integration of chang’e-1 imagery and laser altimeter data ... · apollo missions [1]–[3] and...

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 12, DECEMBER 2011 4889

Integration of Chang’E-1 Imagery and LaserAltimeter Data for Precision Lunar

Topographic ModelingBo Wu, Jian Guo, Yunsheng Zhang, Bruce A. King, Zhilin Li, and Yongqi Chen

Abstract—Lunar orbital imagery and laser altimeter data aretwo major data sources for lunar topographic modeling. Most ofthe previous work has processed imagery and laser altimeter dataseparately. Usually though, there are inconsistencies between thetopographic models derived from them. This paper presents anendeavor to integrate the Chang’E-1 imagery and laser altimeterdata for consistent and precision lunar topographic modeling. Acombined adjustment model for the Chang’E-1 imagery and laseraltimeter data is developed, in which the participants are the laseraltimeter points, image exterior orientation (EO) parameters, andtie points collected from the stereo images. A weighting scheme isdesigned for the participants in the adjustment, and a local surfaceconstraint is imposed to improve the adjustment performance.The output of the combined adjustment is the refined image EOparameters and laser ground points. Experimental results usingthe Chang’E-1 data in the Apollo 15 and 16 landing site areas showthat the proposed combined adjustment approach can reducethe misregistrations between the imagery and the laser altimeterdata by a maximum of 1–18 pixels in image space. The JapaneseSELenological and ENgineering Explorer (SELENE) laser altime-ter data at the Apollo 15 and 16 landing site areas are employedfor comparison analysis. Small shifts between the SELENE andChang’E-1 laser altimeter data were found. The topography de-rived from Chang’E-1 data after the combined adjustment showsa relatively consistent trend with the topography determined bythe SELENE laser altimeter data.

Index Terms—Chang’E-1 imagery, Chang’E-1 laser altimeterdata, imagery and laser altimeter data integration, lunar topo-graphic modeling.

I. INTRODUCTION

LUNAR topographic information is of paramount impor-tance for lunar exploration missions and lunar scientific

investigations. Precision lunar topographic modeling and as-sessment from multisource data is also a challenging task.

Manuscript received January 11, 2011; revised March 29, 2011; acceptedMay 1, 2011 Date of publication June 6, 2011; date of current versionNovember 23, 2011.

B. Wu, J. Guo, B. A. King, Z. Li, and Y. Chen are with the De-partment of Land Surveying and Geo-Informatics, The Hong Kong Poly-technic University, Kowloon, Hong Kong (e-mail: [email protected];[email protected]; [email protected]; [email protected];[email protected]).

Y. Zhang is with the State Key Laboratory of Information Engineeringin Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan430072, China, and also with the Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Kowloon, Hong Kong(e-mail: [email protected]).

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

Digital Object Identifier 10.1109/TGRS.2011.2153206

Starting from the 1960s, a vast amount of lunar imagery andlaser altimeter data have been collected and processed in theApollo missions [1]–[3] and the Clementine mission [4], [5].More recently, China launched its first lunar probe Chang’E-1in October 2007. Onboard the Chang’E-1spacecraft, there is athree-line array charge-coupled device (CCD) camera system(nadir, forward, and backward) providing lunar surface imageryand a laser altimeter generating range measurements coveringthe whole Moon [6], [7]. The Japanese lunar mission SELeno-logical and ENgineering Explorer (SELENE) was successfullylaunched in September 2007 [8]. The U.S. also successfullylaunched its Lunar Reconnaissance Orbiter (LRO) to the Moonin June 2009 [9]. Among the payloads onboard the SELENEand LRO are orbiter cameras and laser altimeters with differentconfigurations that collect data at various levels of resolution.These new data sets enable a new era of lunar topographic mod-eling with the capabilities of providing detailed and precisionlunar topographic information.

In lunar topographic models derived from lunar orbiter im-agery and laser altimeter data, usually, there are inconsistenciesdue to the unavoidable errors (e.g., errors from sensor posi-tions and orientations). Most of the previous related researchprocessed lunar orbiter imagery and laser altimeter data sepa-rately and sometimes performed a comparison [4], [10]–[14].However, it should be noted that correlation of lunar imageryand laser altimeter data has the potential to produce consistenttopographic information [15]. Moreover, based on the previousresearch reports using space/airborne imagery or laser altime-ter data to derive topographic products on earth applications,measurement from stereo imagery will generally provide betteraccuracy in the horizontal direction than in the vertical direction[16], [17], while laser altimetry is known to produce bettervertical accuracy than horizontal accuracy [18], [19]. Therefore,there is also potential to produce lunar topographic informationwith better accuracy through an integration of the lunar imageryand laser altimeter data, which cannot be achieved when onlyusing the data from a single sensor.

This paper aims at the correlation and integration of theChang’E-1 imagery and laser altimeter data through a com-bined adjustment method to reduce the inconsistencies betweenthem and, subsequently, to produce precision lunar topographicmodels. After presenting a literature review on lunar topo-graphic modeling from various lunar orbital imagery and laseraltimeter data, a combined adjustment approach for Chang’E-1imagery and laser altimeter data is presented in detail.Chang’E-1 stereo images (forward and backward) and

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4890 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 12, DECEMBER 2011

associated laser altimeter data at the Apollo 15 and 16 landingsite areas are employed for tests. Based on the developedapproach, precision topographic models from the Chang’E-1data at Apollo 15 and 16 landing site areas are derived. Theyare then compared with the Japanese SELENE laser altimeterdata. Finally, concluding remarks are presented and discussed.

II. RELATED WORK

In the Apollo era, a variety of photographic sources collectedduring the Apollo lunar program were used for topographicmodeling. A series of lunar maps at scales of 1 : 1 000 000 and1 : 250 000 have been produced using the metric camera pho-tographs from Apollo 15, 16, and 17 missions [1], [2]. The U.S.Geological Survey (USGS) conducted metric camera mappingfor experimental maps and specific site maps using Apolloimages. Examining this metric photography on the analyticalstereoplotter showed standard errors of horizontal and verticalrepeatabilities of ±7.4 and ±16.4 m, respectively [3]. The laseraltimeter attached to the metric camera systems onboard thesethree Apollo missions had a ground footprint of about 20 m andhad also been used for topographic modeling tasks.

