ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 1–12

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ISPRS Journal of Photogrammetry and Remote Sensing

journal homepage: www.elsevier .com/ locate/ isprs jprs

A spectral gradient difference based approach for land cover changedetection

0924-2716/$ - see front matter � 2013 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS) Published by Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.isprsjprs.2013.07.009

⇑ Corresponding author at: School of Remote Sensing and Information Engineer-ing, Wuhan University, Wuhan 430079, China. Tel.: +86 13716871324.

E-mail address: lumiao0616@163.com (M. Lu).

Jun Chen a,d, Miao Lu b,a,⇑, Xuehong Chen c, Jin Chen c, Lijun Chen a

a National Geomatics Centre of China, 28 Lianhuachi West Road, Beijing 100830, Chinab School of Remote Sensing and Information Engineering, Wuhan University, Wuhan 430079, Chinac State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, Beijing 100875, Chinad School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China

a r t i c l e i n f o

Article history:Received 4 January 2013Received in revised form 25 May 2013Accepted 31 July 2013

Keywords:Land coverChange detectionSpectral gradient differenceSpectral shapeSGD chain model

a b s t r a c t

Change detection with remotely sensed imagery plays an important role in land cover mapping, processanalysis and dynamic information services. Euclidean distance, correlation and other mathematic metricsbetween spectral curves have been used to calculate change magnitude in most change detection meth-ods. However, many pseudo changes would also be detected because of inter-class spectral variance,which remains a significant challenge for operational remote sensing applications. In general, differentland cover types have their own spectral curves characterized by typical spectral values and shapes.These spectral values are widely used for designing change detection algorithms. However, the shapeof spectral curves has not yet been fully considered. This paper proposes to use spectral gradientdifference (SGD) to quantitatively describe the spectral shapes and the differences in shape betweentwo spectra. Change magnitude calculated in the new spectral gradient space is used to detect thechange/no-change areas. Then, a chain model is employed to represent the SGD pattern both qualitativelyand quantitatively. Finally, the land cover change types are determined by pattern matching with theknowledgebase of reference SGD patterns. The effectiveness of this SGD-based change detectionapproach was verified by a simulation experiment and a case study of Landsat data. The results indicatedthat the SGD-based approach was superior to the traditional methods.� 2013 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS) Published by Elsevier

B.V. All rights reserved.

1. Introduction

Change detection with remote sensed imagery is the process ofidentifying the changed areas and changed types of land cover/landuse using the remotely sensed imagery acquired at different times(Singh, 1989; Coppin et al., 2004; Chen et al., 2003). As timely andaccurate change information of land cover/land use provides astrong support for natural resource management and dynamicinformation services (Xian et al., 2009; Bartholomé and Belward,2005; Lambina et al., 2001; Li, 2010), a number of change detectionmethods have been developed in recent decades (Lu et al., 2004;Coppin et al., 2004; Castellana et al., 2007; Liu et al., 2006; Nielsenet al., 1998). These techniques could be categorized into post-clas-sification methods (Liu et al., 2008; Chen et al., 2011; Bruzzoneet al., 2004) and direct radiometric comparison methods (Singh,1989; Bruzzone, 2000; Chen et al., 2003). Methods such as changevector analysis (CVA), image difference, spectral angle difference

(SAD) and image correlation are optionally unsupervised, morestraightforward and operational (Lu et al., 2004); therefore theyare more commonly used than the former. However, it must benoted that radiometric comparison methods are affected by inter-ference factors, such as the differences in atmospheric conditions,sun angle and inter-class variance (Radke et al., 2005). As a result,many pseudo changes may appear. For example, the spectral vari-ation induced by changes in soil moisture, water turbidity andbuilding depreciation at different collection times could lead tomany detection errors (Chen et al., 2003, 2011). Therefore, themain challenge in change detection is to determine how to pre-serve the real changes while eliminating the pseudo ones.

Even with the number of change detection methods, it appearsthat none of them is sufficiently universal to eliminate variouspseudo changes (Hégarat-Mascle and Seltz, 2004). In general, eachland cover type has a typical spectral curve characterized by itsown spectral values and shape (Tso and Mather, 2001). Previouschange detection methods, including CVA and image difference,detect the changes based on the variations of spectral values,which could lead to many pseudo changes, such as differences insoil moisture, building depreciation, and so on. Fig. 1(a) shows

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Fig. 1. Change magnitude in spectral space between t1 (June, 29th, 2000) and t2 (June, 29th, 2000) which may cause pseudo changes. (a) Spectral difference caused bymoisture; (b) spectral difference caused by turbidity; (c) spectral difference caused by change from soil to water; (d) change magnitude calculated with spectral distance; (e)change magnitude with spectral correlation.

