An assessment of surface matching for the automated co-registration of MOLA, HRSC and HiRISE DTMs

Earth and Planetary Science Letters 294 (2010) 520–533

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Earth and Planetary Science Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e p s l

An assessment of surface matching for the automated co-registration of MOLA, HRSC and HiRISE DTMs Shih-Yuan Lin a,⁎,1, Jan-Peter Muller a, Jon P. Mills b, Pauline E. Miller b a b

Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking, RH5 6NT, UK School of Civil Engineering and Geosciences, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK

a r t i c l e

i n f o

Article history: Accepted 22 December 2009 Available online 13 February 2010 Keywords: Mars DTM co-registration surface matching MOLA HRSC HiRISE

a b s t r a c t Martian topographic data has been collected by various exploration missions over the last decade. These products provide detailed topographic information and are invaluable for scientists to interpret and understand the geological and climate evolution which has occurred on Mars. In order to fully utilise these multi-sensor, multi-resolution and multi-scale Martian topographic products, a co-registration process has been developed which allows co-registration of Digital Terrain Models (DTMs) to be performed to co-align these multiple datasets. Surface matching is the core technique to implement this task and it is here assessed to determine the parameters of the most robust algorithm for DTM co-registration. Once this task was finished, the matching tool was developed accordingly with a decision algorithm. This algorithm was then employed to align DTMs derived from Mars Orbiter Laser Altimeter (MOLA), High Resolution Stereo Camera (HRSC) and High Resolution Imaging Science Experiment (HiRISE). For MOLA and HRSC DTMs, the coregistration was performed directly as the MOLA DTM acted as a reference surface within a bundle adjustment process. DTMs from different versions covering three HRSC orbital strips were used for the assessment process. As a result the mean bias of the height differences of a preliminary version HRSC DTM was significantly reduced from 38.596 m to 2.233 m, when compared against MOLA while the bias of a newer DTM was improved from 1.616 m to 0.161 m after matching. Regarding the co-registration of HiRISE and MOLA DTMs, a hierarchical approach employing a HRSC DTM as an intermediate dataset was assessed. The results demonstrated that the method is feasible and that the three DTMs were co-registered effectively. Due to the success highlighted in this paper, a surface matching tool is recommended to be applied to DTMs derived from multiple sources before these data are further used. Moreover, surface matching can be considered as an additional step of any workflow for Mars DTM creation. © 2010 Elsevier B.V. All rights reserved.

1. Introduction 1.1. Archival Mars DTMs Martian topographic data is an essential element for the scientific exploration of Mars, such as geological analysis, geomorphological interpretation, climatic and potentially astrobiological evolution, and landing site selection, etc. To fulfil increasing demands from geoscientists, more and more Martian Digital Terrain Models (DTMs) derived from various Mars exploration missions have been created and released for public use over the last decade. The first accurate systematic topographic product was based on the elevation measurements from the Mars Orbiter Laser Altimeter (MOLA). This laser altimeter was carried onboard the Mars Global ⁎ Corresponding author. Tel.: +44 1483 204245; fax: +44 1483 278312. E-mail address: [email protected] (S.-Y. Lin). 1 Now at Department of Land Economics, National Chengchi University, No. 64, Sec. 2, ZhiNan Road, Wenshan District, Taipei 11605, Taiwan. 0012-821X/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2009.12.040

Surveyor (MGS), a spacecraft that was launched on the 7th of November 1996. The first comprehensive Mars topography map was produced by the time the primary mission was finished on 30th of June 2001. More details of the MOLA can be found in Smith et al. (1999b, 2001). At the end of the mission, two forms of the MOLA data are available. Firstly, the raw altimetry profile data with precise orbit corrections are stored as the Precision Experiment Data Records (PEDRs). The PEDR data are available at NASA's Planetary Data System (PDS) (Smith et al., 1999a). The along-track spacing of the centre of the MOLA height points is about 330 m. The precision of MOLA range measurements approaches the limiting resolution of 37.5 cm on a smooth level surfaces and decreases down to ∼10 m on 30° slopes (Smith et al., 1999b). Secondly, the gridded format of MOLA, the MOLA Mission Experiment Gridded Data Records (MEGDRs), was produced. Based on the altimetry values from the MOLA PEDR products, the gridded DTM was created at resolutions of 4, 16, 32, 64, and 128 pixels per degree (Smith et al., 2003). After investigation, Neumann et al. (2001) reported that the vertical accuracy of the MOLA DTM is typically better than l m with respect to Mars' centre of