From February to May 1994, the Clementine spacecraftsuccessfully mapped the entire Moon at a resolution of 125–250 m/pixel using the ultraviolet-visible (UVVIS) and near-infrared (NIR) cameras. A global UVVIS Digital Image Modelof the Moon at 100 m/pixel was generated by the USGS [10].Laser altimeter data from Clementine were collected and usedto generate a topographic field of the Moon, which has anabsolute vertical accuracy of approximately 100 m and a spatialresolution of 2.5◦ [4]. In 2006, USGS released Unified LunarControl Network (ULCN) 2005 consisting of the 3-D positionof 272 931 points, which is based on a photogrammetric solu-tion of 43 866 Clementine images and earlier data [20].

The recent Chinese Chang’E-1 mission successfully returned1098 orbiter images with a spatial resolution of 120 m, whichcover the whole lunar surface. A global digital elevation model(DEM) has been produced using these images and preliminaryresults have revealed that the grid size for the DEM is up to500 m and the planar positioning accuracy is about 370 m[11]. The laser altimeter onboard the Chang’E-1 spacecraftgenerated range measurements covering the whole Moon withspacing resolution of 1.4 km for the along-track direction and7 km for the cross-track direction (at the equator). A Chang’E-1Lunar Topography Model s01 (CLTM-s01) was produced us-ing more than 3 million range measurements from the laseraltimeter, which is a global topographic model of the Moonwith a vertical accuracy of approximately 31 m and a spatialresolution of 0.25◦ [12]. Various topographic maps (2- or3-D) of some prominent lunar geologic regions including majormares, mounts, and craters have also been produced using theChang’E-1 imagery or laser altimeter data [21].

The Japanese lunar explorer SELENE successfully acquiredstereoscopic images with 10-m resolution using its push-broomTerrain Camera, which almost covers the entire surface of theMoon. Topographic products including orthophoto maps andDEMs generated from the SELENE images have been released[22]. The laser altimeter onboard SELENE measured more than

10 million ranges covering the entire region of the Moon witha height resolution of 5 m at a sampling interval smaller than2 km. Important lunar global parameters such as the radii, thecenter of mass, and the highest and lowest points were derivedfrom the SELENE laser altimeter data [23]. NASA’s LRO ac-quired images with the highest level of resolution (50 cm/pixel)yet returned from the Moon using its narrow angle camera,which has been used for detailed mapping of the Apollo landingsites and future potential landing sites. The laser altimeteronboard the LRO is a pulse detection altimeter that incorporatesa five-spot X-pattern that measures the distance to the lunarsurface at five spots simultaneously. Each spot has a diameterof 5 m, and the spots are 25 m apart. The five-spot patternprovides five adjacent profiles for each track, 10–12 m apartover a 50–60 m swath, with combined measurements in thealong-track direction every 10–12 m [35]. The ground trackspacing for the laser altimeter data of LRO is 0.1◦ (4.5 kmat the equator). A topographic map of the near side of theMoon has been generated using 1 billion LRO laser altimetermeasurements [24].

Overall, the previous and recent lunar missions have col-lected vast amounts of lunar imagery and laser altimeter data atdifferent resolutions and levels of uncertainty. However, mostof the previous related research, as described previously, pro-cessed the orbiter imagery and laser altimeter data separately.There are rare research reports from the past emphasizing thecorrelation or integration of the lunar imagery and the laseraltimeter data to produce better lunar topographic models.Rosiek et al. [25] endeavored to combine the Clementineimages with the Clementine laser altimeter data, in which theClementine global mosaic was used to establish horizontalcontrol and Clementine laser altimeter points were used forvertical control. However, due to the marginal overlap betweenstereo models, the geometry of the photogrammetric networkwas weak and resulted in stereo models that did not align witheach other. Most recently, Di et al. [15] presented a method ofcoregistration of Chang’E-1 stereo images and laser altimeterdata to reduce the inconsistency between them. In their method,a DEM is generated first from the stereo images, and then, theDEM is registered to another DEM interpolated from the laseraltimeter data through surface matching using a 3-D rigid trans-formation model. Consequently, the exterior orientation (EO)parameters of the images are adjusted using the rigid transfor-mation model so that the images and laser altimeter data arecoregistered. However, the DEM from laser altimeter data arefixed in the registration process; therefore, the quality of thefinal topographic products is dependent on the accuracy of thelaser altimeter data.

Integrated processing of orbital imagery and laser altimeterdata has been used for Mars topographic mapping applications.A combined processing of the Mars Orbiter Camera (MOC)imagery and Mars Orbiter Laser Altimeter (MOLA) data hasbeen studied using an adjustment method, and results indicatedthat the large misregistration between the two data sets canbe corrected to a certain extent [26]. Similar efforts focusingon the precision registration between MOC and MOLA datawith selected candidate landing sites have been made [27]. Thecombination of the High Resolution Stereo Camera (HRSC)

WU et al.: INTEGRATION OF CHANG’E-1 IMAGERY AND LASER ALTIMETER DATA 4891

images and MOLA data has also been studied, in which theHRSC images and MOLA data are processed in the samebundle adjustment and the HRSC images are adjusted to fit theMOLA data [28]. It should be noted that the resolutions of theChang’E-1 data are much less than those of the Mars data (e.g.,the resolution for Chang’E-1 imagery is 120 m/pixel, while forMOC imagery, the resolution is up to 1.4 m/pixel), and this willbring more uncertainties and difficulties to the integrated dataprocessing.

Based on the previous research, this paper presents a methodof integrating Chang’E-1 imagery and laser altimeter datathrough a strict combined adjustment model to take advantagesof the two types of data sets and to reduce the inconsistenciesbetween them and, subsequently, to generate precision lunartopographic models.

