Integration of Chang'E-1 Imagery and Laser Altimeter Data for ...

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

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Integration of Chang’E-1 Imagery and Laser Altimeter Data for Precision Lunar Topographic Modeling Bo Wu, Jian Guo, Yunsheng Zhang, Bruce A. King, Zhilin Li, and Yongqi Chen

Abstract—Lunar orbital imagery and laser altimeter data are two major data sources for lunar topographic modeling. Most of the previous work has processed imagery and laser altimeter data separately. Usually though, there are inconsistencies between the topographic models derived from them. This paper presents an endeavor to integrate the Chang’E-1 imagery and laser altimeter data for consistent and precision lunar topographic modeling. A combined adjustment model for the Chang’E-1 imagery and laser altimeter data is developed, in which the participants are the laser altimeter points, image exterior orientation (EO) parameters, and tie points collected from the stereo images. A weighting scheme is designed for the participants in the adjustment, and a local surface constraint is imposed to improve the adjustment performance. The output of the combined adjustment is the refined image EO parameters and laser ground points. Experimental results using the Chang’E-1 data in the Apollo 15 and 16 landing site areas show that the proposed combined adjustment approach can reduce the misregistrations between the imagery and the laser altimeter data by a maximum of 1–18 pixels in image space. The Japanese SELenological and ENgineering Explorer (SELENE) laser altimeter data at the Apollo 15 and 16 landing site areas are employed for comparison analysis. Small shifts between the SELENE and Chang’E-1 laser altimeter data were found. The topography derived from Chang’E-1 data after the combined adjustment shows a relatively consistent trend with the topography determined by the SELENE laser altimeter data. Index Terms—Chang’E-1 imagery, Chang’E-1 laser altimeter data, imagery and laser altimeter data integration, lunar topographic modeling.

I. I NTRODUCTION

L

UNAR topographic information is of paramount importance for lunar exploration missions and lunar scientific investigations. Precision lunar topographic modeling and assessment from multisource data is also a challenging task.

Manuscript received January 11, 2011; revised March 29, 2011; accepted May 1, 2011 Date of publication June 6, 2011; date of current version November 23, 2011. B. Wu, J. Guo, B. A. King, Z. Li, and Y. Chen are with the Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic 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 Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430072, China, and also with the Department of Land Surveying and GeoInformatics, 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 online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2011.2153206

Starting from the 1960s, a vast amount of lunar imagery and laser altimeter data have been collected and processed in the Apollo missions [1]–[3] and the Clementine mission [4], [5]. More recently, China launched its first lunar probe Chang’E-1 in October 2007. Onboard the Chang’E-1spacecraft, there is a three-line array charge-coupled device (CCD) camera system (nadir, forward, and backward) providing lunar surface imagery and a laser altimeter generating range measurements covering the whole Moon [6], [7]. The Japanese lunar mission SELenological and ENgineering Explorer (SELENE) was successfully launched in September 2007 [8]. The U.S. also successfully launched its Lunar Reconnaissance Orbiter (LRO) to the Moon in June 2009 [9]. Among the payloads onboard the SELENE and LRO are orbiter cameras and laser altimeters with different configurations that collect data at various levels of resolution. These new data sets enable a new era of lunar topographic modeling with the capabilities of providing detailed and precision lunar topographic information. In lunar topographic models derived from lunar orbiter imagery and laser altimeter data, usually, there are inconsistencies due to the unavoidable errors (e.g., errors from sensor positions and orientations). Most of the previous related research processed lunar orbiter imagery and laser altimeter data separately and sometimes performed a comparison [4], [10]–[14]. However, it should be noted that correlation of lunar imagery and laser altimeter data has the potential to produce consistent topographic information [15]. Moreover, based on the previous research reports using space/airborne imagery or laser altimeter data to derive topographic products on earth applications, measurement from stereo imagery will generally provide better accuracy in the horizontal direction than in the vertical direction [16], [17], while laser altimetry is known to produce better vertical accuracy than horizontal accuracy [18], [19]. Therefore, there is also potential to produce lunar topographic information with better accuracy through an integration of the lunar imagery and laser altimeter data, which cannot be achieved when only using the data from a single sensor. This paper aims at the correlation and integration of the Chang’E-1 imagery and laser altimeter data through a combined adjustment method to reduce the inconsistencies between them and, subsequently, to produce precision lunar topographic models. After presenting a literature review on lunar topographic modeling from various lunar orbital imagery and laser altimeter data, a combined adjustment approach for Chang’E-1 imagery and laser altimeter data is presented in detail. Chang’E-1 stereo images (forward and backward) and

