼X3i¼ 1

Pi cos�1ð uið1Þj jÞ 0� � α � 90� (10)

2.3. The otsu algorithm

The Otsu algorithm is a thresholding method for automatic image clustering. The ideabehind this approach is that the threshold value determines the weight of the variancewithin the minimum class value. The variance within the class is the variance of the totalweight of each defined cluster according to Equation (11), (Otsu 1979):

σ2whitinð2Þ ¼ q1ðtÞ σ21ðtÞ þ q2 σ22ðtÞ (11)

where σ21ðtÞ is the variance and q1ðtÞis the weight of each cluster defined based onEquation (12):

q1ðtÞ ¼XI

i¼ tþ 1

PðiÞ (12)

wherePðiÞis the probability of belonging to the class and σ21ðtÞ is defined asEquation (14):

σ21ðtÞ ¼Xt

i¼ 1

ði � μ1ðtÞÞ½ �2 PðiÞq1ðtÞ (13)

INTERNATIONAL JOURNAL OF REMOTE SENSING 5

μ1ðtÞ ¼XI

i¼ tþ 1

iPðiÞq1ðtÞ (14)

Let the gray level of a given image be divided into I values and the average gray level is alsodivided into the same I values. Finally, the variance within the class is calculated asEquation (15):

σ2between ¼ σ2 � σ2withinðtÞ (15)

Generally, the Otsu algorithm uses the following steps to select the threshold: (1) calculatinghistograms and probabilities, (2) calculating the initial value of the average and weights, (3)moving the threshold value to all possible probabilities, (4) updating average and weight, (5)calculating the variance within the class, and (6) finding the threshold with the most possiblevariance. This algorithm is widely used because it is simple, effective and adaptive. Thealgorithm has less computational time and maintains reasonable thresholding results(Hasanlou and Seyed Teymoor 2018b; Vala, Hetal, and Baxi 2013).

3. Change detection based on distance measures between polarimetricdecompositions

In order to apply CD to PolSAR data, we need to use appropriate distance measures. Weintend to measure the pairwise distance between polarimetric decompositions of twodatasets acquired at different times. Considering that the study is carried out on urbanareas, therefore, Yamaguchi four-component and H/A/α decompositions are used. Theinputs are two 7 dimensional vectors containing the elements of PTD, i.e. Yamaguchiand H/A/α decompositions, at two different times, as Equations (16)–(17):

X ¼ ½PYs ; PYd; PYv ; PYh;H;A; α� (16)

Y ¼ ½PYs ; PYd; PYv ; PYh;H;A; α� (17)

where X is the input features at the time ta and Y is the input features at the time tb. Eachelement of the X and Y vectors extracts features from the two subsets of the study areas. Thecorrelation coefficient of each element is calculated and many of these elements have theleast dependency on each other. According to the correlation coefficient, the dependencybetween different elements is less than one and therefore there is no redundancy. Figure 1shows the correlation between the input features. Based on this figure, the used features inthe 7 dimensional vectors for CD have minimum correlation and non-redundancy.

It is desirable that all the conditions of a general metric apply, so that

(1) the distance must be non-negative, i.e. the distance is in the range of [0,1],(2) the distance between two vectors is symmetric so that the distance between

X and Y is equal to the distance between Y and X,(3) If X = Y, thus, the distance is equal to zero.

Two distance measures that meet these requirements are CAD and ED (or L2 metric).CAD uses a numerical measure of the distance between pairs of points in a vector space,

6 A. NAJAFI ET AL.

which was first introduced by Lance and Williams (1966). It is a weighted version of L1(Manhattan) distance (Agarwal, Burgess, and Crammer 2009). CAD between the vectorsX and Y in an n-dimensional real vector space are given as Equation (18):

CADðX;YÞ ¼Xni¼ 1

xi � yij jxij j þ yij j (18)

where X and Y are the corresponding vectors xi and yi are the numerical values of thepixels, |⋅| is the symbol of the absolute value and n is the number of input features.Another choice of distance-based algorithms between two temporal vectors of polari-metric decompositions is ED which is defined as the square root of the sum of thesquared differences between the corresponding vectors (Beldarrain 2006). It is definedas Equation (19):

EDðX;YÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXni¼ 1

ðxi � yiÞ2s

(19)