III. COMBINED ADJUSTMENT OF CHANG’E-1 STEREO

IMAGERY AND LASER ALTIMETER DATA

The Chang’E-1 data set used in this paper is the Level 2Cdata released by the Chinese Academy of Sciences, whichhas already been processed for radiometric, geometric, andspectrophotometric corrections [29]. However, no tracking dataor kernel data covering the spacecraft’s trajectory and pointinginformation are provided. The Mean-Earth/polar axis (ME)system is used for the Chang’E-1 Level 2C data. The longitude,latitude, and altitude coordinates for the laser altimeter pointsare provided. For the imagery, no EO information for theChang’E-1 images is available. Only in the image head fileare the latitude and longitude of the start and end pixels foreach row in the image provided. The backward and forwardimages are used in this paper to form a stereo pair since theyprovide the maximum convergent angle. For the convenienceof algorithm implementation, the experimental data sets ofChang’E-1 imagery and laser altimeter data at the Apollo 15and 16 landing sites used in this paper have been transferredto the local topocentric coordinate systems. The origin of thetopocentric coordinate system is located at the center of thestudy area. Three perpendicular coordinate axes are definedbased on a tangential plane of lunar surface at the origin point.The X-axis is oriented eastward, the Y -axis is northward, andthe Z-axis is toward up perpendicular to the plane.

By using the latitude and longitude of the start and endpixels of each row in the Chang’E-1 image as references, theChang’E-1 laser altimeter points can be overlaid on the imagesdirectly. Fig. 1 shows the Chang’E-1 images and associatedlaser altimeter data at the Apollo 15 landing site. Fig. 1(a)and (b) shows the planar and 3-D views of the laser altimeterdata overlaid on a reference image (backward), respectively.Significant elevation variations are noticed due to the moun-tainous areas in the bottom, middle, and top parts. For the samelaser altimeter points overlaid on the backward and forwardimages, the overlaid locations on both images should be thehomologous points (the same terrain features) in the ideal case;however, there exist large inconsistencies between them due tothe unavoidable errors (e.g., errors from sensor positions andorientations). Fig. 1(c)–(e) shows the detailed views of threetypical areas in Fig. 1(a), in which the left images show the

laser altimeter data overlaid on the backward image and theones on the right show the same laser altimeter data overlaidon the forward image. Using the overlaid laser points on theleft images as references, their correct homologous points onthe right image are marked with lines and dots. As can beseen from Fig. 1(c)–(e), inconsistencies as large as 15 pixels(about 1.8 km on the ground considering the image resolutionof 120 m/pixel) can be found. The following sections describea combined adjustment method that can be used to eliminatethese inconsistencies.

A. Overview of the Approach

The combined adjustment integrates Chang’E-1 stereo im-ages and laser altimeter data through a strict mathematic model.Since the Level 2C data do not provide the spacecraft’s trajec-tory and pointing information, a few 3-D control points selectedfrom ULCN 2005 were used to help derive the initial EOparameters of the Chang’E-1 stereo images using photogram-metric techniques [30]. For the experimental data sets used inthis paper, six control points distributed in the whole study areawere selected from ULCN 2005 and were used to calculate theinitial EO for both the stereo images. Tie points were identifiedfrom the stereo images through image matching, and they areevenly distributed over the images. The ground coordinates ofthe tie points can be obtained using the tie points and the initialimage EO parameters through a space intersection. With theinitial image EO parameters, the image coordinates of the laserground points on the stereo images can also be derived througha backprojection. The image EO parameters, the tie points onthe stereo images, the ground coordinates of the tie points, thelaser ground points, and the image coordinates of laser groundpoints are used as observables in the combined adjustmentmodel. A local surface constraint between the calculated groundcoordinates of the tie points and the laser ground points isemployed in the adjustment model to confine the adjustmentprocess. The final output of the adjustment is the improvedimage EO parameters and improved ground coordinates of thelaser points, from which precision lunar topographic modelscan be produced. The framework of the combined adjustmentapproach for the Chang’E-1 imagery and laser altimeter data isshown in Fig. 2.

B. Combined Adjustment Model

For Chang’E-1 stereo images, the relationship of a 3-Dground point (Xp, Yp, Zp) and its corresponding pixel (xp, yp)is represented by the following colinearity equation [31]:

xp=−f m11(XP −XS)+m12(YP −YS)+m13(ZP −ZS)

m31(XP −XS)+m32(YP −YS)+m33(ZP −ZS)

yp=−f m21(XP −XS)+m22(YP −YS)+m23(ZP −ZS)

m31(XP −XS)+m32(YP −YS)+m33(ZP −ZS)(1)

where (XS , YS , ZS) are the coordinates of the camera centerin object space, f is the focal length (23.33 mm for theChang’E-1 CCD camera), and mij denotes the elements ofa rotation matrix that is determined entirely by three rotation


Fig. 1. Chang’E-1 imagery and laser altimeter data at the Apollo 15 landing site area. (a) Planar view of the laser altimeter data overlaid on the reference image(backward), (b) 3-D view of the laser altimeter data overlaid on the reference image, (c) detailed view for Area 1, where the left image shows the laser altimeterdata overlaid on the backward and the right one shows the results on the forward image, (d) detailed view for Area 2, and (e) detailed view for Area 3.

angles (ϕ, ω, κ). The variables (XS , YS , ZS , ϕ, ω, κ) are theEO parameters of the images.

The Chang’E-1 CCD camera is a three-line pushbroom cam-era, which means each line on the image has one set of EOparameters. Changes of EO parameters can be modeled by apolynomial function. A third-order polynomial function is usedin this paper as follows:

XS(r) = a0 + a1r + a2r2 + a3r

3

YS(r) = b0 + b1r + b2r2 + b3r

3

ZS(r) = c0 + c1r + c2r2 + c3r

3

ϕ(r) = d0 + d1r + d2r2 + d3r

3

ω(r) = e0 + e1r + e2r2 + e3r

3

κ(r) = f0 + f1r + f2r2 + f3r

3 (2)

where r is the row index in the image and Xs(r), Ys(r),Zs(r), ϕ(r), ω(r), and κ(r) are the EO parameters of theimage row r. ai, . . . , fi (i = 0, 1, 2, 3) are the coefficients ofthe polynomials.