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mass based on height differences between orbital crossings. Given its high accuracy and global coverage, the MOLA data is deemed as the most consistent Mars DTM and is considered a topographic “base dataset” (Heipke et al., 2007; Kim and Muller, 2009). DTMs created using the image data provided by the High Resolution Stereo Camera (HRSC) is an increasingly popular Martian topographic product. This nine-look along-track stereo camera system was specially designed to meet the requirements of photogrammetry and cartography for mapping the complete surface of the Mars (Albertz et al., 2005; Scholten et al., 2005; Gwinner et al., 2009, 2010this issue). The acquired image data are therefore well suited for the automatic generation of Martian DTMs. The camera is still operational and up to now, the stereo image coverage of HRSC for images with resolution better than 20 m reaches 46.7% of the Martian surface while the coverage is up to 66.6% for images whose resolution is better than 40 m (Jaumann, 2008). Due to the characteristics of high resolution and the stereo imaging capability of the HRSC, the construction of DTMs of the Mars surface topography with grid spacing of 30–75 m is feasible (Albertz et al., 2005; Scholten et al., 2005; Gwinner et al., 2007; Heipke et al., 2007; Gwinner et al., 2009, 2010-this issue; Kim and Muller, 2009). The HRSC data are being systematically processed by the German Aerospace Centre (DLR) in Berlin (Scholten et al., 2005; Gwinner et al., 2008, 2009, 2010-this issue) and the products are archived both in the ESA's Planetary Science Archive (PSA) and the NASA PDS. In late 2006, the successful deployment of the NASA Mars Reconnaissance Orbiter (MRO) with the 25 cm High Resolution Imaging Science Experiment (HiRISE) instrument began to provide repeat-pass stereo image pairs and has provided an opportunity to produce very high resolution DTMs (McEwen et al., 2007). Typical images cover an area of 6 × 12 km. At this resolution, very detailed topographic information can be viewed in the HiRISE images. The Astrogeology Team at the United State Geology Survey (USGS) is currently the main institution creating and publishing HiRISE stereo DTMs. The USGS in-house software, Integrated Software for Imagers and Spectrometers (ISIS) (Gaddis et al., 1997; Anderson et al., 2004), and the commercial software SOCET SET can be employed to produce HiRISE DTMs with up to 1 m grid resolution. Details on geometric calibration and photogrammetric processing of HiRISE DTMs can be found in Kirk et al. (2008). HiRISE DTMs can be downloaded from the USGS's Planetary Interactive G.I.S.-on-the-Web Analyzable Database (PIGWAD) (USGS, 2008). The topographic products introduced above are all available for public usage. The data accessibility provides great value to scientists who need DTMs for diverse Mars explorations. It is noted that these datasets are obtained from different sensors and have various characteristics. Therefore there will be additional benefits if multiple topographic products can be analysed separately and/or exploited simultaneously. However, due to the differences in sensors and production techniques, these products may have translational shifts or angular rotation between each other. Hence it is crucial to coregister these multiple topographic datasets based on the same reference before further exploitation. To achieve this, a co-registration of the MOLA, HRSC and HiRISE DTMs is proposed and described here. 1.2. Co-registration of multiple Mars DTMs Co-registration of Earth topographic products is a crucial operation which depends on the correct selection and accurate measurement of control points (Fabris and Pesci, 2005) usually obtained from in situ GPS measurements. However although there were control points selected in the 1980s and early 1990s, a comprehensive selection and surveying of control points on the Martian surface has not yet been achieved. Hence an alternative method is here suggested. Surface matching is a technique used to carry out co-registration of point clouds and has been applied broadly in the fields of computer vision