2 J. Chen et al. / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 1–12

the spectral curves of soil collected from a Landsat TM image inJune, 29th, 2000 (t1) and a Landsat ETM + image in June, 29th,2000 (t2), and the spectral curves of water over the same time per-iod is shown in Fig. 1(b). Spectral curves of soil at t1 and water at t2are compared in Fig. 1(c). When change magnitude is calculatedbased on spectral values, the spectral difference of soil whichmay be caused by moisture variation is even greater than thatcaused by the real change from soil to water, as shown inFig. 1(d). This might lead to pseudo change detection and the realland cover type change may not be distinguished correctly. Someother change detection methods, such as SAD and correlation,compare the differences in spectral shape instead of spectral value.These methods can effectively compress the brightness variance;however, they are too sensitive for the spectral shape change ofdark objects such as water. As shown in Fig. 1(e), there is a verylow correlation between the spectra of water with a variance inturbidity, which is even lower than the correlation between waterand soil. Therefore, the water with varying turbidity is easy to mis-takenly interpret as a changed area.

In summary, there are different drawbacks associated withdifferent change detection methods. In light of the abovemen-tioned drawbacks, we propose to use the spectral gradient andits differences for detecting land cover change. The spectralgradient can describe quantitatively the spectral shape of a givenland cover class and the spectral gradient difference (SGD)between two land cover classes may indicate possible a change.It is expected to compress the pseudo change signal more effec-tively compared to traditional change detection methods.Change/no-change areas are then determined by the changemagnitude calculated in a new spectral gradient space, and landcover change types are identified by SGD pattern matching witha knowledgebase described by the SGD chain model. The rest ofthe paper is organized as follows. In Section 2, the proposedmethod is described in detail. In Section 3, simulation experimentand a case study were conducted to validate our proposed meth-od. Finally, the conclusion and future researches are presented inSection 4.

2. Methodology

The basic idea of the SGD based approach is to conduct changedetection in spectral gradient space. Fig. 2 gives the framework ofthis approach with three major steps. First, a spectral gradient isintroduced to illustrate the shape of a spectral curve, and thechange information is projected from the original spectral spaceto gradient space. Secondly, the difference of the spectral gradientbetween the two spectral curves is calculated as the change mag-nitude and is used to determine change areas with a certainthreshold. Thirdly, a chain model is developed to represent theknowledgebase of SGD patterns of typical change types on the ba-sis of the reference spectra, and then land cover change type isidentified by pattern matching.

2.1. Definition of spectral gradient

The spectral gradient method has been used to describe thespectral shape in spectral matching and feature extraction ofhyperspectral data (Robila and Gershman, 2005; Tong et al.,2006). Suppose there are n bands in the remote sensed data, thegradient between band k and k + 1 (k 6 n� 1) is:

gðk;kþ1Þ ¼DRðk;kþ1Þ

Dk¼ Rkþ1 � Rk

kkþ1 � kkð1Þ

where DR(k,k+1) is the difference between Rk+1 and Rk which denotethe reflectance values of band k + 1 and k respectively. kkþ1 and kk

are the wavelengths of band k + 1 and k, and Dk is their difference.The spectral gradient describes the trend between two adjacent

bands. As shown in Fig. 3, if g(k,k+1) > 0, this indicates that the spec-tral value increases from band k to k + 1. By contrast, if g(k,k+1) < 0,the spectral value decreases from band k to k + 1. In addition, ifg(k,k+1) equals 0, reflectance values remain the same. And a greaterkg(k,k+1)k indicates a larger change between the two neighboringbands.

Project original spectra to gradient

space by introducing spectral gradient

Calculate spectral gradient difference (SGD) as change magnitude

Change magnitude> threshold?

Change

No change

Establish knowledgebase of SGD pattern from reference spectral

Change type

Represent by SGD chain model

Bi-temporal, multi-spectral image data

Determine change area

Reference spectra

SGD pattern matching

Yes

No

Fig. 2. Framework of SGD based change detection.

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Fig. 3. Calculation of spectral gradient. (a) Original vegetation spectrum; (b)spectral gradient.

J. Chen et al. / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 1–12 3

The shape of the spectral curve can be described by the follow-ing spectral gradient vector (SGV), which combines the spectralgradients in the following way:

G ¼ ðgð1;2Þ; gð2;3Þ; . . . ; gðn�1;nÞÞT ð2Þ

SGV projects the spectral information from the traditional spec-tral space to gradient space.

2.2. Change/no-change areas detection using SGD

Suppose G1 and G2 are the SGVs of one pixel at times t1 and t2

respectively, then their difference DG can be calculated in theequation below:

DG ¼ G2 � G1 ¼ ðg2;ð1;2Þ; g2;ð2;3Þ; . . . ; g2;ðn�1;nÞÞT � ðg1;ð1;2Þ; g1;ð2;3Þ; . . . ; g1;ðn�1;nÞÞ

T

ð3Þ

where g2,(n�1,n) and g1,(n�1,n) are spectral gradients between bandn � 1 and n at the two acquisition times t2 and t1. Then, the abso-lute values of DG is calculated in the following equation:

jDGj ¼Xn

k¼1

jg2;ðk�1;kÞ � g1;ðk�1;kÞj ð4Þ

As a change magnitude based on SGD, a larger |DG| indicates ahigher possibility of change. After calculating the change magni-tude image of spectral gradient, a specific threshold is establishedto detect the change/no-change areas.