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associated laser altimeter data at the Apollo 15 and 16 landing site areas are employed for tests. Based on the developed approach, precision topographic models from the Chang’E-1 data at Apollo 15 and 16 landing site areas are derived. They are then compared with the Japanese SELENE laser altimeter data. Finally, concluding remarks are presented and discussed. II. R ELATED W ORK In the Apollo era, a variety of photographic sources collected during the Apollo lunar program were used for topographic modeling. A series of lunar maps at scales of 1 : 1 000 000 and 1 : 250 000 have been produced using the metric camera photographs from Apollo 15, 16, and 17 missions [1], [2]. The U.S. Geological Survey (USGS) conducted metric camera mapping for experimental maps and specific site maps using Apollo images. Examining this metric photography on the analytical stereoplotter showed standard errors of horizontal and vertical repeatabilities of ±7.4 and ±16.4 m, respectively [3]. The laser altimeter attached to the metric camera systems onboard these three Apollo missions had a ground footprint of about 20 m and had also been used for topographic modeling tasks. From February to May 1994, the Clementine spacecraft successfully mapped the entire Moon at a resolution of 125– 250 m/pixel using the ultraviolet-visible (UVVIS) and nearinfrared (NIR) cameras. A global UVVIS Digital Image Model of the Moon at 100 m/pixel was generated by the USGS [10]. Laser altimeter data from Clementine were collected and used to generate a topographic field of the Moon, which has an absolute vertical accuracy of approximately 100 m and a spatial resolution of 2.5◦ [4]. In 2006, USGS released Unified Lunar Control Network (ULCN) 2005 consisting of the 3-D position of 272 931 points, which is based on a photogrammetric solution of 43 866 Clementine images and earlier data [20]. The recent Chinese Chang’E-1 mission successfully returned 1098 orbiter images with a spatial resolution of 120 m, which cover the whole lunar surface. A global digital elevation model (DEM) has been produced using these images and preliminary results have revealed that the grid size for the DEM is up to 500 m and the planar positioning accuracy is about 370 m [11]. The laser altimeter onboard the Chang’E-1 spacecraft generated range measurements covering the whole Moon with spacing resolution of 1.4 km for the along-track direction and 7 km for the cross-track direction (at the equator). A Chang’E-1 Lunar Topography Model s01 (CLTM-s01) was produced using more than 3 million range measurements from the laser altimeter, which is a global topographic model of the Moon with a vertical accuracy of approximately 31 m and a spatial resolution of 0.25◦ [12]. Various topographic maps (2- or 3-D) of some prominent lunar geologic regions including major mares, mounts, and craters have also been produced using the Chang’E-1 imagery or laser altimeter data [21]. The Japanese lunar explorer SELENE successfully acquired stereoscopic images with 10-m resolution using its push-broom Terrain Camera, which almost covers the entire surface of the Moon. Topographic products including orthophoto maps and DEMs 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 with a height resolution of 5 m at a sampling interval smaller than 2 km. Important lunar global parameters such as the radii, the center of mass, and the highest and lowest points were derived from the SELENE laser altimeter data [23]. NASA’s LRO acquired 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 landing sites and future potential landing sites. The laser altimeter onboard the LRO is a pulse detection altimeter that incorporates a five-spot X-pattern that measures the distance to the lunar surface at five spots simultaneously. Each spot has a diameter of 5 m, and the spots are 25 m apart. The five-spot pattern provides five adjacent profiles for each track, 10–12 m apart over a 50–60 m swath, with combined measurements in the along-track direction every 10–12 m [35]. The ground track spacing for the laser altimeter data of LRO is 0.1◦ (4.5 km at the equator). A topographic map of the near side of the Moon has been generated using 1 billion LRO laser altimeter measurements [24]. Overall, the previous and recent lunar missions have collected vast amounts of lunar imagery and laser altimeter data at different resolutions and levels of uncertainty. However, most of the previous related research, as described previously, processed the orbiter imagery and laser altimeter data separately. There are rare research reports from the past emphasizing the correlation or integration of the lunar imagery and the laser altimeter data to produce better lunar topographic models. Rosiek et al. [25] endeavored to combine the Clementine images with the Clementine laser altimeter data, in which the Clementine global mosaic was used to establish horizontal control and Clementine laser altimeter points were used for vertical control. However, due to the marginal overlap between stereo models, the geometry of the photogrammetric network was weak and resulted in stereo models that did not align with each other. Most recently, Di et al. [15] presented a method of coregistration of Chang’E-1 stereo images and laser altimeter data to reduce the inconsistency between them. In their method, a DEM is generated first from the stereo images, and then, the DEM is registered to another DEM interpolated from the laser altimeter data through surface matching using a 3-D rigid transformation model. Consequently, the exterior orientation (EO) parameters of the images are adjusted using the rigid transformation model so that the images and laser altimeter data are coregistered. However, the DEM from laser altimeter data are fixed in the registration process; therefore, the quality of the final topographic products is dependent on the accuracy of the laser altimeter data. Integrated processing of orbital imagery and laser altimeter data 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 has been studied using an adjustment method, and results indicated that the large misregistration between the two data sets can be corrected to a certain extent [26]. Similar efforts focusing on the precision registration between MOC and MOLA data with selected candidate landing sites have been made [27]. The combination of the High Resolution Stereo Camera (HRSC)