Fig. 2. Framework of the combined adjustment approach for the Chang’E-1imagery and laser altimeter data.

After linearization of (1), the observation equations for thecombined adjustment can be represented in matrix form as

V = AX − L,P (3)

where X is the unknown vector to be solved, L is the obser-vation vector, A is the coefficient matrix containing the partialderivatives from each observation, and P is the a priori weightmatrix of the observations that reflects measurement quality andthe contributions of the observations to the final result. The par-ticipants in the combined adjustment include measurements andweighted parameters. In this paper, all image points are treatedas measurements and all ground points and the EO parametersof the images are treated as weighted parameters. The weightedparameters will form a set of pseudo-observation equations inthe adjustment [32]. In particular, the combined adjustmentmodel in this paper includes the following four parts:

V1 =A1X1 − L1, P1

V2 =A2X1 +BX2 − L2, P2

V3 =A2X1 +BX3 − L3, P3

V4 =CX4 − L4, P4 (4)

where the first equation is the pseudo-observation equation forthe image EO parameters and X1 is the vector of unknowncoefficients ai, . . . , fi (i = 0, 1, 2, 3) in the polynomials in (2).The second equation is the observation equation for the tiepoints directly measured on the stereo images, and X2 isthe vector of unknown ground coordinates of the tie points.The third equation is the observation equation for the imagecoordinates of the laser points, and X3 is the vector of unknownground coordinates of the laser points. The fourth equation isa pseudo-observation equation related to a local surface con-straint in the adjustment model, which indicates that the groundpositions of the tie points obtained through an intersection using

the image EO parameters should be consistent with a localsurface determined by the nearby laser ground points. X4 linksto the elevation of the ground positions of the tie points (thedetails regarding the local surface constraint are discussed inSection III-D).

As mentioned before, the image coordinates of the laserpoints are initially derived by backprojecting the laser groundpoints onto the stereo images using the initial image EO param-eters. The initially determined image coordinates of the laserpoints on the stereo images are not necessarily the same ho-mologous points. Instead, there will be inconsistencies betweenthem, as shown in Fig. 1. However, they will be corrected in thecombined adjustment and the consistent image point locations,the improved image EO parameters, and the refined groundlocations of the laser points can be obtained. The adjustmentis based on a least squares approach.

C. Weight Determination in the Combined Adjustment

Introducing pseudo observation equations is a useful andcommon treatment in adjustment methodology since it providesthe flexibility to properly weight the participants in the adjust-ment [32]. However, it also brings difficulties about how toassign appropriate weights to the participants in the combinedadjustment.

In this paper, the tie points directly identified from theChang’E-1 stereo images are considered to be the most accu-rate measurements in the adjustment model. Therefore, a unitweight of 1 is assigned to all the tie points, whose estimatedstandard deviation is one pixel in image space. The weights forother observations and weighted parameters can be determinedaccordingly. The laser altimeter ground coordinates are consid-ered to be the second accurate data source in the adjustment,and a weight smaller than 1 is assigned to them based on theira priori variance. The image coordinates of the backprojectedlaser altimeter points and the ground coordinates of the tiepoints from space intersection receive much smaller weights inthe adjustment due to the fact that they are calculated basedon the inaccurate initial image EO parameters. It should benoted that, from previous experiences in photogrammetry [26]and this study, the adjustment model is less sensitive to theassignment of weights. Moderate changes in weight magnitudeyield the same results.

As for the weights of the image EO parameters in theadjustment, since the positional parameters and the orienta-tion parameters are correlated and their exact precision isunclear, it is more difficult to determine proper weights forthem. In this paper, a series of experiments using the dataset at the Apollo 15 landing site area was performed tohelp determine the influences of different weights for eachof the EO parameters on the adjustment results. First, a setof default weights of (10−10, 10−10, 10−10, 10−5, 10−5, 10−5)heuristically determined were assigned to the EO parameters(XS , YS , ZS , ϕ, ω, κ), respectively. Then, a change interval of10−5 was added to the weight of one of the EO parametersuntil it reached 10−50. At the same time, the weights for theother EO parameters remained unchanged. A series of DEMsassociated with different weights for each of the EO parameters


Fig. 3. Different influences on the topography with different weights for the EO parameters in the adjustment. (a) DEM generated from the stereo images usingthe adjusted EO parameters by applying different weights to XS , YS , ϕ, and ω, (b) DEM obtained by applying different weights to ZS , (c) DEM obtained byapplying different weights to κ, and (d) DEM obtained using the heuristic weights for the EO parameters, in which the inset image shows the DEM directlyinteroperated from the laser altimeter data as a reference.

was generated from the stereo images using the final adjustedEO parameters. Fig. 3 shows the experimental results. Fig. 3(a)shows the 3-D view of the DEM generated by applying differentweights to the EO parameters XS , YS , ϕ, and ω. No matterhow the weights were assigned to these four parameters, thefinally obtained DEMs remain the same. However, for the EOparameters ZS and κ, when the weights assigned to them werechanged to 10−30 and 10−15, respectively, the final DEMschanged significantly, as shown in Fig. 3(b) and (c), and theyremain the same until the weights reached to 10−50. Theexperiments indicate that the variations of the weights for XS ,YS , ϕ, and ω in the adjustment have very little influences on thefinal surface topography, while the weights for ZS (related tothe altitude of the sensor) and κ (related to the yaw angle of thesensor) play important roles in the adjustment. Then, a new setof weights (10−10, 10−10, 10−30, 10−5, 10−5, 10−15) for the EOparameters (XS , YS , ZS , ϕ, ω, κ) were used in the adjustmentmodel, and the DEM finally derived is shown in Fig. 3(d). Theinset image in Fig. 3(d) shows the DEM directly interoperatedfrom the laser altimeter data, which can be used as a referencefor the actual topography.