Based on the calculation of spectral gradient, the original spec-tra of examples in Fig. 1 were projected into gradient space, asshown in Fig. 4(a–c) respectively. As shown in Fig. 4(d), the spec-tral gradient difference between soils with different moistureshows a relatively small variance. Similarly, the spectral gradientdifference of water with different turbidity also has a small vari-ance. In contrast, the spectral gradient difference of change typefrom soil to water is much larger. It means that the pseudo changescaused by differences of soil moisture and water turbidity can beeliminated effectively in the spectral gradient space. Therefore,SGD could serve as an effective method to detect change/no-change areas compared to traditional methods.

2.3. Change type discrimination using an SGD chain model

Previously, change type discrimination was conducted in twoways: (1) classification based on training samples selected fromno change area (Xian et al., 2009; Chen et al., 2012); and (2) dis-crimination based on the direction of the change vector (Malila,1980; Michalek et al., 1993). The former requires training samplesof good quality, which is difficult to obtain. The latter, for exampletrigonometric functions of vector angle and sector coding, has lackof physical meaning. Therefore, we proposed a new change typediscrimination method based on an SGD chain model.

Because different types of land cover have distinctive shape fea-tures, certain change type between two land cover types also hasdistinctive change pattern in gradient space. Fig. 5(a) and (d)shows the spectra of two change types from vegetation to soiland from water to soil respectively. As mentioned above, the sign(positive/negative) of the gradient reflects the trend of spectralsegment, which consists of the two adjacent bands. As shown in

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Fig. 4. Change magnitudes in gradient space. Figures (a), (b) and (c) shows the spectral gradients of soil, water and change type from soil to water at times t1 and t2respectively, and figure (d) describes the spectral gradient change magnitudes of (a), (b) and (c).

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Fig. 5. Panels from top to bottom are change types from vegetation to soil and from water to soil. Panels from left to right are original spectra, gradient signs and gradientvalue differences.

4 J. Chen et al. / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 1–12

Fig. 5(b), vegetation and soil have the same gradient signs in spec-tral segments (1, 2), (3, 4) and (5, 6) but different gradient signs inspectral segments (2, 3) and (4, 5). When the changes occur from

water to soil (Fig. 5(e)), the gradient signs in the spectral segments(1, 2) and (5, 6) are consistent but differ in other spectral segments.This finding implies that different land cover change types have

J. Chen et al. / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 1–12 5

different change patterns of gradient signs. Furthermore, the valuedifferences of spectral gradients between the two land cover typesshould also be considered because the change patterns of gradientsigns are not enough to distinguish different change types. Forexample, spectral segments (4, 5) and (5, 6) show the same changepatterns of gradient sign for these two kinds of change types(Fig. 5(c) and (f)). Therefore, change patterns should be analyzedaccording to different spectral gradient signs (qualitatively) andgradient values (quantitatively).

Capitalizing on the idea of the topological chain model pro-posed by Chen et al. (2007), an SGD chain model was proposedhere to describe the gradient change pattern both qualitativelyand quantitatively. If the reference spectra of each land cover typeare known, a SGD pattern knowledgebase of typical land coverchange types could be established with the proposed SGD chainmodel. And the change type of each change pixel can be deter-mined by pattern matching based on the knowledgebase.

2.3.1. SGD chain modelThe SGD chain model describes the difference between two

spectral gradient vectors, both qualitatively and quantitatively.Qualitatively, p(k-1,k) describes the change of gradient signs withinthe spectral segment (k � 1, k)

pðk�1;kÞ ¼1; if g1;ðk�1;kÞ � g2;ðk�1;kÞ P 0�1; if g1;ðk�1;kÞ � g2;ðk�1;kÞ < 0

(ð5Þ

With the exception of the gradient signs, the value of the gradi-ent can also reflect the change type information. Therefore, themodel further considers the change of spectral gradient valuesquantitatively. C(k�1,k) describes the value difference within thespectral segment (k � 1, k):

cðk�1;kÞ ¼ g2;ðk�1;kÞ � g1;ðk�1;kÞ ð6Þ

(a)

(c)

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Fig. 6. The simulated spectra of pseudo changes. (a) Spectra of vegetation in different grwith varying turbidity; (d) spectra of buildings with different ages.

Finally, the SGD chain f(p, c) could be expressed in the equationbelow:

f ðp; cÞ ¼ pð1;2Þcð1;2Þpð2;3Þcð2;3Þ � � � pðn�1;nÞcðn�1;nÞ ð7Þ

The model intuitively takes into consideration the qualitativeand quantitative change of the spectral gradient vector which con-tains enough information to determine the change type.