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

images and MOLA data has also been studied, in which the HRSC images and MOLA data are processed in the same bundle adjustment and the HRSC images are adjusted to fit the MOLA data [28]. It should be noted that the resolutions of the Chang’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 for MOC imagery, the resolution is up to 1.4 m/pixel), and this will bring more uncertainties and difficulties to the integrated data processing. Based on the previous research, this paper presents a method of integrating Chang’E-1 imagery and laser altimeter data through a strict combined adjustment model to take advantages of the two types of data sets and to reduce the inconsistencies between them and, subsequently, to generate precision lunar topographic models. III. C OMBINED A DJUSTMENT OF C HANG ’E-1 S TEREO I MAGERY AND L ASER A LTIMETER DATA The Chang’E-1 data set used in this paper is the Level 2C data released by the Chinese Academy of Sciences, which has already been processed for radiometric, geometric, and spectrophotometric corrections [29]. However, no tracking data or kernel data covering the spacecraft’s trajectory and pointing information 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 points are provided. For the imagery, no EO information for the Chang’E-1 images is available. Only in the image head file are the latitude and longitude of the start and end pixels for each row in the image provided. The backward and forward images are used in this paper to form a stereo pair since they provide the maximum convergent angle. For the convenience of algorithm implementation, the experimental data sets of Chang’E-1 imagery and laser altimeter data at the Apollo 15 and 16 landing sites used in this paper have been transferred to the local topocentric coordinate systems. The origin of the topocentric coordinate system is located at the center of the study area. Three perpendicular coordinate axes are defined based on a tangential plane of lunar surface at the origin point. The X-axis is oriented eastward, the Y -axis is northward, and the Z-axis is toward up perpendicular to the plane. By using the latitude and longitude of the start and end pixels of each row in the Chang’E-1 image as references, the Chang’E-1 laser altimeter points can be overlaid on the images directly. Fig. 1 shows the Chang’E-1 images and associated laser altimeter data at the Apollo 15 landing site. Fig. 1(a) and (b) shows the planar and 3-D views of the laser altimeter data overlaid on a reference image (backward), respectively. Significant elevation variations are noticed due to the mountainous areas in the bottom, middle, and top parts. For the same laser altimeter points overlaid on the backward and forward images, the overlaid locations on both images should be the homologous points (the same terrain features) in the ideal case; however, there exist large inconsistencies between them due to the unavoidable errors (e.g., errors from sensor positions and orientations). Fig. 1(c)–(e) shows the detailed views of three typical areas in Fig. 1(a), in which the left images show the

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laser altimeter data overlaid on the backward image and the ones on the right show the same laser altimeter data overlaid on the forward image. Using the overlaid laser points on the left images as references, their correct homologous points on the right image are marked with lines and dots. As can be seen from Fig. 1(c)–(e), inconsistencies as large as 15 pixels (about 1.8 km on the ground considering the image resolution of 120 m/pixel) can be found. The following sections describe a combined adjustment method that can be used to eliminate these inconsistencies. A. Overview of the Approach The combined adjustment integrates Chang’E-1 stereo images and laser altimeter data through a strict mathematic model. Since the Level 2C data do not provide the spacecraft’s trajectory and pointing information, a few 3-D control points selected from ULCN 2005 were used to help derive the initial EO parameters of the Chang’E-1 stereo images using photogrammetric techniques [30]. For the experimental data sets used in this paper, six control points distributed in the whole study area were selected from ULCN 2005 and were used to calculate the initial EO for both the stereo images. Tie points were identified from the stereo images through image matching, and they are evenly distributed over the images. The ground coordinates of the tie points can be obtained using the tie points and the initial image EO parameters through a space intersection. With the initial image EO parameters, the image coordinates of the laser ground points on the stereo images can also be derived through a backprojection. The image EO parameters, the tie points on the stereo images, the ground coordinates of the tie points, the laser ground points, and the image coordinates of laser ground points are used as observables in the combined adjustment model. A local surface constraint between the calculated ground coordinates of the tie points and the laser ground points is employed in the adjustment model to confine the adjustment process. The final output of the adjustment is the improved image EO parameters and improved ground coordinates of the laser points, from which precision lunar topographic models can be produced. The framework of the combined adjustment approach for the Chang’E-1 imagery and laser altimeter data is shown in Fig. 2. B. Combined Adjustment Model For Chang’E-1 stereo images, the relationship of a 3-D ground 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 ) (1) m31 (XP −XS )+m32 (YP −YS )+m33 (ZP −ZS )

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

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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 altimeter data 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 the EO parameters of the images. The Chang’E-1 CCD camera is a three-line pushbroom camera, which means each line on the image has one set of EO parameters. Changes of EO parameters can be modeled by a polynomial function. A third-order polynomial function is used in this paper as follows: XS (r) = a0 + a1 r + a2 r2 + a3 r3 YS (r) = b0 + b1 r + b2 r2 + b3 r3

ZS (r) = c0 + c1 r + c2 r2 + c3 r3 ϕ(r) = d0 + d1 r + d2 r2 + d3 r3 ω(r) = e0 + e1 r + e2 r2 + e3 r3 κ(r) = f0 + f1 r + f2 r2 + f3 r3

(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 the image row r. ai , . . . , fi (i = 0, 1, 2, 3) are the coefficients of the polynomials.


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the image EO parameters should be consistent with a local surface determined by the nearby laser ground points. X4 links to the elevation of the ground positions of the tie points (the details regarding the local surface constraint are discussed in Section III-D). As mentioned before, the image coordinates of the laser points are initially derived by backprojecting the laser ground points onto the stereo images using the initial image EO parameters. The initially determined image coordinates of the laser points on the stereo images are not necessarily the same homologous points. Instead, there will be inconsistencies between them, as shown in Fig. 1. However, they will be corrected in the combined adjustment and the consistent image point locations, the improved image EO parameters, and the refined ground locations of the laser points can be obtained. The adjustment is based on a least squares approach. C. Weight Determination in the Combined Adjustment