Comparing the DEMs generated using different weights forthe EO parameters with the DEM directly interoperated fromthe laser altimeter data, the DEM shown in Fig. 3(a) has anaverage height difference of 692.97 m, the DEM in Fig. 3(b) hasan average height difference of 675.03 m, the DEM in Fig. 3(c)has an average height difference of 708.57 m, and the DEM inFig. 3(d) has an average height difference of 64.21 m. It can

be seen that the last one is the closest one. This indicates thatspecial considerations for the weights of ZS and κ are necessaryto derive the correct topography.

D. Local Surface Constraint in the Combined Adjustment

To alleviate the situation that the adjustment results aredependent on specific data sets and the specific weights ofthe participants in the adjustment, particularly for the weightsassigned to the image EO parameter ZS and κ, an additionalconstraint is incorporated in the adjustment model, which isthe local surface constraint. The idea behind the local surfaceconstraint is that the ground positions of the tie points obtainedthrough the intersection using the image EO parameters shouldbe consistent with a local surface determined by the nearbylaser ground points (Fig. 4).

As shown in Fig. 4, a ground point O that is derived froma pair of tie points on the stereo images using the image EOparameters, its four neighbors A, B, C, and D from the nearestlaser altimeter points can be obtained through searching thefour quadrant directions in a local region (100 ∗ 100 pixels)centered at the tie point location. From the derived local surface,an elevation Z for the ground point O can be obtained. Z0 is theoriginal height of ground point O. d is the difference betweenZ and Z0. We use d = 0 as an additional pseudo-observation inthe combined adjustment, which is the last equation in (4).

From the experiments in this paper, it is shown that addingthe local surface constraint in the combined adjustment model


Fig. 4. Principle of the local surface constraint.

Fig. 5. Chang’E-1 laser altimeter points projected on the stereo images after the combined adjustment at the three selected areas in the Apollo 15 landing sitearea. (a) Detailed view for Area 1, where the left image shows the laser altimeter points projected on the backward image and the right one shows the results onthe forward image, (b) detailed view for Area 2, and (c) detailed view for Area 3.

TABLE ISTATISTICS OF DISCREPANCIES BEFORE AND AFTER ADJUSTMENT FOR THE DATA SETS AT THE APOLLO 15 LANDING SITE AREA

is able to eliminate possible blunders in the adjustmentparticipants. It alleviates the dependences on specific weights ofthe participants in the adjustment. It also enables the adjustmentprocess to converge quickly.

E. Results From the Combined Adjustment

The Chang’E-1 data sets at the Apollo 15 landing site areahave been used to evaluate the developed adjustment model.At first, 475 tie points are identified on the stereo imagesthrough image matching, which are evenly distributed over theimages. They are used in the combined adjustment model asinputs. The residuals of the tie points before and after adjust-ment have been calculated. Before adjustment, the residual is3.65 pixels in average with a maximum of 10.05 pixels. Whileafter the adjustment, the residual is 1.62 pixels in average witha maximum of 2.51 pixels. This indicates that it is feasibleto use the third-order polynomial function to model the EOparameters, and it also proves the good performance of theadjustment model in general.

Fig. 5 shows the detailed results of the combined adjustmentof the Chang’E-1 data sets at the Apollo 15 landing site

area. For the three selected areas marked on Fig. 1(a), thesame point pairs of significant inconsistencies, as marked onFig. 1(c)–(e), have been identified again using the lines shownin Fig. 5(a)–(c), respectively. As can be seen from Fig. 5, theprevious inconsistencies have been removed, and now, the pointpairs are almost the homologous points representing the sameterrain features on the stereo images. One also notes that theinconsistencies in both the along- and cross-track directionshave been reduced.

To quantitatively evaluate the performance of the approach,we take the projected positions of the laser altimeter points onthe backward image as references and calculate the discrepan-cies between their homologous points (from image matching)and the projected positions on the forward image to depictthe inconsistencies between the imagery and the laser altimeterdata. Table I lists the discrepancies in image space before andafter the combined adjustment process for the three areas. FromTable I, we can observe that the maximum and the RMSE ofthe discrepancies have been greatly reduced. Particularly forArea 3, which is a highly mountainous area with significantelevation changes, the RMSE of the discrepancies has beenreduced from over ten pixels to about the one-pixel level.


Fig. 6. Comparison of different DEMs at the Apollo 15 landing site area. (a) DEM interpolated from the Chang’E-1 laser altimeter data directly, (b) DEMgenerated from the Chang’E-1 stereo images using the initial image EO parameters, and (c) DEM generated from the Chang’E-1 stereo images using the refinedimage EO parameters after the combined adjustment.

Fig. 7. Two tracks selected from the laser altimeter data at the Apollo 15 landing site area and the related information.

Three DEMs were generated to examine the experimentalresults in object space. Fig. 6(a) is the DEM directly interpo-lated using the Chang’E-1 laser altimeter data at the Apollo 15landing site area. Its resolution is 1.4 km (same as the spacingresolution in the along-track direction of the laser altimeterdata). Through a reliable image matching method [33], 15 487homologous points were obtained on the Chang’E-1 stereoimages. Three-dimensional coordinates of these homologouspoints can be derived through a space intersection using theimage EO parameters, and then, DEMs can be interpolatedfrom them. Fig. 6(b) is the DEM generated from the Chang’E-1stereo imagery using the initial image EO parameters. Theresolution of this DEM is 360 m, which is three times theimage resolution. As can be seen from Fig. 6(b), this DEMprovides much more details compared with the DEM directlyinterpolated from the laser altimeter data in Fig. 6(a). However,its topography deviates from the latter due to the inaccurateimage EO parameters. Fig. 6(c) shows the DEM generated fromthe stereo imagery using the refined image EO parameters afterthe combined adjustment. The DEM shows generally consistenttopography with the DEM directly interpolated from the laseraltimeter data and, at the same time, provides more topographicdetails, which indicates the good performance of the combinedadjustment approach.