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and geomatics. Its applications can be characterised as (i) registration of objects or surfaces comprised of 2.5-dimensional or threedimensional point feature data, (ii) detection of differences between objects or surfaces, and (iii) integration of datasets generated from different sources (Mitchell and Chadwick, 1999). Once the matching is finished, one surface is transformed and re-aligned to match more closely to the other surface. Examples of the applications of employing surface matching for co-registering multi-resolution, multi-temporal, multi-scale, and multi-sensor datasets can be found in Rosenholm and Torlegard (1988), Mills et al. (2005), Gruen and Akca (2005), Miller et al. (2007) and Waser et al. (2007). Due to these features, a surface matching technique is proposed here to perform automatic co-registration of point clouds representing the Mars topographic surface. The base algorithm for surface matching used in this paper is described by Mills et al. (2003). It is based on a seven-parameter, 3D conformal co-ordinate transformation, which defines the three rotations (ω, φ, and κ), three translations (Tx, Ty, and Tz) and a scale factor (s) required to relate two sets of 3D point clouds (Wolf and Dewitt, 2000). The 3D conformal co-ordinate transformation has been applied to match topographic surfaces derived from multiple sources, such as a matching between a DTM derived from Global Positioning System (GPS) and a photogrammetric DTM (Mills et al., 2003), DTMs created from the DMC digital airborne camera and Light Detection And Ranging (LiDAR) system (Zhang et al., 2006), Shuttle Radar Topography Mission (SRTM) C-Band and X-Band DTMs (Akca, 2007), and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) and LiDAR DTMs (Miller et al., 2009). It has been shown that the 3D conformal transformation is feasible when matching multiple sets of topographic surfaces, although distortions may be inherited in any DTM generated as a result of the fusion of various sensors. Here, the algorithm is employed to match multiple Mars topographic data. The following equation of a 3D conformal transformation is here applied: T

Xo = sM Xi + T

ð1Þ

where Xi are the 3D coordinates of a point in the initial object space. After an implementation of a function of the rotation matrix M (which is a combination of the three rotations ω, φ and κ), the translation vector T (which contains Tx, Ty and Tz) and the scale parameter s, the transformed 3D coordinates of the point (Xo) are achieved. Due to the lack of in situ control points on Mars, each point on Mars topographic surface effectively acts as a control point in height and contributes towards the solution of the transformation parameters. In this manner, the best fit of two surfaces is found by minimising the surface differences. Let us assume that there are two surfaces, S1 and S2, being matched, where S1 is the reference surface and S2 is the surface to be transformed. Instead of simply taking the nearest point on S2 to a point on S1 and using its height value, a better approximation can be made using an enclosing surface patch. A Delaunay triangulation of S1 is therefore constructed to give a table of triangles describing the reference surface. This can be used to find the enclosing triangle in the triangulation for a point on S2, enabling a better height value to be interpolated than if the single closest point was used. Clearly, any consistently large difference between the interpolated height values will imply that the surfaces are not in the correct position, and then computation of the least squares minimisation of vertical differences globally across the surfaces will be iterated. The transformation parameters are updated until a convergence criterion is reached and the transformation of S2 will take place at the end of the match (Buckley, 2003). As the Mars MOLA data provides an accurate global topographic dataset (Neumann et al., 2001), it is used as the reference surface (S1) for matching multiple Mars DTMs here.

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This paper first assesses the factors which might affect the performance of surface matching for Mars DTM co-registration. The results are applied to develop a robust matching tool in MATLAB to implement DTM co-registration. In order to test the feasibility and transferability, the tool is then applied to aligning MOLA, HRSC and HiRISE DTMs obtained from the public domain. Finally the results of the co-registration are analysed and presented.

formats of MOLA heights available from the NASA PDS: MOLA height points and a regular gridded MOLA DTM. The MOLA height points are a semi-regular 3D point cloud, while the gridded DTM is at 1 km resolution. This was created based on the irregular MOLA height points. As the reference surface plays such an important role during matching, an experiment was carried out to assess if different formats of reference DTM affected the results of the surface matching.