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

After linearization of (1), the observation equations for the combined 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 observation vector, A is the coefficient matrix containing the partial derivatives from each observation, and P is the a priori weight matrix of the observations that reflects measurement quality and the contributions of the observations to the final result. The participants in the combined adjustment include measurements and weighted parameters. In this paper, all image points are treated as measurements and all ground points and the EO parameters of the images are treated as weighted parameters. The weighted parameters will form a set of pseudo-observation equations in the adjustment [32]. In particular, the combined adjustment model in this paper includes the following four parts: V1 V2 V3 V4

= A1 X1 − L1 , P1 = A2 X1 + BX2 − L2 , = A2 X1 + BX3 − L3 , = CX4 − L4 , P4

P2 P3 (4)

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

Introducing pseudo observation equations is a useful and common treatment in adjustment methodology since it provides the flexibility to properly weight the participants in the adjustment [32]. However, it also brings difficulties about how to assign appropriate weights to the participants in the combined adjustment. In this paper, the tie points directly identified from the Chang’E-1 stereo images are considered to be the most accurate measurements in the adjustment model. Therefore, a unit weight of 1 is assigned to all the tie points, whose estimated standard deviation is one pixel in image space. The weights for other observations and weighted parameters can be determined accordingly. The laser altimeter ground coordinates are considered to be the second accurate data source in the adjustment, and a weight smaller than 1 is assigned to them based on their a priori variance. The image coordinates of the backprojected laser altimeter points and the ground coordinates of the tie points from space intersection receive much smaller weights in the adjustment due to the fact that they are calculated based on the inaccurate initial image EO parameters. It should be noted that, from previous experiences in photogrammetry [26] and this study, the adjustment model is less sensitive to the assignment of weights. Moderate changes in weight magnitude yield the same results. As for the weights of the image EO parameters in the adjustment, since the positional parameters and the orientation parameters are correlated and their exact precision is unclear, it is more difficult to determine proper weights for them. In this paper, a series of experiments using the data set at the Apollo 15 landing site area was performed to help determine the influences of different weights for each of the EO parameters on the adjustment results. First, a set of 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 of 10−5 was added to the weight of one of the EO parameters until it reached 10−50 . At the same time, the weights for the other EO parameters remained unchanged. A series of DEMs associated with different weights for each of the EO parameters

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Fig. 3. Different influences on the topography with different weights for the EO parameters in the adjustment. (a) DEM generated from the stereo images using the 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 by applying different weights to κ, and (d) DEM obtained using the heuristic weights for the EO parameters, in which the inset image shows the DEM directly interoperated from the laser altimeter data as a reference.

was generated from the stereo images using the final adjusted EO parameters. Fig. 3 shows the experimental results. Fig. 3(a) shows the 3-D view of the DEM generated by applying different weights to the EO parameters XS , YS , ϕ, and ω. No matter how the weights were assigned to these four parameters, the finally obtained DEMs remain the same. However, for the EO parameters ZS and κ, when the weights assigned to them were changed to 10−30 and 10−15 , respectively, the final DEMs changed significantly, as shown in Fig. 3(b) and (c), and they remain the same until the weights reached to 10−50 . The experiments indicate that the variations of the weights for XS , YS , ϕ, and ω in the adjustment have very little influences on the final surface topography, while the weights for ZS (related to the altitude of the sensor) and κ (related to the yaw angle of the sensor) play important roles in the adjustment. Then, a new set of weights (10−10 , 10−10 , 10−30 , 10−5 , 10−5 , 10−15 ) for the EO parameters (XS , YS , ZS , ϕ, ω, κ) were used in the adjustment model, and the DEM finally derived is shown in Fig. 3(d). The inset image in Fig. 3(d) shows the DEM directly interoperated from the laser altimeter data, which can be used as a reference for the actual topography. Comparing the DEMs generated using different weights for the EO parameters with the DEM directly interoperated from the laser altimeter data, the DEM shown in Fig. 3(a) has an average height difference of 692.97 m, the DEM in Fig. 3(b) has an 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 in Fig. 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 that special considerations for the weights of ZS and κ are necessary to derive the correct topography. D. Local Surface Constraint in the Combined Adjustment To alleviate the situation that the adjustment results are dependent on specific data sets and the specific weights of the participants in the adjustment, particularly for the weights assigned to the image EO parameter ZS and κ, an additional constraint is incorporated in the adjustment model, which is the local surface constraint. The idea behind the local surface constraint is that the ground positions of the tie points obtained through the intersection using the image EO parameters should be consistent with a local surface determined by the nearby laser ground points (Fig. 4). As shown in Fig. 4, a ground point O that is derived from a pair of tie points on the stereo images using the image EO parameters, its four neighbors A, B, C, and D from the nearest laser altimeter points can be obtained through searching the four 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 the original height of ground point O. d is the difference between Z and Z0 . We use d = 0 as an additional pseudo-observation in the combined adjustment, which is the last equation in (4). From the experiments in this paper, it is shown that adding the local surface constraint in the combined adjustment model


Fig. 4.