To further examine the performances of the combined adjust-ment, two tracks of the laser altimeter data were selected for

detailed analyses at the Apollo 15 landing site area, as shown inFig. 7. The information regarding the acquisition details of thetwo tracks of the laser altimeter data and the used stereo imagesare also shown in Fig. 7. For each track, three profiles were de-rived. The first profile was obtained by directly connecting thelaser points on the track. The second profile was derived fromthe DEM generated from the stereo images before applyingadjustment, as shown in Fig. 6(b). The third profile was derivedfrom the DEM generated from the stereo images after applyingadjustment, as shown in Fig. 6(c). Fig. 8 shows the elevationcomparison of the profiles for the two tracks, in which theelevation values are in a local topocentric coordinate system.

From Fig. 8, one can note that three profiles have gener-ally the same trend for both tracks. However, the profiles de-rived from the DEMs before adjustment have large differencescompared with the other two due to the inaccurate initial imageEO parameters. Particularly for Track 2, the middle part ofthe profile (green line) is below the other two profiles, whileit is much higher than the other two at the right part, whichcorresponds to the highly mountainous area. The detailed statis-tics of the elevation differences between the profiles derivedfrom the DEMs before or after adjustment and the profilesfrom the laser altimeter points are listed in Table II. The resultsindicate that the combined adjustment can significantly reducethe inconsistencies between the topographic models derivedfrom the laser altimeter data and imagery.


Fig. 8. Profile comparison for the two selected tracks at the Apollo 15 landing site area. (a) Profiles for Track 1 and (b) profiles for Track 2.

TABLE IISTATISTICS OF ELEVATION DIFFERENCES BETWEEN THE PROFILES FOR THE DATA SETS AT THE APOLLO 15 LANDING SITE AREA

IV. FURTHER EXPERIMENTS AND COMPARISON ANALYSES

A. Experiments at the Apollo 16 Landing Site Area

The same photogrammetric process and the combined ad-justment approach have also been applied to the Chang’E-1laser altimeter data and CCD imagery at the Apollo 16 landingsite area, as shown in Fig. 9. Fig. 9(a) and (b) shows theplanar and 3-D views of the laser altimeter data overlaid ona reference image (backward), respectively. Fig. 9(c) and (d)shows the detailed view of two selected areas in Fig. 9(a), inwhich the backward images are on the left side and the forwardimages on the right side. Points marked with red crosses wereobtained by overlaying the laser altimeter points on the imagesdirectly. Using the overlaid laser points on the left images asreferences, their correct homologous points on the right imageare marked with red lines and dots. As can be seen from theright images in Fig. 9(c) and (d), inconsistencies as large aseight pixels can be found. Points marked with cyan circles areobtained by backprojecting the same laser altimeter points onthe images using the image EO parameters after adjustment.They are almost homologous points, as indicated by cyan lines.

Table III lists the discrepancies in image space before andafter the combined adjustment process for the two areas. FromTable III, we can observe that the maximum and the RMSE ofthe discrepancies have been effectively reduced.

Similar to the experiments using the data sets at theApollo 15 landing site area, two tracks of the laser altimeterdata were selected for detailed analyses at the Apollo 16 landingsite area, as shown in Fig. 10. The information regarding theacquisition details of the two tracks of the laser altimeter dataand the used stereo images are also shown in Fig. 10. For each

track, three profiles were derived from the laser altimeter points,the DEM from the stereo images before adjustment, and theDEM from the stereo images after adjustment, respectively.Fig. 11 shows the profiles for the two tracks.

Similar to the experimental results using the data sets atthe Apollo 15 landing site area, the inconsistencies betweenthe topographic models derived from the laser altimeter dataand imagery have been reduced after the combined adjustment.The detailed statistics of the elevation differences between theprofiles derived from the DEMs before or after adjustment andthe profiles from the laser altimeter points are listed in Table IV.

For Track 1, there is a place showing reversed elevationsbetween the profile generated from the laser altimeter pointsand the profile derived from the stereo images, as marked witha cyan rectangle in Fig. 11(a). We examined the distribution ofthe laser altimeter points and the actual image at this place andfound that there is a crater in that region and the laser altimeterpoints just happen to pass across the crater. The inset image inFig. 11(a) shows the crater, in which the laser altimeter pointsinside the crater are marked with blue points. The shape ofthe profile from laser altimeter points is the actual case in thisregion, while there are mistakes in the profile from the DEMsgenerated from images due to insufficient matched points (reddots on the inset image) at the crater due to the poor textures,which causes problems in the subsequent DEM interpolation.

B. Comparison Between the Results From Chang’E-1 Dataand SELENE Data

In this paper, the generated topographic models at theApollo 15 and 16 landing site areas from the Chang’E-1


Fig. 9. Chang’E-1 imagery and laser altimeter data at the Apollo 16 landing site area. (a) Planar view of the laser altimeter data overlaid on the reference image(backward), (b) 3-D view of the laser altimeter data overlaid on the reference image, (c) detailed view for Area 1, and (d) detailed view for Area 2.

TABLE IIISTATISTICS OF DISCREPANCIES BEFORE AND AFTER ADJUSTMENT FOR THE DATA SETS AT THE APOLLO 16 LANDING SITE AREA

Fig. 10. Two tracks selected from the laser altimeter data at the Apollo 16 landing site area and the related information.

data are compared with the Japanese SELENE laser altimeterdata (https://www.soac.selene.isas.jaxa.jp/archive/index.html.en). Iz et al. [34] examined the consistency of the Chang’E-1

and SELENE reference frames in the global scale through theanalysis of a large number of nearly colocated laser altimeterpoints from these two missions using a 12-parameter affine


Fig. 11. Profile comparison for the two selected tracks at the Apollo 16 landing site area. (a) Profiles for Track 1 and (b) profiles for Track 2.

TABLE IVSTATISTICS OF ELEVATION DIFFERENCES BETWEEN THE PROFILES FOR THE DATA SETS AT THE APOLLO 16 LANDING SITE AREA

Fig. 12. Comparison between the DEMs interpolated from the Chang’E-1 and SELENE laser altimeter data at the Apollo 15 landing site area. (a) DEMs directlyoverlaid together and (b) DEMs after registration.

transformation model cast in the form of rigid body motions anddeformations. They found that the estimated relative rigid bodymotion and deformation parameters between the two referenceframes are consistent (i.e., nearly zero estimates for the trans-lations, rotations, and shear parameters) while the three strainparameters, which are similar in magnitude and sign, reveala statistically significant scale difference of about 0.9× 10−6

between the Chang’E-1 and SELENE reference frames. Thispaper provides detailed comparison in local regions betweenthe data sets from these two missions.