2. Assessment of surface matching for DTM co-registration 2.1. Factors for assessment An assessment of surface matching parameters for the automated co-registration of multi-resolution DTMs was carried out. A test section of HRSC h1011 DTMs (covering part of eastern Ares Vallis at approximately 1.12° to 8.776°N and 335.32° to 336.42°E) and the corresponding MOLA data were employed as test datasets in the experiment (Fig. 1). As the characteristics of DTMs derived from different sources are varied, four key features described below (reference DTM formats; number of points in the DTM; computation of surface differences; and threshold method) were tested to determine how these factors would affect the performance of surface matching for Mars DTM co-registration. 2.1.1. Reference DTM formats To perform surface matching, a reference surface needs to be triangulated and then a least squares minimisation of differences between the matching surface and the triangulated reference surface calculated. As MOLA is assumed to represent the most accurate terrain model of Mars it was inputted as the reference surface during the matching. As discussed in Section 1.1, there are currently two

2.1.2. Number of points in the DTMs It is commonplace to have DTMs with different spatial resolution. As a result, the number of points contained within the DTMs is likely to be different when they are employed for surface matching. For the test datasets used in this assessment, the spacing of the MOLA height points along each track is about 330 m (Smith et al., 1999b) while the resolution of the MOLA DTM is 1 km. The spatial resolution of archival HRSC DTMs on the ESA PSA ranges from 50 to 100 m (Gwinner et al., 2007, 2008, 2009, 2010-this issue). These DTMs with various numbers of points were used in this experiment to examine its influence on surface matching. For MOLA data coverage, there are 9725 MOLA height points (Fig. 1(c)) and 10 132 grid points derived from the 1 km MOLA DTM (Fig. 1(d)) covering the test area. While for the HRSC DTMs obtained from PSA, the spatial resolution was 75 m and the number of grid points was about one million. Due to the unbalanced point numbers between the adopted MOLA data and the HRSC DTM, and also considering the limited computer processing capability, the HRSC DTM was resized to produce DTMs with lower resolution varying from 200 m to 1200 m (only the original height values were used in the creation of resized DTM). They were all employed to match the MOLA data for assessment.

Fig. 1. HRSC and MOLA datasets used in the assessment. Left to right: (a) Colourised by height hill-shaded HRSC DTM, (b) HRSC ortho-image, (c) MOLA height point locations (colourised by height) superimposed on (b) and (d) MOLA grid points (colourised by height) superimposed on (b).

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2.1.3. Computation of surface differences Surface matching is a procedure which employs least squares iterative minimisation of differences between a reference and a matching surface. For this reason the method of calculating the surface difference is crucial. Two approaches for computing surface differences are commonly adopted in surface matching studies, namely vertical surface differences (Mitchell and Chadwick, 1999; Maas, 2002; Mills et al., 2003) and Euclidean distance (Wang et al., 2003; Bhandarkar et al., 2004; Gruen and Akca, 2005). In order to examine their effect on surface matching, two methods for computing surface differences were assessed in this paper.

The weight function proposed by Kraus and Pfeifer (1998) is adopted in this paper. However, as the type of the detected blunders is different, the function was further modified based on a multiple of the standard deviation of the residuals. In Eq. (2), σvi is the standard deviation of the residuals (vi), and the value for g is computed with a histogram of the residuals. For more details refer to Pfeifer et al. (1998) and Kraus and Pfeifer (1998). It is noted that the g value was re-calculated in each iteration. 8 1 vi ≤g < 4 wi = 1 = ½1 + ðvi −gÞ  g < vi ≤g + 3σvi ð2Þ : 0 g + 3σvi < vi