2.3.2. Knowledgebase of reference SGD patternsIn order to determine the change types of changed pixels, a

knowledgebase of reference SGD patterns is required for patternmatching. In this study, the reference SGD patterns are derivedfrom reference spectra of various land cover types. The referencespectra are either acquired from a spectral library or an image data.Here, we use the image data to avoid inconsistencies between thespectra from the library and image. The reference spectra from theimage data are calculated based on a known classification map ont1. The mean spectral vector of each land cover class at t1 can becalculated in the equation below:

X ¼ ð�xi1; �xi2; �xi3; . . . ; �xinÞT ; i ¼ 1; . . . ;m ð8Þ

and the spectral gradient vector �Giði ¼ 1; . . . ;mÞ could be acquiredsimultaneously, where m is the number of classes. Then, the refer-ence SGD patterns between any two kinds of land cover types i and jare described using the SGD chain model based on �Gi, and �Gj, asshown in Eq. (9):

f ijðpij; cijÞ ¼ pijð1;2Þcijð1;2Þpijð2;3Þcijð2;3Þ � � �pijðn�1;nÞcijðn�1;nÞ; i; j ¼ 1; . . . ;m

ð9Þ

The knowledgebase consists of these reference SGD patterns.Generally, the spectral feature differences between any two typesof land-use/land-covers on t1 are similar to their spectral changefeatures from t1 to t2 after atmospheric correction (Chen et al.,2003). Therefore, this knowledgebase calculated based on a known

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owth status; (b) spectra of soil with varying moisture content; (c) spectra of water

6 J. Chen et al. / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 1–12

classification map on t1 could be used for pattern matching to dis-criminate change types from t1 to t2. Because some land coverchange types are impossible in reality, these impossible typesshould be removed from the knowledgebase according to expertknowledge (Liu et al., 2006; Huang and Jia, 2012).

2.3.3. Change type discrimination by SGD pattern matchingA changed pixel’s SGD pattern can also be described by its SGD

chain:

f 0ðp0; c0Þ ¼ p0ð1;2Þc0ð1;2Þp

0ð2;3Þc

0ð2;3Þ � � � p0ðn�1;nÞc

0ðn�1;nÞ ð10Þ

Suppose the pixel belongs to type i at t1, the corresponding ref-erence SGD patterns from class i to others would be selected fromthe knowledgebase. Then, the change type would be determinedby SGD pattern matching. Specifically, variations in gradient signsdij(n�1,2) and values vij(n�1,2) between the reference SGD patternsand the SGD pattern of the change pixel are calculated as follows:

dijðk�1;kÞ ¼ jpijðk�1;kÞ � p0ðk�1;kÞj; v ijðk�1;kÞ

¼ jcðk�1Þ;k � c’ðk�1Þ;kj k ¼ 1; . . . ;n ð11Þ

Finally, the overall matching coefficient Mij is obtained, asshown in Eq. (12):

Mij ¼Xn

k¼2

dijðk�1;kÞ �Xn

k¼2

v ijðk�1;kÞ ð12Þ

A smaller value indicates a higher similarity, and the changetype of the changed pixel is determined by the minimum valueof overall matching coefficient.

3. Experiments and analysis

3.1. Simulation experiment

To test the performance of the SGD, we applied the method to asimulated experiment involving pseudo changes and real changesand compared the results of the SGD with that of the other fourchange detection methods, including CVA, image difference, SADand image correlation.

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(d) (e)Fig. 7. The simulated spectra of real land cover changes. (a) Change between vegetationand buildings; d. change between soil and water; (e) change between soil and building

3.1.1. Data simulationIn this paper, four kinds of land cover spectra, including vegeta-

tion, soil, water, and building, were selected from the JHU spectrallibrary via ENVI software. Interference factors were added tosimulate pseudo changes. And the real land cover changes weresimulated by the six pair combinations among the spectra of fourland cover types. Simulated spectra of pseudo changes are illus-trated in Fig. 6, where solid lines denote the standard spectra fromthe spectral library and the dotted lines represent the simulatedspectra caused by noise. Fig. 6(a) shows the spectra of vegetationin different growth status, which is simulated by varying the infra-red reflectance. Fig. 6(b) shows the spectra of soil with varyingmoisture content. This simulated noise elevated the reflectanceby 20% in every band; therefore the spectral shape remained un-changed. Fig. 6(c) shows the spectra of water with different turbid-ity. The simulated water spectrum has a higher reflectance inbands 3 and 4, which significantly alters the shape of the spectralcurve but only affects the absolute reflectance value slightly.Fig. 6(d) shows the spectra of buildings of different ages. The olderbuilding lowered the standard reflectance by 10%, whereas theshape remained unchanged. Meanwhile, real land cover changeswere simulated by six pair combinations among the spectra of fourland cover types (Fig. 7).

3.1.2. ResultsFig. 8 shows the results of five change metrics, in which the

change magnitudes of pseudo land cover changes are depicted byorange columns, and the change magnitudes of real land coverchanges are represented by blue columns. In order to comparethe five change metrics conveniently, the change magnitudes ofSAD S and correlation R are transformed in the following equation:

S ¼ 1�Pn

k¼1R2;k � R1;kffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPnk¼1R2

2;k �Pn

k¼1R21;k

q ð13Þ

R ¼ 1�Pn

k¼1ðR2;k � R2Þ � ðR1;k � R1ÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPnk¼1ðR2;k � R2Þ

2 �Pn

k¼1ðR1;k � R1Þ2

q�������

������� ð14Þ

Vegetation

Water

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(µm)

0.400 0.900 1.400 1.900 2.400

Wavelength (µm)

(f) and soil; (b) change between vegetation and water; (c) change between vegetation

s; (f) change between water and buildings.