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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 site area. (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 on the forward image, (b) detailed view for Area 2, and (c) detailed view for Area 3. TABLE I S TATISTICS OF D ISCREPANCIES B EFORE AND A FTER A DJUSTMENT FOR THE DATA S ETS AT THE A POLLO 15 L ANDING S ITE A REA

is able to eliminate possible blunders in the adjustment participants. It alleviates the dependences on specific weights of the participants in the adjustment. It also enables the adjustment process to converge quickly. E. Results From the Combined Adjustment The Chang’E-1 data sets at the Apollo 15 landing site area have been used to evaluate the developed adjustment model. At first, 475 tie points are identified on the stereo images through image matching, which are evenly distributed over the images. They are used in the combined adjustment model as inputs. The residuals of the tie points before and after adjustment have been calculated. Before adjustment, the residual is 3.65 pixels in average with a maximum of 10.05 pixels. While after the adjustment, the residual is 1.62 pixels in average with a maximum of 2.51 pixels. This indicates that it is feasible to use the third-order polynomial function to model the EO parameters, and it also proves the good performance of the adjustment model in general. Fig. 5 shows the detailed results of the combined adjustment of the Chang’E-1 data sets at the Apollo 15 landing site

area. For the three selected areas marked on Fig. 1(a), the same point pairs of significant inconsistencies, as marked on Fig. 1(c)–(e), have been identified again using the lines shown in Fig. 5(a)–(c), respectively. As can be seen from Fig. 5, the previous inconsistencies have been removed, and now, the point pairs are almost the homologous points representing the same terrain features on the stereo images. One also notes that the inconsistencies in both the along- and cross-track directions have been reduced. To quantitatively evaluate the performance of the approach, we take the projected positions of the laser altimeter points on the backward image as references and calculate the discrepancies between their homologous points (from image matching) and the projected positions on the forward image to depict the inconsistencies between the imagery and the laser altimeter data. Table I lists the discrepancies in image space before and after the combined adjustment process for the three areas. From Table I, we can observe that the maximum and the RMSE of the discrepancies have been greatly reduced. Particularly for Area 3, which is a highly mountainous area with significant elevation changes, the RMSE of the discrepancies has been reduced from over ten pixels to about the one-pixel level.

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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) DEM generated 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 refined image 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 experimental results in object space. Fig. 6(a) is the DEM directly interpolated using the Chang’E-1 laser altimeter data at the Apollo 15 landing site area. Its resolution is 1.4 km (same as the spacing resolution in the along-track direction of the laser altimeter data). Through a reliable image matching method [33], 15 487 homologous points were obtained on the Chang’E-1 stereo images. Three-dimensional coordinates of these homologous points can be derived through a space intersection using the image EO parameters, and then, DEMs can be interpolated from them. Fig. 6(b) is the DEM generated from the Chang’E-1 stereo imagery using the initial image EO parameters. The resolution of this DEM is 360 m, which is three times the image resolution. As can be seen from Fig. 6(b), this DEM provides much more details compared with the DEM directly interpolated from the laser altimeter data in Fig. 6(a). However, its topography deviates from the latter due to the inaccurate image EO parameters. Fig. 6(c) shows the DEM generated from the stereo imagery using the refined image EO parameters after the combined adjustment. The DEM shows generally consistent topography with the DEM directly interpolated from the laser altimeter data and, at the same time, provides more topographic details, which indicates the good performance of the combined adjustment approach. To further examine the performances of the combined adjustment, two tracks of the laser altimeter data were selected for

detailed analyses at the Apollo 15 landing site area, as shown in Fig. 7. The information regarding the acquisition details of the two tracks of the laser altimeter data and the used stereo images are also shown in Fig. 7. For each track, three profiles were derived. The first profile was obtained by directly connecting the laser points on the track. The second profile was derived from the DEM generated from the stereo images before applying adjustment, as shown in Fig. 6(b). The third profile was derived from the DEM generated from the stereo images after applying adjustment, as shown in Fig. 6(c). Fig. 8 shows the elevation comparison of the profiles for the two tracks, in which the elevation values are in a local topocentric coordinate system. From Fig. 8, one can note that three profiles have generally the same trend for both tracks. However, the profiles derived from the DEMs before adjustment have large differences compared with the other two due to the inaccurate initial image EO parameters. Particularly for Track 2, the middle part of the profile (green line) is below the other two profiles, while it is much higher than the other two at the right part, which corresponds to the highly mountainous area. The detailed statistics of the elevation differences between the profiles derived from the DEMs before or after adjustment and the profiles from the laser altimeter points are listed in Table II. The results indicate that the combined adjustment can significantly reduce the inconsistencies between the topographic models derived from the laser altimeter data and imagery.


Fig. 8.

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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 II S TATISTICS OF E LEVATION D IFFERENCES B ETWEEN THE P ROFILES FOR THE DATA S ETS AT THE A POLLO 15 L ANDING S ITE A REA

