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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS 1

An Improved Subpixel Mapping Algorithm Basedon a Combination of the Spatial Attraction and

Pixel Swapping Models for MultispectralRemote Sensing Imagery

Shangrong Wu , Zhongxin Chen, Jianqiang Ren, Wujun Jin, Hasituya, Wenqian Guo, and Qiangyi Yu

Abstract— To obtain spatial feature distributions from themixed pixels of remote sensing images and increase the accuracyof land-cover classification and recognition, a double-calculatedspatial attraction model (DSAM) based on the combination ofspatial attraction model (SAM) and pixel swapping model (PSM)is presented and verified by introducing the law of universal grav-itation to describe the attraction between pixels. In DSAM, SAMwas used to improve the initialization algorithm of PSM, and theoptimization algorithm of PSM was improved accordingly. Usinga SPOT-5 remote sensing image, related subpixel mapping (SPM)experiments were performed to verify the SPM effect of DSAMand to test its accuracy. The experimental results indicated thatthe DSAM SPM results were superior to the SPM results ofSAM and PSM. DSAM was proven effective and applicable forthe SPM of remotely sensed images, and the model can improvethe accuracy of SPM and landcover classification.

Index Terms— Pixel swapping model (PSM), spatial attractionmodel (SAM), spatial correlation, subpixel mapping (SPM)

I. INTRODUCTION

M IXED pixels increase the uncertainty of pixel attributes,such as land-cover classes and their proportions

(abundance) [1], [2], and increase the difficulty of land-coverclassification and recognition, which has hindered the applica-tion of low-spatial-resolution images for extracting land-coverinformation. The traditional hard classification technologyassigns pixel types based on the highest proportion of landcover. And it is difficult to extract actual feature coverageinformation from mixed pixels. Such issues have formed a

Manuscript received January 4, 2017; revised May 2, 2017and September 29, 2017; accepted April 4, 2018. This work was supportedin part by the National Natural Science Foundation of China underGrant 41471364 and Grant 61661136006, in part by the Introductionof International Advanced Agricultural Science and Technology, Ministryof Agriculture, China, through 948 Program under Grant 2016-X38,in part by Open Project Fund for Key Laboratory of Agricultural RemoteSensing, Ministry of Agriculture under Grant 201708, and in part by theNational High Technology Research and Development Program of Chinathrough 863 Program under Grant 2012AA12A307. (Corresponding author:Jianqiang Ren.)

S. Wu, Z. Chen, J. Ren, Hasituya, W. Guo, and Q. Yu are with the Instituteof Agricultural Resources and Regional Planning, Chinese Academy of Agri-cultural Sciences, Beijing 100081, China, and also with the Key Laboratory ofAgricultural Remote Sensing, Ministry of Agriculture, Beijing 100081, China(e-mail: wushangrong@caas.cn; renjianqiang@caas.cn).

W. Jin is with the Exploration and Production Research Institute, SINOPEC,Beijing 100083, China.

Color versions of one or more of the figures in this letter are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LGRS.2018.2825472

bottleneck in the quantitative development of remote sensingtechnology [3]. Thus, determining how to decompose mixedpixels scientifically has become an important issue in quanti-tative remote sensing analysis.

Spectral unmixing has been studied for decades to estimatethe proportions of classes within a mixed pixel and has playedan important role in improving the accuracy of the quan-titative extraction of land cover [4]. However, conventionalspectral unmixing can only obtain the percentage of each end-member from a mixed pixel and cannot obtain the spatialdistribution of classes within mixed pixels. To improve thequality of remotely sensed image classification, the subpixelmapping (SPM) technique was developed by Atkinson [5].SPM, also called superresolution mapping in the remotesensing community [6]–[8], is a technique for thematicmapping at a finer resolution relative to the original spatialresolution of input image. Using the spectral unmixing results(i.e., coarse spatial resolution proportions) as input values,SPM results can be achieved by dividing the original pixelinto multiple subpixels and predicting their classes.

Since the concept of SPM was proposed, SPM technologyhas become an important method for the extraction of quantita-tive remotely sensed information. Many scholars have studiedSPM in detail including theories and algorithms of SPM,result error analysis, and their accuracy assessment. Prominentrepresentative SPM models include spatial attraction models(SAMs) [9], [10], neural network models [2], [4], [11], pixelswapping models (PSMs) [12]–[14], Markov random fieldmodels [15], and Kriging interpolation models [16]. TheseSPM models have different characteristics and can over-come the restrictions associated with the spatial resolution ofremotely sensed images, as well as provide important technicalsupport to ensure the accuracy of land-cover classification [3].