V-V' S-S' W-W' B-B' V-S V-W V-B S-W S-B B-W

Cha

nge

Mag

nitu

de

V-V' S-S' W-W' B-B' V-S V-W V-B S-W S-B B-W

Cha

nge

Mag

nitu

de

V-V' S-S' W-W' B-B' V-S V-W V-B S-W S-B B-W

Cha

nge

Mag

nitu

de

00.20.40.60.8

11.21.41.61.8

2

V-V' S-S' W-W' B-B' V-S V-W V-B S-W S-B B-W

Cha

nge

Mag

nitu

de

00.10.20.30.40.50.60.70.80.9

V-V' S-S' W-W' B-B' V-S V-W V-B S-W S-B B-W

Cha

nge

Mag

nitu

de

(b)

(c) (d) (e)

(a)

Fig. 8. Change magnitude histograms of five change metrics including CVA (a), image difference (b), SAD (c), image correlation (d) and SGD (e). (V: Vegetation; S: soil; W:water; B: building; V0: simulated vegetation; S0: simulated soil; W0: simulated water; B0: simulated building).

J. Chen et al. / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 1–12 7

where R2,k and R1,k are the reflectance values of band k at t2 and t1

respectively; R2 and R1 denote the mean values of reflectance at t2

and t1 respectively.An ideal change metric should separate the real changes from

the pseudo changes effectively which means that the change mag-nitudes of pseudo changes are smaller than that of real changes.Namely, the red line representing the maximum change magnitudeof pseudo changes should be lower than the green line which de-notes the minimum change magnitude of real changes in Fig. 8.Among the five methods, the red lines are higher than the blueones except for the SGD (Fig. 8(e)). In detail, all of the five metricscan address the spectral variance caused by difference of vegeta-tion status. However, CVA and image difference are oversensitiveto the changes in brightness of soil and buildings, while SAD andimage correlation are oversensitive to the turbidity changes inwater. In contrast, SGD can reflect all six of the real change typeseffectively and restrain all of the four pseudo changes. Therefore,

(a) 0 42

Fig. 9. Landsat Images of the study area captured o

we found that SGD achieved the best performance compared toother methods.

3.2. A case study of landsat imagery

3.2.1. Study area and dataA case study was conducted based on a couple of Landsat

images acquired in Liquan County, Shaanxi Province, China(34�290N, 108�250E), on June,29th, 2000 and June, 29th, 2009. Col-lecting images in the same season can reduce the spectral variationcaused by different sun angles and phenological status. As shownin Fig. 9, the land covers in this area changed dramatically in thelast decade because of the population explosion and urbanexpansion. Meanwhile, a 2009 land cover map (Fig. 10), from theNational Geoinformatics Center of China, which was generatedfrom Landsat data by visual interpretation referring to the high

(b)6km

n June, 29th, 2000 (a) and June, 29th, 2009 (b).

Cropland

Urban

Water

Wetland

Barren land

Fig. 10. Land Cover map of 2009.

Fig. 12. Detected change areas (in white).

8 J. Chen et al. / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 1–12

spatial resolution images is available for change type discrimina-tion by SGD. According to this map, there were five land covertypes in the study area, including cropland, urban, water, barrenland and wetland.

3.2.2. Change/no-change areas detectionImage preprocessing is a necessary step for detecting changes.

In the first step, the image-to-image geometric registration wasconducted between the two Landsat images. The registration errorwas less than 0.5 pixels. Then, atmospheric correction wasperformed using ATCOR2 of ERDAS to eliminate the impact ofatmospheric conditions.

According to Eq. (4), the change magnitude image based on SGDbetween 2000 and 2009 images was acquired and is shown inFig. 11(a). The brighter value indicates a higher possibility ofchange in land cover. Then, a specific threshold of change magni-tude image was used to determine the change/no-change areas.As the histogram of the change magnitude image follows a uni-modal distribution instead of bimodal distribution (Fig. 11(b)),we selected a semi-automatic method called Double-windowsFlexible Pace Search (DFPS) algorithm (Chen et al., 2003) insteadof an automatic method which assumes a bimodal distributionfor the change magnitude images (Otsu, 1979; Yen et al., 1995;Kittler and Illingworth, 1986; Bruzzone, 2000) to determine thethreshold. DFPS searches the optimal threshold that can be usedto obtain the maximum accuracy of change detection for thetraining samples. In this case study, the threshold of change mag-nitude image was 2.524. Next, the pixels with larger magnitudesthan the threshold were labeled as changed areas. The final change

(a)Fig. 11. Change magnitude image based on SGD of

detection result was formatted as a binary image (Fig. 12). It hasbeen proven that changes associated with urban development inthe boundary areas between city and countryside were identifiedsuccessfully.

3.2.3. Change type discriminationCompared to the historical image of 2000, it is easier to acquire

ground truth data and ancillary documentation for classification ofimage in 2009. Therefore, the classification result of 2009 imagewas obtained as shown in Fig. 10. According to the results ofchange/no-change pixels detection, the 2000 image was dividedinto areas of change and no change. For the unchanged area, landcover type of 2000 image remained the same with 2009. Mean-while, the mean values of each land cover type were extracted asreference spectra. Next, the spectral gradients of these referencespectra were calculated. The SGD patterns of reference spectrabetween any two kinds of land cover types were obtained. Mathe-matically, there were 20 (5 � 4) possible types of land coverchanges from 2000 to 2009 in the study. However, the buildingsdid not experience any type of change until 2009 according toour field investigation and reference data. Therefore, if pixelsbelonged to an urban area in 2000 which changed into other landcover types such as cropland, water, wetland or barren land in2009, it was assumed to be improbable and the correspondingchange type should be prohibited. The change types of all changepixels were labeled by SGD pattern matching with knowledgebase.