2.1.4. Threshold method During surface matching, minimisation of height differences between the two surfaces is calculated iteratively. At each iteration, the points with height differences over a given threshold value are flagged as outliers and marked for removal from the next iteration. Hence the determination of a threshold value is another critical task which might affect the performance of surface matching for DTM coregistration. Two manners of determining threshold values were assessed. The first one is referred to here as a global threshold. A pre-specified tolerance value was given prior to commencing the matching, and this fixed value was applied through an iterative computation to exclude points from the solution if they exceeded a certain value. The algorithm applied in Mills et al. (2003) employed the global threshold method. Regarding the Mars datasets, Ebner et al. (2004) investigated the height differences between the MOLA and HRSC DTMs, demonstrating that the average difference in height was on the order of 70 m. This value has proved to be reliable in the application of surface matching for noise reduction in the HRSC DTMs (Lin et al., 2008). An empirical value of 70 m was therefore adopted as the global threshold value in this experiment. An adaptive threshold was the other algorithm assessed in the experiment. This algorithm is based on the residual of each point derived from each iteration of the least squares adjustment. These residuals were inputted to an appropriate weight function to compute weights for each point, in which the points with large residuals were treated as blunders and their influence were mitigated through down-weighting (Pilgrim, 1996; Li et al., 2001; Miller et al., 2008).

In order to assess the factors introduced above, a total of 48 tests with various settings were performed. These tests were implemented using an in-house tool developed in the MATLAB programming system. The algorithms for various tests were modified based on the work explained in Section 1.2. Fig. 2 shows the overall workflow of the experiment on surface matching, the features for assessment during the matching are highlighted in the figure. 2.2. Assessment of surface matching First of all, the two datasets were converted to the sinusoidal map projection and the height was checked as being relative to a spherical reference body using the radius as 3396.190 km (this reference system was applied to all DTMs processed in this paper). Once the surface matching was finished in each test, the original HRSC DTM was transformed based on the resultant transformation parameters. Subsequently, the height differences between the MOLA height points and the grid points of the transformed HRSC DTM were computed. The derived height difference was considered as an indicator of DTM quality and was used to assess whether there was any improvement after surface matching. As the spot size of a MOLA footprint on the Martian surface is about 160 m (Smith et al., 1999b), a buffer distance of 160 m was applied to each MOLA point for the corresponding HRSC points. The HRSC grid points located in the buffer zone of the MOLA height points were selected and their height differences were computed. Using this method, the accuracy of the original HRSC DTM used for assessment was 1.400 ± 18.618 m. The factors stated in Section 2.1 were then assessed and described below.

Fig. 2. Workflows of the surface matching with the factors for assessment indicated in italic.

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Table 1 Statistics of height differences for assessing format of the MOLA.

Table 3 Statistics of height differences for assessing methods of computing surface difference.

MOLA format

Global threshold Count of convergent set

Average number of iterations

Mean bias (m)

Count of convergent set

Adaptive threshold Average number of iterations

Mean bias (m)

Global threshold

Points Grid

9 10

21 73

0.801 0.872

12 8

16 82

0.740 0.332

2.2.1. Format of the reference DTM The most obvious consequence was the long iteration time required to achieve convergence when a MOLA DTM of a regular grid format was used (Table 1). Compared with the distribution of the MOLA height points, the MOLA gridded DTM has a more comprehensive coverage across the area. Hence a longer computation time for iteration for the least squares adjustment was expected. With further investigation, it was found that the long iterative computation also resulted in more accurately matched DTMs when automatic adaptive threshold method was utilised (the mean bias was 0.332 m). 2.2.2. Number of points of the DTMs In order to understand the effects of the number of points in the DTMs employed for surface matching, a count of convergent sets and mean bias of the matched DTMs are listed in Table 2. It was observed that no matter what global or adaptive threshold method was applied, a lower mean bias was achieved when HRSC DTMs with resolutions of 600 m and 800 m were employed in the matching process. Although accurate results were also obtained from the DTM of 1200 m resolution, this was not considered in the assessment due to the small number of convergent matches. The results indicate that the ideal number of points of the matching DTM was one to two times higher than the one of the reference DTM. 2.2.3. Computation of surface difference Statistics related to the application of vertical and Euclidean distance are summarised in Table 3. In all cases it took less iterations to achieve a convergent matching when the vertical distance measure was used to compute the surface difference. In addition, except for the sets utilising global thresholds for matching HRSC and MOLA grid DTMs, the general trend shows that more accurate results were obtained when the vertical distance metric was applied. The lowest mean bias reached 0.268 m when MOLA gridded DTM, vertical distance and an adaptive threshold were employed. This result agrees with the suggestions made by Mitchell and Chadwick (1999), that topographic surfaces such as grid-based or irregular DTMs were highly favourable for minimisation of vertical differences in surface matching (Miller et al., 2008). 2.2.4. Threshold method As shown in Fig. 2, the algorithms were varied when different threshold methods were applied. The test results demonstrated that a lower number of iterations and more accurate matching were achieved when an automated adaptive threshold approach was