However, current available SPM models have several disad-vantages such as lower accuracy and larger computation cost,and it is difficult to obtain accurate mapping results whenrelying on a single model [17]–[19]. The spatial correlation-based SPM model is an important subpixel level mappingtechnique that can be combined with a variety of simulationalgorithms to map subpixels in a quick, simple, and efficientmanner. The SAM and PSM are based on spatial correlation,allowing for the creation of combinations of the two models.Some scholars have published papers regarding innovativecombinations of the models [7], [8], [17]–[21]. For example,Shen and Wang [20] proposed modified PSM (MPSM) byusing SAM for initialization of PSM, but the advantages ofPSM were not fully exploited.

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2 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS

Due to the characteristics of PSM and SAM, when thereconstruction scale is large, the random initializing process ofPSM must swap a large number of subpixels, and the numberof computations will increase accordingly. The SPM results ofSAM are obtained via a single calculation, but the accuracyof SPM using SAM can be increased to a certain extent bycombining the model with other subpixel models with iterationprocesses.

Therefore, through introducing the law of universal gravi-tation into SPM research, a double-calculated SAM (DSAM)is proposed to utilize the advantages of both SAM and PSM.Compared to the existing MPSM, an SPM experiment wasconducted to verify the new model using Spot-5 remotelysensed imagery, and we hope to further improve the accuracyand quality of the maps obtained from remotely sensed imageclassification at subpixel level.

II. METHODSA. Model Principles

The proposed DSAM is an SPM model based on spatialcorrelation theory. DSAM utilizes the advantages of SAM andPSM by identifying subpixels in mixed pixels and calculatingthe attraction between pixels. SAM was initially proposed byMertens et al. [9], and it was assumed that the attractiononly existed between a subpixel and its eight surroundingmixed pixels in a homogeneous land-cover class; otherwise,the attraction was considered negligible. Instead of iterativelyoptimizing the spatial correlations among subpixels, SAMdirectly estimates the class of each subpixel according tothe class proportion of its neighboring pixels. The initialPSM was proposed by Atkinson [12] and relied on a randominitialization algorithm. Its objective was to change the spatialarrangement of subpixels in such a way that the spatial corre-lation between neighboring subpixels would be maximized.

In SPM models based on spatial correlation theory,the attraction between pixels is an important index fordescribing the spatial correlations of pixels; therefore,an important area of research is determining how to assess thevalue of attraction between pixels. Thus, the law of universalgravitation was introduced to describe the attraction betweenpixels, particularly the spatial correlation between pixels.

The law of universal gravitation states that a natural forceof attraction between any two massive particles is directlyproportional to the product of their masses and is inverselyproportional to the square of the distance between them. If weregard each pixel as a particle, the mixed pixel’s abundancecan be treated as the pixel’s mass. Thus, the mass productof two particles in the law of universal gravity can be usedto describe the pixel weight which reflects a certain land-cover proportion in a mixed pixel, and the square of distancebetween two particles in the law of universal gravitation couldbetter reflect the actual land-cover distribution. It should benoted that, in the mapping process of DSAM, the constantterm in law of universal gravitation was a common factorwhich could be simplified by reduction of a fraction and therewere no effects on the SPM results whether the constant termwas added or not. Therefore, a different constant term wasnot considered in this letter. The calculation of the attractionbetween pixels can be expressed as follows.

We assume that w land-cover classes are included in theremotely sensed image and that pm is a mixed pixel of class z,which can be divided into s × s subpixels. The proportionof land-cover class z in a mixed pixel z(p) can be obtained

Fig. 1. Schematic of attraction calculation (a) Step (1). (b) Step (3).

depending on the end-member selection model and the spectralunmixing model. Thus, the attraction between a subpixel andan adjacent mixed pixel in DSAM is described as follows:

z (ωin) = z (pm) · z (pn) ·⎛⎝1

k

k∑j=1

1

R2i j

⎞⎠ (1)

where z(pm) is the abundance value of class z in the centralmixed pixel pm; z(pn) is the abundance value of class z in themixed pixel pn adjacent to pm ; i is the subscript of subpixel xiin pm , where i = 1, 2, 3, . . . , s2; k is the number of classesz in pn; j is the subscript of subpixel x j of class z in pn ,where j = 1, 2, 3, . . . , k; z(ωin) is the attraction between eachsubpixel in pm and each subpixel of class z in pn; and Rij isthe Euclidean distance from subpixel xi to subpixel x j

Ri j =√

(mi − m j )2 + (ni − n j )2 (2)

where (mi , ni ) represents the coordinates of xi and (m j , n j )represents the coordinates of x j in the subpixel map.