(b)

Num

ber

of P

ixel

s

Change Magnitude

2000 and 2009 images (a) and histogram (b).

Cropland Urban Water Wetland Barren land

(a) (b)

Fig. 13. Classification results for 2000 image. (a) Classification result for change area in 2000; (b) overall classification result for 2000 image.

Table 1Confusion matrix of change/no-change detection results.

Number ofpixels

Reference changed

Unchangedpixels

Changedpixels

Sum Commission error(%)

Classified changedUnchanged

pixels1522 66 1588 1.90

Changed pixels 15 776 791 4.16Sum 1537 842 2379Omission error 0.98% 7.84%

Overall accuracy = 96.595%, Kappa coefficient = 0.924

Table 2Confusion matrix of classification results in 2000.

Classifieddata (%)

Reference data (%)

Water Barrenland

Cropland Wetland Urban UserAccuracy

Water 91.00 2.00 0.20 1.00 0.00 95.79Barren land 4.50 87.67 4.80 7.00 7.00 79.46Cropland 0.00 6.00 94.80 7.00 4.25 91.86Wetland 4.50 1.00 0.20 69.00 1.00 80.23Urban 0.00 3.33 0.00 16.00 87.75 93.10

Overall accuracy = 89.266%, Kappa coefficient = 0.858

Table 3Accuracies of five change detection methods.

CVA Imagedifference

SAD Imagecorrelation

SGD

Thresholds 78.581 158.000 0.078 0.112 2.524Overall

accuracy (%)93.064 88.860 93.106 84.699 96.595

Kappacoefficient

0.847 0.754 0.849 0.675 0.924

J. Chen et al. / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 1–12 9

The classes of change pixels in 2000 are shown in Fig. 13(a). Mean-while, the land cover classification image of 2000 was obtained, asshown in Fig. 13(b) by combining classification results of changearea and no-change area in 2000.

3.2.4. Accuracy assessmentIn order to evaluate the performance of the proposed method,

samples were randomly taken for assessing the accuracy ofchange/no-change areas detection and change type discrimination.The samples for the accuracy assessment of change/no-changeareas detection consisted of 842 changed pixels and 1537unchanged pixels. As the confusion matrix shown in Table 1, SGDacquired change detection accuracies with an overall accuracy of96.6% and Kappa coefficient of 0.924. Similarly, the confusion ma-trix was also applied to assess the accuracy of classification resultsof 2000. 1500 Samples including all land cover types were used foraccuracy assessment. Table 2 presents the confusion matrix of clas-sification results from the Landsat image of 2000. A Kappa coeffi-cient of 0.858 and overall accuracy of 89.266% were also acquired.

3.2.5. Comparison and analysisTo assess improvements of change detection using SGD, the

change/no-change areas detection results of four other traditionalchange detection methods, including CVA, image difference, SADand image correlation, were implemented for comparison andanalysis.

These methods were performed to calculate change magnitudeof the study area, and then the DFPS algorithm with the sametraining samples of SGD was applied to discriminate change and

no-change areas. The accuracies with the same test samples areshown in Table 3. It is clear that SGD acquired the highest accuracyamong all five methods.

To visually compare the five methods in detail, two subareas ofthe change/no-change areas detection results in the study areawere selected (Figs. 14 and 15). Fig. 14 shows the subarea of urban.The area inside the yellow polygon generally remained unchangedfrom 2000 to 2009, except that a small amount of vegetation in theurban area was replaced by buildings. It is clear that CVA, imagedifference and image correlation significantly overestimated thechanged area. By contrast, SGD and SAD perform well in this re-gion. However, SAD performs poorly in the subarea of water. Asshown in Fig. 15, SAD and image correlation fail to compress thepseudo change of water, whereas the SGD method performs muchbetter. The results are consistent with the simulation experiment.In summary, our proposed SGD method is more accurate comparedto the other four change detection methods.

Because the accuracy figures are dependent on the change met-ric’s threshold level (Fung and Ellsworth, 1988; Morisette andKhorram, 2000), we made use of accuracy assessment curves to

Fig. 14. Subareas of urban captured on June, 29th, 2000 (a) and June, 29th, 2009 (b); and change detection result of SGD (c), CVA (d), image difference (e), SAD (f), and imagecorrelation (g).

Fig. 15. Subareas of water captured on June, 29th, 2000 (a) and June, 29th, 2009 (b); and change detection result of SGD (c), CVA (d), image difference (e), SAD (f), and imagecorrelation (g).

Table 4Mean and standard deviation values of the five change detection methods.