Euclidean distance and MOLA points Vertical distance and MOLA points Euclidean distance and MOLA DTM Vertical distance and MOLA DTM

Adaptive threshold

Average number of iterations

Mean bias (m)

Average number of iterations

Mean bias (m)

29 15 182 10

0.831 0.771 0.836 0.908

18 16 139 10

0.772 0.708 0.396 0.268

Table 4 Statistics of height differences for assessing threshold methods. Threshold method

Count of convergent set

Average number of iteration

Mean bias (m)

Global Adaptive

19 20

52 46

0.840 0.583

employed (see Table 4). In addition, Sets 4 and 28 were taken as examples to investigate the convergent behaviour with the different threshold methods. Once the matching was convergent in each set, the translations in the X and Y directions derived from each iteration were illustrated (Fig. 3). From the plot, it is clear that the set utilising an adaptive threshold (Set 28) took a shorter computation iteration time to reach a stable solution. As all the other settings were identical in Sets 4 and 28, the depicted convergence curves imply that the adaptive threshold was a more robust algorithm for the matching. 2.3. Summary of assessments Although the accuracy of the archived HRSC DTMs was improved by updating the exterior orientation files by performing bundle adjustment with MOLA data (Ebner et al., 2004; Gwinner et al., 2009, 2010-this issue), our experiments have shown the feasibility of upgrading the accuracy of the archived HRSC DTMs by applying surface matching. The resultant statistics (Tables 1–4) indicated that the HRSC DTM fitted to the MOLA data better through a smaller mean bias. Meanwhile this also implied that the alignment of the two topographic datasets was improved. This experiment not only showed the feasibility of the application of surface matching for the co-registration of Mars MOLA and HRSC DTMs, but also assessed critical key features for matching MOLA and HRSC DTMs. As a result, a regular gridded MOLA DTM was more suitable for this technique to be a reference surface rather than an irregular MOLA point cloud. In addition, an accurate result could be achieved if the number of matched points from the HRSC DTM was one to two times higher than the number of points in the reference DTM. Regarding the implementation of the algorithms, it was demonstrated that the least squares surface matching was more robust when performing a vertical distance minimisation using the automated adaptive threshold method. Since such a potentially significant tool for the co-registration of Mars MOLA and HRSC DTM

Table 2 Statistics of height differences for assessing number of points of the matching DTM. Spatial resolution

Number of points

Global threshold Convergent matching

Mean bias (m)

Convergent matching

Adaptive threshold Mean bias (m)

200 400 600 800 1000 1200

212 364 53 091 23 664 13 398 8618 5916

Sets 1, 7, and 19 Sets 2, 8, 14, and 20 Sets 3, 9, 15, and 21 Sets 4, 10, 16, and 22 Sets 11, 17, and 23 Set 24

1.196 0.979 0.682 0.635 0.892 0.520

Sets Sets Sets Sets Sets Sets

0.910 0.721 0.482 0.447 0.522 0.487

25, 31, and 37 26, 32, and 38 27, 33, 39, and 45 28, 34, 40, and 46 29, 35, 41, and 47 30 and 36

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Fig. 3. Convergence behaviour for global and adaptive threshold methods.