Followed hypothesis of Mertens et al. [9], attractiononly existed between the subpixel and mixed pixels’ eightsurrounding mixed pixels that were in a homogeneous land-cover class. So the attraction z(ωi ) between the central mixedpixel pm and its eight surrounding mixed pixels of class z wascalculated as follows:

z (ωi ) =8∑

n=1

z (ωin). (3)

B. DSAM Mapping Process

The DSAM mapping process consisted of the following fivesteps.

1) Calculating the Spatial Attraction: The spatial attractionbetween the central mixed pixel pm and each adjacent mixedpixel containing each land-cover class was calculated usingformula (1). Due to not assigning land-cover class to subpixelin mixed pixel, the mixed pixels pm and pn were regardedas an entire pixel in the calculation, and formula (1) needs tobe simplified as formula (4). The schematic of step (1) wasshown in Fig. 1(a)

z(ωin) = z(pm) · z(pn). (4)

2) Initialization Algorithm: In this step, if the randomallocations of subpixels were applied in the initialization ofsubpixel, all of different classes of subpixels needed swapping,which led to too much iteration and would spent too muchoperation time. In order to save time required for SPMeffectively, the symmetric pattern was used to initialize thesubpixels in the central mixed pixel in this letter. In this way,only the different subpixels of the symmetrical region neededto be swapped and efficiency of the operation was greatlyimproved.

We assumed that the coordinate of the center mixed pixelpm was (i , j), and from upper left corner, its adjacent mixed

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WU et al.: IMPROVED SPM ALGORITHM 3

TABLE I

ASSIGNMENT ORDER OF SUBPIXELS

Fig. 2. Central mixed pixel pm and the adjacent mixed pixels. Note that thefigure in the top left corner is a part of an image, the bottom left corner isthe mixed pixel, and the right is the subpixels of the mixed pixel.

Fig. 3. Subpixel distribution.

pixels were A, B, C, D, E, F, G, and H, respectively. Andtheir coordinates of the adjacent mixed pixel of A–H were(i − 1, j − 1), (i − 1, j), (i − 1, j + 1), (i , j + 1),(i + 1, j + 1), (i + 1, j), (i + 1, j − 1), and (i, j − 1),respectively, as shown in Fig. 2. First, compared with thevalue of attraction z(ωi ) between central mixed pm and allits adjacent mixed pixels, the coordinate of the maximumattraction value z(ωi )max was selected. Then, according to theabove coordinate of the maximum attraction value and Table I,the subpixel assignment order was determined. Finally, theinitial distribution was obtained by assigning subpixels.

It is more advantageous to form a symmetric initial subpixeldistribution when first assigning small numbers of subpixels.Thus, before assigning values to large numbers of subpixels,subpixels with small abundance values in a mixed pixel mustbe assigned values. After initialization, the subpixels of class zin a mixed pixel are located near the adjacent pixels containingthe largest number of subpixels of class z.

3) Second Spatial Attraction Calculation: Accordingto formula (1) and based on the initialization assignment,attraction was calculated between subpixel xi in central mixedpixel pm and all subpixels in adjacent mixed pixel containingeach land-cover class. Then, according to formula (3), the totalattraction between pm and the adjacent mixed pixel of eachland-cover class was calculated. The schematic of step (3) wasshown in Fig. 1(b).