The general block diagram of the proposed CD approach is shown in Figure 2, which is madeup of four main steps. (1) pre-processing: the matrix data of PolSAR datasets are co-registeredand speckle-filtered with the refined Lee filter. This filter uses an edge-aligned window andapplies local statistics in order to better preserve edge and spatial resolution as well as detailfeatures. This filter is adaptive and preserves the scattering mechanism of each pixel; it is alsovery fast and simple and has no blurry image (Lee and Pottier 2009); (2) feature extraction: PTDfeatures are extracted from the matrix data and normalized between [0,1] for each data, andalso the extracted features are formed in vector form Equations (16)–(17). We use the Cmatrix

Figure 1. Correlation Coefficient (CC) between input features.

INTERNATIONAL JOURNAL OF REMOTE SENSING 7

for Yamaguchi four-component decomposition and the Tmatrix for H/A/α decomposition; (3)computing distance-based methods: the distance-based algorithms described above areapplied to the vector of extracted features from bi-temporal data to create DI; (4) makinga decision based on the analysis of the distance-based methods computed in step three totest the hypotheses of change versus no-change. Several algorithms have been proposed inthe literature to determine the threshold in a completely unsupervised manner. In this paper,we choose to apply the Otsu algorithm (Otsu 1979) on DI.

4. The study area and datasets

The study area of this dataset is located in the San Francisco city. Two L-band (witha wavelength of 23.84 cm and a frequency of 1.26 GHz) fully-polarimetric images are acquiredby the Jet Propulsion Laboratory/National Aeronautics and Space Administration UAVSAR on18 September 2009, and 11 May 2015. This airborne polarimetric repeat-pass interferometricradar system has obtained the data with a spatial resolution of 1.66m in the range and 1.00min the azimuth direction. Incidence angles range from 25° to 65°. In this paper, two pairs ofsubset images are selected as the areas of interest from the full scene for the performanceevaluation of the proposed CD. Figure 3 (a)–(b) and (c)–(d) show the RGB (Red: |HH – VV|;Green: 2|HV|; Blue: |HH + VV|) Pauli images of the two subsets of the PolSAR scene. The firstand second subsets are 200 × 200 and 100 × 100, respectively. Figure 3(e,f) show the referencetest maps associated with these subsets, made for the quantitative analysis of the CD results.The reference test maps of the two subsets are generated by Google earth images and falsecolor of radar images (Pauli images) at a different time. In fact, the regions labeled as change

Figure 2. Flowchart of utilized methodology for change detection.

8 A. NAJAFI ET AL.

and no-change in the reference test maps are extracted manually using these images and thecomparison method. These two data sets can be found online in http://rslab.ut.ac.ir.

5. Experiments results

To evaluate the capability of the proposed change detectors, two cases are investigated. Thefirst case shortly named C1, utilizes the CD methods without speckle filtering. The secondcase shortly named C2, utilizes CD methods filtered with the refined Lee filter. These twocases are compared in terms of CD performance of the CAD, ED and HLT algorithms.

Figure 3. Experimental subsets over an urban area in San Francisco, United States of America (USA).(a) and (c) Pauli RGB composite of quad-pol UAVSAR images captured on 18 September 2009. (b)and (d) Pauli RGB composite of quad-pol UAVSAR images captured on 11 May 2015 multi-lookedwith 36 looks. (e) and (f) Reference change map; color legend: white, change; black, no-change.

INTERNATIONAL JOURNAL OF REMOTE SENSING 9

Figure 4 shows the CD results of the proposed algorithms for both subsets under twodifferent cases including filtered with the refined Lee (C1) and without filtering (C2). Thechange maps of the two subsets in the two cases for the CAD algorithm are shown inFigure 4(a)–(b) and (g)–(h). The change map outputs of the CAD algorithm are similar tothe reference change map of two subsets. Further, the change maps of the ED algorithmare shown in Figure 4(c)–(d) and (i)–(j) for the two subsets in the designed cases. Table 1provides a quantitative evaluation of the distance-based algorithms which contain theoverall accuracy (OA), false alarm rate (FAR), and area under the curve (AUC) of the ROC(Metz 1978). Table 1 reports the values for both subsets under the two cases mentionedabove. By comparing the quantitative results in Table 1, we can conclude that both theCAD and ED methods work slightly better when data are filtered with the refined Lee

Figure 4. Results of CAD, ED and HLT algorithms. (a) CAD on subset 1, C1. (b) CAD on subset 1, C2. (c) ED onsubset 1, C1. (d) ED on subset 1, C2. (e) HLT on subset 1, C1. (f) HLT on subset 1, C2. (g) CAD on subset 2, C1.(h) CAD on subset 2, C2. (i) ED on subset 1, C1. (j) ED on subset 2, C2. (k) HLT on subset 2, C1. and (l) HLT onsubset 2, C2.