At the Apollo 15 landing site area, two DEMs were firstinterpolated using the Chang’E-1 and SELENE laser altimeterdata. Fig. 12(a) shows the 3-D view of the two DEMs directlyoverlaid together. As can be seen, there are inconsistenciesbetween the two DEMs, as indicated by the misalignments ofthe mountain peaks in the area. A six-parameter transformation(three translation parameters and three rotation parameters) wasperformed to register the SELENE DEM to the Chang’E-1

TABLE VTRANSFORMATION PARAMETERS BETWEEN THE CHANG’E-1

AND SELENE LASER ALTIMETER DATA AT THE

APOLLO 15 AND 16 LANDING SITE AREAS

DEM using a few conjugate points (mountain peaks). Theinternal relative positions and orientations of the two DEMsremain the same after the transformation. Table V shows theobtained transformation parameters between the Chang’E-1DEM and the SELENE DEM, which indicates the differences


Fig. 13. SELENE laser altimeter data overlaid on the Chang’E-1 imagery. (a) At the Apollo 15 landing site area and (b) at the Apollo 16 landing site area.(c) Information about the selected tracks at the two landing site areas.

in the positional and orientation components between these twodata sets. For the Apollo 15 landing site area, there is abouta 350-m offset between these two data sets in the horizontaldirection, and the SELENE laser altimeter data is higher thanthe Chang’E-1 laser altimeter data by about 150 m. The devi-ations in rotations between these two data sets are small. Afterregistering the SELENE DEM to the Chang’E-1 DEM using theobtained transformation parameters, they are aligned as shownin Fig. 12(b).

The same process was performed for the Chang’E-1 andSELENE data sets at the Apollo 16 landing site area, and theresults are shown in Table V. For the Apollo 16 landing sitearea, the horizontal deviation between these two data sets isabout 1.5 km, which is larger than that in the Apollo 15 landingsite area. The SELENE laser altimeter data are also higher thanthe Chang’E-1 laser altimeter data by about 90 m in the Apollo16 landing site area. The deviations in rotations between thesetwo data sets are quite small.

The obtained transformation parameters were used to reg-ister the SELENE laser altimeter data to the Chang’E-1 ref-erence frame and remove the systematic shifts between them.Fig. 13(a) and (b) shows the registered SELENE laser altimeterdata directly overlaid on the Chang’E-1 images (backward im-ages) at the Apollo 15 and 16 landing site areas, respectively. Aswith previous experimental analysis, two tracks of the SELENElaser altimeter data at each landing site area were selected forfurther analysis. They are shown in Fig. 13(a) and (b), and thedetails about the tracks are given in Fig. 13(c).

For each track at the two experimental areas, three profileswere derived, as shown in Fig. 14. The first profile was obtainedby directly connecting the SELENE laser altimeter points onthe track (blue lines in Fig. 14). The second profile was derivedfrom the DEM generated using the Chang’E-1 stereo imagesafter applying adjustment (red lines in Fig. 14). The thirdprofile was derived from the DEM directly interpolated fromthe Chang’E-1 laser altimeter points (cyan lines in Fig. 14).These profiles can be used to examine the relative topographyderived from the data sets from these two missions.

From Fig. 14, it can be noticed that the general trend amongthese profiles is consistent for the four tracks in the two exper-imental areas. The profiles derived from the DEMs generatedusing the Chang’E-1 laser altimeter data show relatively smoothtopography compared with the other two. This is because theDEMs are interpolated from the relatively sparse laser altimeterpoints, and they may not be sufficient to represent the actualtopography in the area. The relative shapes of the SELENEprofiles and the profiles from DEMs generated using theChang’E-1 stereo images after applying adjustment are consis-tent. The detailed statistics of the elevation differences betweenthese two types of profiles are listed in Table VI. The differ-ences may be caused by the possible errors in the registrationof the two data sets and the possible errors in the SELENE laseraltimeter data and the Chang’E-1 data.

V. CONCLUSION AND DISCUSSION

The combined adjustment approach presented in this paperprovides a mathematical model to integrate the Chang’E-1imagery and laser altimeter data for precision lunar topographicmodeling. The experiment analyses using the data sets at theApollo 15 and 16 landing site areas lead to the followingconclusions.

1) This study reveals that inconsistencies may exist betweenthe Level 2C Chang’E-1 imagery and laser altimeter datadue to the unavoidable errors (e.g., errors from sensorpositions and orientations), as indicated by the misreg-istrations from a few pixels to 18 pixels in image space atthe Apollo 15 and 16 landing site areas.

2) The combined adjustment between the Chang’E-1 im-agery and laser altimeter data can effectively reducethe misregistrations in image space to about the one-pixel level and provide improved image EO parametersas well as improved laser ground points, which can befurther used to produce consistent and precision lunartopographic models.


Fig. 14. Profile comparison between the SELENE and Chang’E-1 data sets. (a) Profiles for Track 1 in the Apollo 15 land site area, (b) profiles for Track 2 in theApollo 15 land site area, (c) profiles for Track 1 in the Apollo 16 land site area, and (d) profiles for Track 2 in the Apollo 16 land site area.

TABLE VISTATISTICS OF ELEVATION DIFFERENCES BETWEEN THE PROFILES FROM THE SELENE DATA AND THE CHANG’E-1 IMAGERY

3) The derived lunar topographic models from Chang’E-1data at the Apollo 15 and 16 landing site areas werecompared with the Japanese SELENE laser altimeterdata, and small shifts (350 m and 1.5 km in the horizontaldirection, 150 and 90 m in altitude for the Apollo 15and 16 data sets, respectively) between these two datasets were found. The topography derived from Chang’E-1data after the combined adjustment shows a relativelyconsistent trend with the topography determined by theSELENE laser altimeter data.