IV. F URTHER E XPERIMENTS AND C OMPARISON A NALYSES A. Experiments at the Apollo 16 Landing Site Area The same photogrammetric process and the combined adjustment approach have also been applied to the Chang’E-1 laser altimeter data and CCD imagery at the Apollo 16 landing site area, as shown in Fig. 9. Fig. 9(a) and (b) shows the planar and 3-D views of the laser altimeter data overlaid on a reference image (backward), respectively. Fig. 9(c) and (d) shows the detailed view of two selected areas in Fig. 9(a), in which the backward images are on the left side and the forward images on the right side. Points marked with red crosses were obtained by overlaying the laser altimeter points on the images directly. Using the overlaid laser points on the left images as references, their correct homologous points on the right image are marked with red lines and dots. As can be seen from the right images in Fig. 9(c) and (d), inconsistencies as large as eight pixels can be found. Points marked with cyan circles are obtained by backprojecting the same laser altimeter points on the 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 and after the combined adjustment process for the two areas. From Table III, we can observe that the maximum and the RMSE of the discrepancies have been effectively reduced. Similar to the experiments using the data sets at the Apollo 15 landing site area, two tracks of the laser altimeter data were selected for detailed analyses at the Apollo 16 landing site area, as shown in Fig. 10. The information regarding the acquisition details of the two tracks of the laser altimeter data and 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 the DEM 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 at the Apollo 15 landing site area, the inconsistencies between the topographic models derived from the laser altimeter data and imagery have been reduced after the combined adjustment. The detailed statistics of the elevation differences between the profiles derived from the DEMs before or after adjustment and the profiles from the laser altimeter points are listed in Table IV. For Track 1, there is a place showing reversed elevations between the profile generated from the laser altimeter points and the profile derived from the stereo images, as marked with a cyan rectangle in Fig. 11(a). We examined the distribution of the laser altimeter points and the actual image at this place and found that there is a crater in that region and the laser altimeter points just happen to pass across the crater. The inset image in Fig. 11(a) shows the crater, in which the laser altimeter points inside the crater are marked with blue points. The shape of the profile from laser altimeter points is the actual case in this region, while there are mistakes in the profile from the DEMs generated from images due to insufficient matched points (red dots 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 Data and SELENE Data In this paper, the generated topographic models at the Apollo 15 and 16 landing site areas from the Chang’E-1

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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 III S TATISTICS OF D ISCREPANCIES B EFORE AND A FTER A DJUSTMENT FOR THE DATA S ETS AT THE A POLLO 16 L ANDING S ITE A REA

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 altimeter data (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 the analysis of a large number of nearly colocated laser altimeter points from these two missions using a 12-parameter affine


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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 IV S TATISTICS OF E LEVATION D IFFERENCES B ETWEEN THE P ROFILES FOR THE DATA S ETS AT THE A POLLO 16 L ANDING S ITE A REA

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 directly overlaid together and (b) DEMs after registration.

transformation model cast in the form of rigid body motions and deformations. They found that the estimated relative rigid body motion and deformation parameters between the two reference frames are consistent (i.e., nearly zero estimates for the translations, rotations, and shear parameters) while the three strain parameters, which are similar in magnitude and sign, reveal a statistically significant scale difference of about 0.9 × 10−6 between the Chang’E-1 and SELENE reference frames. This paper provides detailed comparison in local regions between the data sets from these two missions. At the Apollo 15 landing site area, two DEMs were first interpolated using the Chang’E-1 and SELENE laser altimeter data. Fig. 12(a) shows the 3-D view of the two DEMs directly overlaid together. As can be seen, there are inconsistencies between the two DEMs, as indicated by the misalignments of the mountain peaks in the area. A six-parameter transformation (three translation parameters and three rotation parameters) was performed to register the SELENE DEM to the Chang’E-1

TABLE V T RANSFORMATION PARAMETERS B ETWEEN THE C HANG ’E-1 AND SELENE L ASER A LTIMETER DATA AT THE A POLLO 15 AND 16 L ANDING S ITE A REAS

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

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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 two data sets. For the Apollo 15 landing site area, there is about a 350-m offset between these two data sets in the horizontal direction, and the SELENE laser altimeter data is higher than the Chang’E-1 laser altimeter data by about 150 m. The deviations in rotations between these two data sets are small. After registering the SELENE DEM to the Chang’E-1 DEM using the obtained transformation parameters, they are aligned as shown in Fig. 12(b). The same process was performed for the Chang’E-1 and SELENE data sets at the Apollo 16 landing site area, and the results are shown in Table V. For the Apollo 16 landing site area, the horizontal deviation between these two data sets is about 1.5 km, which is larger than that in the Apollo 15 landing site area. The SELENE laser altimeter data are also higher than the Chang’E-1 laser altimeter data by about 90 m in the Apollo 16 landing site area. The deviations in rotations between these two data sets are quite small. The obtained transformation parameters were used to register the SELENE laser altimeter data to the Chang’E-1 reference frame and remove the systematic shifts between them. Fig. 13(a) and (b) shows the registered SELENE laser altimeter data directly overlaid on the Chang’E-1 images (backward images) at the Apollo 15 and 16 landing site areas, respectively. As with previous experimental analysis, two tracks of the SELENE laser altimeter data at each landing site area were selected for further analysis. They are shown in Fig. 13(a) and (b), and the details about the tracks are given in Fig. 13(c). For each track at the two experimental areas, three profiles were derived, as shown in Fig. 14. The first profile was obtained by directly connecting the SELENE laser altimeter points on the track (blue lines in Fig. 14). The second profile was derived from the DEM generated using the Chang’E-1 stereo images after applying adjustment (red lines in Fig. 14). The third profile was derived from the DEM directly interpolated from the Chang’E-1 laser altimeter points (cyan lines in Fig. 14). These profiles can be used to examine the relative topography derived from the data sets from these two missions.

From Fig. 14, it can be noticed that the general trend among these profiles is consistent for the four tracks in the two experimental areas. The profiles derived from the DEMs generated using the Chang’E-1 laser altimeter data show relatively smooth topography compared with the other two. This is because the DEMs are interpolated from the relatively sparse laser altimeter points, and they may not be sufficient to represent the actual topography in the area. The relative shapes of the SELENE profiles and the profiles from DEMs generated using the Chang’E-1 stereo images after applying adjustment are consistent. The detailed statistics of the elevation differences between these two types of profiles are listed in Table VI. The differences may be caused by the possible errors in the registration of the two data sets and the possible errors in the SELENE laser altimeter data and the Chang’E-1 data.