CVA Imagedifference

SAD Imagecorrelation

SGD

Mean 43.618 90.211 0.024 0.044 1.293Standard

derivation24.322 54.565 0.041 0.095 0.903

10 J. Chen et al. / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 1–12

compare the accuracy assessments of the five change metrics atdifferent threshold levels. Accuracy assessment curves provide agraphic and quantitative representation of the relationship be-tween the threshold level and the accuracy assessment figures(Morisette and Khorram, 2000). A series of thresholds are set byusing different adjustable parameters and are calculated asfollows:

Tm ¼ lþm � r;m ¼ 0; . . . ;2:5 ð15Þ

where Tm is the corresponding threshold at a certain adjustableparameter m; l and r denote the mean value and standard devia-tion of the change magnitude image respectively. Table 4 showsthe mean and standard deviation values of the five change detectionmetrics. The assessment curves of overall accuracy and Kappa coef-ficient are shown in Fig. 16, in which the x-axis pertains to thethreshold level and the y-axis pertains to the accuracy assessmentfeatures. SGD achieved the best performance when the threshold

level ranged from 0.5 to 2.5 standard deviations, and the overallaccuracy and Kappa coefficient reached a peak at the threshold levelbetween 1 and 1.5 standard deviations. The threshold of SGDdetermined by DFPS was equal to 1.364 standard deviations whichwas firmly in this range. The thresholds of the four other methodsdetermined by DFPS also were within the optimal range, whichindicated that DFPS was an effective method for determining thebest threshold.

(b)

(a)

0.75

0.80

0.85

0.90

0.95

1.00

0 0.5 1 1.5 2 2.5

Ove

rall

Acc

urac

y

Threshold Values (in units of Standard Deviation)

SGD

CVA

Image Differencing

SAD

Image Correlation

0.50

0.60

0.70

0.80

0.90

1.00

0 0.5 1 1.5 2 2.5

Kap

pa C

oeff

icie

nt

Threshold Values (in units of Standard Deviation)

SGD

CVA

Image Differencing

SAD

Image Correlation

Fig. 16. Accuracy assessment curves. (a) Overall Accuracy; (b) Kappa coefficient.

J. Chen et al. / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 1–12 11

4. Conclusion and future researches

As spectral shape information plays an important role in inter-pretation of remote sensed imagery, spectral gradient is used inthis paper to quantitatively describe the spectral shape and aSGD based approach is proposed for the change detection of mul-tispectral image.

With this proposed method, change magnitude is calculated inspectral gradient space instead of traditional spectral space. Com-pared to CVA and image difference which only consider the changeof reflectance values, our method can eliminate the pseudochanges caused by interference factors which alter the spectral val-ues without changing the shape characteristics of the spectrum.Unlike both correlation and SAD, SGD describes the spectral shapeinformation more directly and completely. As spectral gradient isalso determined by the spectral value to some extent, it is not assensitive to the spectral shapes of dark objects. Therefore, it is ableto compress these types of pseudo shapes. The simulation experi-ment and case study of Landsat imagery have shown that changemagnitude based on SGD outperformed other traditional methodsin change detection.

Based on the typical shape features of different spectral curves,a chain model is used for describing gradient change patterns bothqualitatively and quantitatively, corresponding to the variation ofspectral gradient signs and gradient values respectively. Then,change types are determined by pattern matching with knowl-edgebase of SGD patterns from reference spectra. Because thetraining samples are not required by both dates, the method canaid in the classification of historical imagery that lacks ancillaryinformation and training samples. Meanwhile, it also can be usedto update land cover database.

Even with all its advantages, there are still limitations for theproposed change detection method. Firstly, the SGD based

approach is still unsuitable for analyzing the images acquired indifferent phenological seasons because the vegetation spectrumdoes not necessarily maintain a stable shape in different seasons.In the future, the SGD algorithm should be improved by enhancingmulti-data fusion of high spatial and temporal resolution toaddress this issue. Secondly, a classification mapping is necessaryto obtain the change patterns. One possible solution is to use stan-dard spectra from the spectral library as the reference. The chal-lenge is how to modify the standard spectra to the image spectrain corresponding conditions. Thirdly, it is assumed in this paperthat each land cover has one unique spectral shape. In reality,the same land cover might have different spectral shape, and cur-rent approach needs to be extended for dealing with it. It is possi-ble to divide each land cover into sub-classes and develophierarchical SGD chain models and multiple matching patternsfor sub-classes.

Acknowledgements

This study was partially funded by the National Science Foun-dation of China (Project #41231172 and #41001216) and the 863Project of China (2009AA122001). The authors wish to thank anon-ymous reviewers for their constructive comments, which helpedimprove the paper.

References

Bartholomé, E., Belward, A.S., 2005. GLC2000: a new approach to global land covermapping from Earth Observation data. International Journal of Remote Sensing26 (9), 1959–1977.

Bruzzone, L., 2000. Automatic analysis of the difference image for unsupervisedchange detection. IEEE Transactions on Geoscience and Remote Sensing 38 (3),1171–1182.

Bruzzone, L., Cossu, R., Vernazza, G., 2004. Detection of land-cover transitions bycombining multidate classifiers. Pattern Recognition Letters 25 (13), 1491–1500.