It is very valuable to integrate lunar imagery and laser altime-ter data from different sensors to produce consistent and preciselunar topographic models. This will be more in demand whenprocessing other high-resolution data for detailed topographic

modeling of the lunar surface, such as the data from the LROmission and the Chinese Chang’E-2 mission. The experimentalresults reported in this paper are promising. Future research willstudy cross-mission data integration. Tests over areas coveredby a larger number of images are also of interest.

ACKNOWLEDGMENT

The authors would like to thank the National AstronomicalObservatories of the Chinese Academy of Sciences for provid-ing the Chang’E-1 data sets. The work described in this paperwas supported in part by a grant from the Research GrantsCouncil of Hong Kong under Project PolyU 5312/10E and inpart by the Hong Kong Polytechnic University under GrantA/C 1-BB83.


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Bo Wu received the Ph.D. degree in photogrammetryand remote sensing from Wuhan University, Wuhan,China, in June 2006.

From July 2006 to July 2009, he was a Postdoc-toral Researcher and a Research Associate (Engi-neering) with the Mapping and GIS Laboratory, OhioState University, Columbus, working on NASA-funded projects for Mars and Lunar exploration mis-sions including Mars Rover localization and landingsite mapping, and lunar topographic mapping. SinceJuly 2009, he has been an Assistant Professor with

the Department of Land Surveying and Geo-Informatics, The Hong Kong Poly-technic University, Kowloon, Hong Kong, mainly working on planetary map-ping, automated photogrammetry, and 3-D geographic information systems.He is the Principal Investigator of a project for precision lunar topographicmapping by integrating multisource lunar imagery and laser altimeter datafunded by the Research Grants Council of Hong Kong.

Dr. Wu was a recipient of the Duane C. Brown Senior Award (Photogram-metry) in 2009.


Jian Guo received the B.S. degree in geographicinformation system from Liaoning Technical Uni-versity, Fuxin, China, and the M.S. degrees in pho-togrammetry and remote sensing from the ChineseAcademy of Surveying and Mapping, Beijing,China, and Liaoning Technical University. She iscurrently working toward the Ph.D. degree with amajor in photogrammetry and remote sensing atThe Hong Kong Polytechnic University, Kowloon,Hong Kong.

Subsequent to finishing her M.S. degree, she waswith The Hong Kong Polytechnic University as a Research Associate fromApril to September 2009. Her research interests include global mapping usingmultitemporal MODIS data and lunar mapping using multisource data. She iscurrently working on a project for precision lunar topographic mapping fromthe integration of multisource lunar imagery and laser altimetry data.

Miss Guo was a corecipient of the second prize for Science and TechnologyProgress in 2010 and the recipient of the second prize for Youth OutstandingPapers of 2008 “MapGIS Cup” in China.

Yunsheng Zhang received the B.E. degree in pho-togrammetry and remote sensing from Wuhan Uni-versity, Wuhan, China, in 2006. He is currentlyworking toward the Ph.D. degree in the State KeyLaboratory of Information Engineering in Surveying,Mapping and Remote Sensing, Wuhan University,major in photogrammetry and remote sensing.

During 2010, he was a Research Assistant withThe Hong Kong Polytechnic University, Kowloon,Hong Kong, and joined a research project on Marsand lunar mapping. His research activities include

image-based modeling, image matching for precise digital surface modelgeneration, computer vision in photogrammetry, and automated registration ofimage and LiDAR data.

Bruce A. King received the B.S. degree in surveyingfrom the University of Newcastle, Newcastle, NSW,Australia, in 1981.

During his studies, he was a Trainee Surveyor,Surveyor, and finally, Senior Surveyor with theBroken Hill Proprietary Ltd., Melbourne, Vic.,Australia, at the Newcastle Iron and Steel Works.In 1984, he joined the University of Tasmania,Tasmania, as a Lecturer in surveying where he de-veloped his interest in close-range photogrammetry.In 1989, Bruce returned to Newcastle to work on

research projects with TUNRA, ADAM Technology, and the MPS-2 analyticalstereoplotter and to undertake his Ph.D. studies on bundle adjustment of con-strained stereo pairs. Since 1995, he has been with The Hong Kong PolytechnicUniversity, Kowloon, Hong Kong, where he teaches and does research inphotogrammetry and LASER scanning.

Zhilin Li received the B.Sc. degree in photogramme-try and remote sensing from Southwestern JiaotongUniversity, Chengdu, China, in 1982 and the Ph.D.and D.Sc. (Doctor of Science) degrees from theUniversity of Glasgow, Glasgow, U.K., in 1990 and2009, respectively.

He is a Full Professor in geoinformatics(cartography/remote sensing/geographic informationsystem) with the Department of Land Surveyingand Geo-Informatics, The Hong Kong PolytechnicUniversity, Kowloon, Hong Kong. Since 1990, he

had worked at the University of Newcastle upon Tyne, Tyne, the University ofSouthampton, Southampton, and the Technical University of Berlin, Berlin,Germany, as Research Staff. In 1994, he took up a lectureship at CurtinUniversity of Technology, Perth, WA, Australia. He joined The Hong KongPolytechnic University as an Assistant Professor in 1996. He was promoted toAssociate Professor in 1998 and to Professor in 2003. He has published over120 journal papers.

Dr. Li was the recipient of the Schwidefsky Medal and Gino Cassinis Awardfrom the International Society for Photogrammetry and Remote Sensing in2004 and 2008, respectively.

Yongqi Chen received the Ph.D. degree from theUniversity of New Brunswick, Fredericton, NB,Canada, in 1983.

He is currently a Professor Emeritus and aVisiting Chair Professor with the Departmentof Land Surveying and Geo-Informatics, TheHong Kong Polytechnic University, Kowloon, HongKong. Before his retirement in 2009, he was ChairProfessor and Head of the department. He was amember of the Scientific Application Committee forthe China Chang’E-1 lunar mission.

integration of chang’e-1 imagery and laser altimeter data ... · apollo missions [1]–[3] and...

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