10 A. NAJAFI ET AL.

filter. Moreover, both methods are better than the HLT method. It means that higher OA,lower FAR, and larger AUC is achieved for the filtered matrix data. By comparing the twodistances, the CAD algorithm obtains higher detection rates, lower FARs, and largerAUCs. To further evaluate the performance of the change detectors, the ROC curves ofthe two tests are presented in Figure 5 which presents the hit (detection) rate asa function of FAR. The ROC plots of the CAD detector (red line) is above that of theED detector (blue line) and HLT detector (green line), indicating better detectionperformance obtained from ED for both subsets. Figure 5(b,d) show again how theROC curves are improved when filtering the matrix data. For comparing the proposed

Table 1. Results of CAD, ED and HLT algorithms for C1: without speckle filtering, and C2: filtered withthe Refined Lee filter.

Subset 1 Subset 2

Algorithm Scenario OA (%) FAR (%) AUC OA (%) FAR (%) AUC

CAD C1 95.81 4.03 0.95 95.63 5.71 0.96C2 96.37 3.19 0.97 97.52 2.62 0.97

ED C1 94.90 5.85 0.90 93.24 6.33 0.92C2 96.05 4.95 0.93 95.19 5.54 0.95

HLT C1 92.56 7.34 0.86 92.69 7.26 0.83C2 93.65 6.12 0.90 93.55 5.98 0.88

Figure 5. ROC curve of both subsets under two different cases. (a) Subset 1 for C1. (b) Subset 1 forC2. (c) Subset 2 for C1. (d) Subset 2 for C2.

INTERNATIONAL JOURNAL OF REMOTE SENSING 11

algorithm with the HLT method based on Table 1, the numerical results of this algorithmare lower than of the proposed distance algorithms. This algorithm has higher FAR butlowers OA and AUC than the proposed algorithms. Moreover, we compare the changemaps of this algorithm in Figure 4(e)–(f) and (k)–(l) with the proposed distance algo-rithms. This algorithm does not show change and no-change regions the same as theproposed algorithms. The ROC curve of this algorithm (green line) is plotted in Figure 5.Comparing the ROC curves of this algorithm and the proposed distance algorithm showsthat the HLT algorithms have high FAR but low AUC.

6. Conclusion

This paper implements and evaluates distance-based methods between polarimetricdecompositions using bi-temporal polarimetric UAVSAR images. In this paper, thetwo most popular PTD features are first extracted for each speckle-filtered polari-metric matrix data. These features include Yamaguchi four-component and H/A/αdecompositions extracted from covariance and coherency matrix data, respectively,and normalized between [0,1] for each data. The extracted features are formed invector mode based Equations (16)–(17). Then, two well-known distance-based algo-rithms, CAD and ED, are used to measure the similarity between two vectors ofpolarimetric decompositions at different times. CAD uses a numerical measure of thedistance between pairs of points in a vector space. It is a weighted version of L1(Manhattan) distance. ED (or L2 metric) is defined as the square root of the sum ofthe squared differences between the corresponding vectors. Moreover, as a part ofthis study, we compare the results of the proposed distance algorithms with therecently published HLT PolSAR change detector. According to numerical and visualresults of the distance based algorithms, the proposed algorithms have betterperformances for CD. The CAD algorithm produces slightly higher OA, lower FAR,and larger AUC than the other algorithms. These algorithms are more suitable for CDthan the HLT algorithm because of high FAR and low AUC. The proposed algorithmsare very fast and simple for SAR CD applications.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Amir Najafi http://orcid.org/0000-0003-1609-1835Mahdi Hasanlou http://orcid.org/0000-0002-7254-4475Vahid Akbari http://orcid.org/0000-0002-9621-8180

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