4) Optimization Algorithm (PixelSwapping Algorithm): Thespatial distribution of the subpixels in a mixed pixel wasdivided into eight parts using horizontal and vertical axes andmain diagonal and subdiagonal lines after the initial assign-ment, as shown in Fig. 3. The parts were labeled with I–VIII,and the subpixels in the neighboring parts were symmetricabout the bold lines. We assumed that the subpixel x was ready

Fig. 4. x and its symmetric y.

to be swapped, and the subpixel y was in the symmetricalposition of the subpixel x . Taking subpixel x in part III asan example, possible location of its symmetric subpixel y isshown in Fig. 4. If subpixel x and y were categorized to adifferent class, we assumed that the attribute of x is z1 andthe attribute of y is z2 (Fig. 4); z1(wx) is the value of theattraction of class z1 between subpixel x and its neighboringmixed pixels; z2(wx ) is the value of the attraction of class z2between subpixel x and its neighboring pixels; z1(wy) is thevalue of the attraction of class z1 between subpixel y and itsneighboring pixels; and z2(wy) is the value of the attractionof class z2 between subpixel y and its neighboring pixels.If z1(wy)− z1(wx )+ z2(wx )− z2(wy) > 0, the attributes of xand y were swapped, i.e., the attribute of x became z2 and theattribute of y became z1.

5) Iterative Algorithm: Steps (1)–(4) were repeated until noadditional swapping occurred.

As observed from the mapping process described above,after improving the PSM initialization algorithm using theSAM, the subpixel distribution had a greater spatial correla-tion, and the initialization accuracy and calculation speed weremuch better than those obtained using random assignment.In addition, the initial assignment of pixels was performedaccording to a specific process, which always resulted in thesame output. The improved optimization algorithm was usedto optimize the results by employing an initialization algorithmbased on a second calculation of the spatial attraction betweensubpixels and their adjacent mixed pixels. The improvedoptimization algorithm increased the computational speed byreducing the number of iterations required.

C. Main Processes and Procedures

The program was written in MATLAB 7.1 and run using theWindows 7 operating system. The experiment was conductedbased on the following four steps.

1) The experimental image was classified using a hardclassification algorithm, and the classification resultswere used as a reference image to evaluate SPM effectsand the accuracy of the results. From a lot of similarpublished papers, we could see that directly using theK -mean classification products as a reference image tocarry out SPM technology research was a more commonpractice [6], [9], [19].To avoid inconsistencies associatedwith sample selection, the K -means classification algo-rithm (a type of unsupervised classification method) wasselected to classify the experimental image.

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4 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS

Fig. 5. SPM results using the SPOT-5 remote sensing image (s = 4). (a) Reference image. (b) K -means. (c) SAM. (d) PSM. (e) MPSM. (f) DSAM.

2) The experimental image was degraded. To accuratelyand conveniently evaluate the SPM results, the degrada-tion scale was the same as the reconstruction scale. Thus,if the degradation scale was s, the weighted mean valueof s×s pixel values in the original image was assigned tothe pixels with the same spatial locations in the degradedimage. To objectively evaluate the effectiveness of theSPM model and to make the fraction image simulatedwithout error, the numbers of different land-cover classeswere calculated from the reference image.

3) SAM, PSM, MPSM, and DSAM were used to mapthe degraded image subpixels at different reconstructionscales (s = 2, 3, 4, 5, 6). To evaluate the effects of theSPM model objectively and prevent the introduction ofadditional errors, the abundance of each land-cover classin the pixels was obtained from a reference image.

4) Each SPM result was verified using the referenceimage, and the accuracy of each map was analyzed andevaluated.

III. MATERIALS

In this letter, a Spot-5 (10-m resolution) image was used tovalidate the accuracy of SPM using DSAM. The experimentalregion is located in the major farming area of NortheastChina (N46°07′32′′–N46°01′54′′, E123°12′19′′–E123°17′37′′).The Spot-5 image acquisition date was August 11, 2012, andthe image covered an area of 900 pixels × 900 pixels.

Moreover, to validate the hard classification results obtainedfrom the Spot-5 image, a satellite-ground synchronous exper-iment was performed to obtain ground samples of land-coverinformation using systematic and random sampling. Eachground sample covered an area of at least 200 m × 200 m,and 32 ground samples was obtained. After validation,the overall accuracy (OA) and kappa coefficient were 95.51%and 0.953, respectively. The accuracy of K -means classifica-tion resulted in higher quality reference image to verifyingSPM results.

TABLE II

SPM RESULTS AT DIFFERENT RECONSTRUCTION SCALES AND WITH

DIFFERENT RELATIONSHIPS BETWEEN PIXELS

In the reference image [Fig. 5(a)], the complex land-coverclasses included maize, meadowland, saline–alkali soil, andwater. The boundaries between different land-cover classeswere clear and reflected the spatial structure and detailedinformation associated with different land-cover classes.