V. C ONCLUSION AND D ISCUSSION The combined adjustment approach presented in this paper provides a mathematical model to integrate the Chang’E-1 imagery and laser altimeter data for precision lunar topographic modeling. The experiment analyses using the data sets at the Apollo 15 and 16 landing site areas lead to the following conclusions. 1) This study reveals that inconsistencies may exist between the Level 2C Chang’E-1 imagery and laser altimeter data due to the unavoidable errors (e.g., errors from sensor positions and orientations), as indicated by the misregistrations from a few pixels to 18 pixels in image space at the Apollo 15 and 16 landing site areas. 2) The combined adjustment between the Chang’E-1 imagery and laser altimeter data can effectively reduce the misregistrations in image space to about the onepixel level and provide improved image EO parameters as well as improved laser ground points, which can be further used to produce consistent and precision lunar topographic models.


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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 the Apollo 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 VI S TATISTICS OF E LEVATION D IFFERENCES B ETWEEN THE P ROFILES F ROM THE S ELENE DATA AND THE C HANG ’E-1 I MAGERY

3) The derived lunar topographic models from Chang’E-1 data at the Apollo 15 and 16 landing site areas were compared with the Japanese SELENE laser altimeter data, and small shifts (350 m and 1.5 km in the horizontal direction, 150 and 90 m in altitude for the Apollo 15 and 16 data sets, respectively) between these two data sets were found. The topography derived from Chang’E-1 data after the combined adjustment shows a relatively consistent trend with the topography determined by the SELENE laser altimeter data. It is very valuable to integrate lunar imagery and laser altimeter data from different sensors to produce consistent and precise lunar topographic models. This will be more in demand when processing other high-resolution data for detailed topographic

modeling of the lunar surface, such as the data from the LRO mission and the Chinese Chang’E-2 mission. The experimental results reported in this paper are promising. Future research will study cross-mission data integration. Tests over areas covered by a larger number of images are also of interest. ACKNOWLEDGMENT The authors would like to thank the National Astronomical Observatories of the Chinese Academy of Sciences for providing the Chang’E-1 data sets. The work described in this paper was supported in part by a grant from the Research Grants Council of Hong Kong under Project PolyU 5312/10E and in part by the Hong Kong Polytechnic University under Grant A/C 1-BB83.

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[22] J. Haruyama, M. Ohtake, T. Matunaga, T. Morota, C. Honda, Y. Yokota, and Y. Ogawa, “SELENE (KAGUYA) Terrain camera observation results of nominal mission period,” presented at the 40th Lunar, Planetary Science Conf., Houston, TX, Mar. 23–27, 2009. [23] H. Noda, H. Araki, S. Tazawa, S. Goossens, and Y. Ishihara, “KAGUYA (SELENE) laser altimeter: One year in orbit,” Geophys. Res. Abstracts, vol. 11, p. EGU2009-3841-1, 2009. [24] H. Riris, J. Cavanaugh, X. Sun, P. Liiva, M. Rodriguez, and G. Neuman, “The Lunar Orbiter Laser Altimeter (LOLA) on NASA’s Lunar Reconnaissance Orbiter (LRO) Mission,” presented at the Int. Conf. Space Optics, Rhodes, Greece, Oct. 4–8, 2010. [25] M. R. Rosiek, R. Kirk, T. Hare, and E. Howington-Kraus, “Combining lunar photogrammetric topographic data with Clementine LIDAR data,” presented at the ISPRS WG IV/9—Extraterrestrial Mapping Workshop “Planetary Mapping”, Flagstaff, AZ, Oct. 14–15, 2001. [26] J.-S. Yoon and J. Shan, “Combined adjustment of MOC stereo imagery and MOLA altimetry data,” Photogramm. Eng. & Remote Sens., vol. 71, no. 10, pp. 1179–1186, 2005. [27] F. S. Anderson and T. J. Parker, “Characterization of MER landing sites using MOC and MOLA,” presented at the 33rd Lunar, Planetary Science Conf., League City, TX, Mar. 11–15, 2002. [28] H. Ebner, M. Spiegel, A. Baumgartner, B. Giese, and G. Neukum, “Improving the exterior orientation of Mars express HRSC imagery,” presented at the 21st ISPRS Congr., Beijing, China, Jul. 3–11, 2008. [29] Chinese Academy of Sciences, Lunar Exploration Project, General Design Section, Working References for the Lunar Explorer Project Scientific Application Users, Beijing, China2008. [30] B. King, J. Guo, Y. Q. Chen, J. X. Zhang, Y. H. Zhang, and X. G. Ning, “The lunar DEM generation process based on Clementine and Chang’E-1 images,” presented at the Int. Conf. Geo-Spatial Solutions Emergency Management, Beijing, China, Sep. 14–16, 2009. [31] Z. Z. Wang, Principles of Photogrammetry [With Remote Sensing]. Beijing, China: Press Wuhan Tech. Univ. Survey. Mapping, Publ. House Survey. Mapping, 1990. [32] E. M. Mikhail, J. S. Bethel, and J. C. McGlone, Introduction to Modern Photogrammetry. Hoboken, NJ: Wiley, 2001. [33] B. Wu, Y. S. Zhang, and Q. Zhu, “A triangulation-based hierarchical image matching method for wide-baseline images,” Photogramm. Eng. Remote Sens., vol. 77, no. 7, pp. 1–14, 2011. [34] H. B. ˙Iz, Y. Q. Chen, X. L. Ding, B. A. King, C. K. Shum, C. Wu, and M. Berber, “Assessing consistency of Chang’E-1 and SELENE reference frames using nearly-colocated laser altimetry footprint positions,” Chin. J. Sci., special issue on recent lunar missions, to be published. [35] D. E. Smith, M. T. Zuber, G. B. Jackson, J. F. Cavanaugh, G. A. Neumann, H. Riris, X. Sun, R. S. Zellar, C. Coltharp, J. Connelly, R. B. Katz, I. Kleyner, P. Liiva, A. Matuszeski, E. M. Mazarico, J. F. McGarry, A. Novo-Gradac, M. N. Ott, C. Peters, L. A. Ramos-Izquierdo, L. Ramsey, D. D. Rowlands, S. Schmidt, V. S. Scott, G. B. Shaw, J. C. Smith, J. Swinski, M. H. Torrence, G. Unger, A. W. Yu, and T. W. Zagwodzki, “The lunar orbiter laser altimeter investigation on the lunar reconnaissance orbiter mission,” Space Sci. Rev., vol. 150, no. 1–4, pp. 209–241, 2010.