Castellana, L., D’Addabbo, A., Pasquariello, 2007. A composed supervised/unsupervised approach to improve change detection from remote sensing.Pattern Recognition Letters 28 (4), 405–413.

Chen, J., Chen, X., Cui, X., Chen, J., 2011. Change vector analysis in posteriorprobability space: a new method for land cover change detection. Geoscienceand Remote Sensing Letters 8 (2), 317–321.

Chen, J., Gong, P., He, C., Pu, R., Shi, P., 2003. Land-use/Land-cover change detectionusing improved change-vector analysis. Photogrammetric Engineering andRemote Sensing 69 (4), 369–379.

Chen, J., Liu, W., Li, Z., Zhao, R., Cheng, T., 2007. Detection of spatial conflictsbetween rivers and contours in digital map updating. International Journal ofGIS 21 (20), 1093–1114.

Chen, X., Chen, J., Shi, Y., Yamaguchi, Y., 2012. An automated approach for updatingland cover maps based on integrated change detection and classificationmethods. ISPRS Journal of Photogrammetry and Remote Sensing 71 (7), 86–95.

Coppin, P., Jonckheere, I., Nackaerts, K., Muys, B., 2004. Digital change detectionmethods in ecosystem monitoring: a review. International Journal of RemoteSensing 25 (9), 1565–1596.

Fung, T., Ellsworth, L., 1988. The determination of optimal threshold levels forchange detection using various accuracy indices. Photogrammetric Engineeringand Remote Sensing 54 (10), 1449–1454.

Hégarat-Mascle, S.L., Seltz, R., 2004. Automatic change detection by evidentialfusion of change indices. Remote Sensing of Environment 91 (4), 390–404.

Huang, Z., Jia, X., 2012. Integrating remotely sensed data, GIS and expert knowledgeto update object-based land use/land cover information. International Journal ofRemote Sensing 33 (4), 905–921.

Kittler, J., Illingworth, J., 1986. Minimum error thresholding. Pattern Recognition 19(1), 41–47.

Lambina, E.F., Turnerb, B.L., Geist, H.J., et al., 2001. The causes of land-use and land-cover change: moving beyond the myths. Global Environmental Change 11 (11),261–269.

Li, D., 2010. Remotely sensed images and GIS data fusion for automatic changedetection. International Journal of Image and Data Fusion 1 (1), 99–108.

Liu, D., Kelly, M., Gong, P., 2006. A spatial–temporal approach to monitoring forestdisease spread using multi-temporal high spatial resolution imagery. RemoteSensing of Environment 101 (12), 167–180.

Liu, D., Song, K., Townshend, J.R.G., Gong, P., 2008. Using local transition probabilitymodels in Markov random fields for forest change detection. Remote Sensing ofEnvironment 112, 2222–2231.

Lu, D., Mausel, P., Brondizio, E., Moran, E., 2004. Change detection techniques.International Journal of Remote Sensing 25 (12), 2365–2407.

12 J. Chen et al. / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 1–12

Malila, W.A., 1980. Change vector analysis: an approach for detecting forest changeswith Landsat. In: Proceedings of the 6th Annual Sym-posium on MachineProcessing of Remotely Sensed Data, 03–06 June. Purdue University, WestLafayette, Indiana, pp. 326–335.

Michalek, J.L., Wagner, T.W., Luczkovich, J.J., Stoffle, R.W., 1993.Multispectral change vector analysis for monitoring coastal marineenvironments. Photogrammetric Engineering and Remote Sensing 59,381–384.

Morisette, J.T., Khorram, S., 2000. Accuracy assessment curves for satellite-basedchange detection. Photogrammetric Engineering and Remote Sensing 66, 875–880.

Nielsen, A., Conradsen, K., Simpson, J., 1998. Multivariate alteration detection(MAD) and MAF postprocessing in multispectral, bitemporal image data: newapproaches to change detection studies. Remote Sensing of Environment 64 (1),1–19.

Otsu, N., 1979. A threshold selection method from gray-level histograms. IEEETransactions on Geoscience and Remote Sensing 9 (1), 62–66.

Radke, R.J., Andra, S., Al-Kofahi, O., Roysam, B., 2005. Image change detectionalgorithms: a systematic survey. IEEE Transactions on Image Processing 14 (3),294–307.

Robila, S., Gershman, A., 2005. Spectral matching accuracy in processinghyperspectral data. IEEE ISSCS, pp. 163–166.

Singh, A., 1989. Digital change detection techniques using remotely-sensed data.International Journal of Remote Sensing 10 (6), 989–1003.

Tso, B., Mather, P., 2001. Classification Methods for Remote Sense Data. Taylor &Francis Press, New York.

Tong, Q., Zhang, B., Zheng, F., 2006. Hyperspectral Remote Sensing. HigherEducation Press.

Xian, G., Collin, H., Fry, J., 2009. Updating the 2001 National Land Cover Databaseland cover classification to 2006 by using Landsat imagery change detectionmethods. Remote Sensing of Environment 113 (6), 1133–1147.

Yen, J., Change, F., Change, S., 1995. A new criterion for automatic multilevelthresholding. IEEE Transaction on Geoscience and Remote Sensing 4 (3), 370–378.