IV. RESULTS

In this letter, the DSAM was verified and compared to SAM,PSM, MPSM, and K -means hard classification at differentreconstruction scales using the SPOT-5 remote sensing image.To evaluate the accuracy of the SPM model, the OA and kappacoefficient were used as quality evaluation indexes. The resultsare shown in Table II.

Table II shows that all the SPM results were better thanthe K -means hard classification results. At the same recon-structions scale, the SPM results of MPSM were better thanthose of SAM and PSM, which were consistent with theresults of Shen and Wang [20]. Compared to SAM, PSM, andMPSM, the DSAM mapping results were the best at the samereconstruction scale. Among the results, the OA of DSAM fors = 2, 3, 4, 5, and 6 was 91.07%, 87.03%, 83.67%, 81.08%and 79.15%, respectively. Compared to that of MPSM, theOA increased by 2.12%, 2.14%, 2.69%, 2.93%, and 3.35%,respectively. In addition, the kappa coefficient of DSAM fors = 2, 3, 4, 5, and 6 was 0.880, 0.825, 0.780, 0.747, and0.724, respectively. Compared to that of MPSM, the kappacoefficient increased by 0.023, 0.035, 0.042, 0.044, and 0.049,respectively.

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WU et al.: IMPROVED SPM ALGORITHM 5

Moreover, from Table II, with the increase of the recon-struction scale, the accuracy of the SPM results of SAM,PSM, MPSM, and K -means hard classification decreased.In addition, the SPM effect became more prominent, and theaccuracy increased between different SPM models. Regardlessof the value of reconstruction scale s, the SPM results ofDSAM were the best among those of all the models. Thisproved that DSAM mapping remained effective when thereconstruction scale increased.

Due to length limitations, only the SPM results fors = 4 were selected to show the effect of SPM in Fig. 5.The hard classification results of the degraded image resultedin the loss of a large proportion of the spatial structure anddetailed information; thus, the classification results were blurryand rough, and these adverse effects were more prominentfor small drainages and areas of linear land cover. Whenusing SAM, PSM, MPSM and DSAM to get the SPM results,the spatial structure and detailed information lost due to imagedegradation could be partially rebuilt.

Lacking of abundance limitation, the visual effects of SAMwere worse among four models. The SPM results of MPSMwere closer to the results of SAM because MPSM wasdirectly iterated using the PSM algorithm based on SAM.The SPM results of DSAM were better than those of MPSMbecause DSAM performed pixel initialization by partitioningthe subpixel allocation region. In addition, when using PSM toperform iterations in DSAM, the constraint associated with theabundance value in two-pixel exchange played an importantrole in improving the accuracy of SPM using DSAM.

V. CONCLUSION

The following conclusions were reached.1) In this letter, based on spatial correlation theory and

combinations of SAM and PSW, DSAM was proposedand based on the law of universal gravitation to describethe attraction between pixels. In addition, it was verifiedusing a SPOT-5 remote sensing image. Compared tothe results of SAM, PSM, and MPSM, the DSAMmapping results were the best at the same reconstructionscale. Thus, we showed that the proposed DSAM couldeffectively perform SPM using remotely sensed images.

2) DSAM was more robust and minimally influenced bythe reconstruction scale. In addition to its effectivenessand applicability, DSAM has some other advantages. Forexample, DSAM is simpler and more transparent thando general SPM models such as neural network models.In addition, based on the spatial relationships betweenpixels, the SPM results of DSAM are reproducible.Moreover, DSAM can be applied to images that includemore than two land-cover classes. Therefore, DSAMcan overcome the disadvantages associated with remotesensing images with low spatial resolutions because poorresolutions remain an important limiting factor of currentremote sensing satellite technology.

Although the proposed DSAM achieved a good performancein SPM experiments based on Spot-5 remotely sensed imagery,DSAM is affected by the abundance of subpixels. During theexperiment, to avoid additional error, the ideal abundances ofsubpixels obtained by spectral unmixing were used in ruralregions; however, to better verify the effectiveness of DSAM,the validation should be further performed in urban and forestregions or using other multispectral remote sensing imagesin the future. In addition, based on the initial assumption ofSAM, attraction only considered the eight-pixel neighborhood

in this letter, but when introducing attraction beyond theeight-pixel neighborhood into DSAM, whether the accuracyof SPM can be improved or not should be another futureresearch focus.

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