Bo Wu received the Ph.D. degree in photogrammetry and remote sensing from Wuhan University, Wuhan, China, in June 2006. From July 2006 to July 2009, he was a Postdoctoral Researcher and a Research Associate (Engineering) with the Mapping and GIS Laboratory, Ohio State University, Columbus, working on NASAfunded projects for Mars and Lunar exploration missions including Mars Rover localization and landing site mapping, and lunar topographic mapping. Since July 2009, he has been an Assistant Professor with the Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, mainly working on planetary mapping, automated photogrammetry, and 3-D geographic information systems. He is the Principal Investigator of a project for precision lunar topographic mapping by integrating multisource lunar imagery and laser altimeter data funded by the Research Grants Council of Hong Kong. Dr. Wu was a recipient of the Duane C. Brown Senior Award (Photogrammetry) in 2009.


Jian Guo received the B.S. degree in geographic information system from Liaoning Technical University, Fuxin, China, and the M.S. degrees in photogrammetry and remote sensing from the Chinese Academy of Surveying and Mapping, Beijing, China, and Liaoning Technical University. She is currently working toward the Ph.D. degree with a major in photogrammetry and remote sensing at The Hong Kong Polytechnic University, Kowloon, Hong Kong. Subsequent to finishing her M.S. degree, she was with The Hong Kong Polytechnic University as a Research Associate from April to September 2009. Her research interests include global mapping using multitemporal MODIS data and lunar mapping using multisource data. She is currently working on a project for precision lunar topographic mapping from the integration of multisource lunar imagery and laser altimetry data. Miss Guo was a corecipient of the second prize for Science and Technology Progress in 2010 and the recipient of the second prize for Youth Outstanding Papers of 2008 “MapGIS Cup” in China.

Yunsheng Zhang received the B.E. degree in photogrammetry and remote sensing from Wuhan University, Wuhan, China, in 2006. He is currently working toward the Ph.D. degree in the State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, major in photogrammetry and remote sensing. During 2010, he was a Research Assistant with The Hong Kong Polytechnic University, Kowloon, Hong Kong, and joined a research project on Mars and lunar mapping. His research activities include image-based modeling, image matching for precise digital surface model generation, computer vision in photogrammetry, and automated registration of image and LiDAR data.

Bruce A. King received the B.S. degree in surveying from the University of Newcastle, Newcastle, NSW, Australia, in 1981. During his studies, he was a Trainee Surveyor, Surveyor, and finally, Senior Surveyor with the Broken 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 developed 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 analytical stereoplotter and to undertake his Ph.D. studies on bundle adjustment of constrained stereo pairs. Since 1995, he has been with The Hong Kong Polytechnic University, Kowloon, Hong Kong, where he teaches and does research in photogrammetry and LASER scanning.

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Zhilin Li received the B.Sc. degree in photogrammetry and remote sensing from Southwestern Jiaotong University, Chengdu, China, in 1982 and the Ph.D. and D.Sc. (Doctor of Science) degrees from the University of Glasgow, Glasgow, U.K., in 1990 and 2009, respectively. He is a Full Professor in geoinformatics (cartography/remote sensing/geographic information system) with the Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Kowloon, Hong Kong. Since 1990, he had worked at the University of Newcastle upon Tyne, Tyne, the University of Southampton, Southampton, and the Technical University of Berlin, Berlin, Germany, as Research Staff. In 1994, he took up a lectureship at Curtin University of Technology, Perth, WA, Australia. He joined The Hong Kong Polytechnic University as an Assistant Professor in 1996. He was promoted to Associate Professor in 1998 and to Professor in 2003. He has published over 120 journal papers. Dr. Li was the recipient of the Schwidefsky Medal and Gino Cassinis Award from the International Society for Photogrammetry and Remote Sensing in 2004 and 2008, respectively.

Yongqi Chen received the Ph.D. degree from the University of New Brunswick, Fredericton, NB, Canada, in 1983. He is currently a Professor Emeritus and a Visiting Chair Professor with the Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Kowloon, Hong Kong. Before his retirement in 2009, he was Chair Professor and Head of the department. He was a member of the Scientific Application Committee for the China Chang’E-1 lunar mission.