was developed and tested, more datasets were tested. These are introduced in the following section. 3. Co-registration of HRSC and MOLA DTMs The co-registration tool was shown to be suitable for aligning MOLA and HRSC DTMs. In order to demonstrate its transferability and general applicability, this tool was further tested on the coregistration of datasets over various topographic features. Because not all of the HRSC DTMs have been updated using bundle adjustment and archived in the PSA, the other purpose of the experiment was to inspect the performance of surface matching on different versions of HRSC DTMs. Three orbital HRSC DTMs (h1196_0000, h1947_0001 and h1984_0000) were downloaded from the PSA and the preliminary version DTMs obtained through the Topographic Mars Information System (TMIS), the Co-investigator database of HRSC on Mars Express, were inputted for examinations. To clarify the HRSC DTMs of different versions, the data extracted from PSA but processed at DLR are refereed as “new” DTMs while the ones obtained from TMIS are called “old” DTMs in this paper. 3.1. h1196_0000 The first one was the DTM for HRSC orbit h1196. The DTM covered the Persbo Crater and is located over the eastern part of Athabasca Valles at 6.764° to 8.957°N and 156.377° to 157.791°E. Surface matching was performed to match the old (version 04) and new versions of HRSC h1196 DTMs to the MOLA DTM respectively. The colour shaded relief HRSC and the corresponding MOLA DTM are shown in Fig. 4(a) and (b). From the colourised by height hill-shaded DTM, it is observed that the DTM generally represented a low relief terrain, except the two craters and a couple of hills. The procedure for DTM quality assessment followed the method described in Section 2.2. The statistics derived from the assessments before and after surface matching are listed in Table 5. For the case of the old HRSC DTM, the accuracy (defined hereafter as the mean bias) was considerably upgraded after surface matching (from − 54.871 m to − 4.228 m). For further analysis of the resolved vertical difference between the two surfaces, an accuracy map was drawn. The HRSC DTM points located in the buffer of the MOLA height points were plotted in their correct sinusoidal planimetric positions. Moreover, these points were classified into 19 levels according to the difference values and colour-coded. As shown superimposed in Fig. 4(d) and (e), the tracks of MOLA points over h1196 HRSC DTM and the associated HRSC DTM points before and after surface matching respectively, are well illustrated in the accuracy maps. From the rendered colour it was evident that the overall HRSC points were lifted to fit the MOLA points after matching, reflecting the information revealed by the statistics. In

addition, some areas with obvious vertical difference, such as the edge of the northernmost large crater in the DTM, were improved after surface matching. While for the new HRSC DTM, although its accuracy has been largely improved through bundle adjustment (Ebner et al., 2004; Gwinner et al., 2009, 2010-this issue), the potential of achieving improved accuracy by applying surface matching was also demonstrated (from 0.865 m to − 0.153 m, listed in Table 5). 3.2. h1947_0001 The DTM covering HRSC orbital strip h1947 covers the middle part of Ares Vallis at 6.278° to 12.635°N and 332.133° to 333.246°E. The DTM includes diverse terrain features. The main outflow channel of Ares Vallis is across the top half part of the DTM, and a number of craters of various sizes were distributed in the remaining part of the DTM. The colour shaded relief HRSC DTM and the corresponding MOLA DTM are shown in Fig. 5(a) and (b). The statistics and the accuracy maps of the h1947 DTM assessment before and after surface matching are shown in Table 6 and Fig. 5(d) and (e). The application of surface matching again showed its utility for aligning old HRSC and MOLA DTMs (from − 20.475 m to −0.158 m). In this case, the matched old DTM was even more accurate than the new DTM (3.255 m). From the accuracy map of the old HRSC DTM, it was observed that the large differences occurring at the edge of the top and bottom craters (refer to as C1 and C3 outlined in Fig. 5(d) and (e)) were diminished after surface matching, although some large difference points still remained in the edge of the middle crater (C2). 3.3. h1984_0000 The DTM covering HRSC orbital strip h1984 covers the eastern part of Candor Chasma and a small section of Coprates Labes. The extent of the DTM is 6.799° to 13.848°S and 295.381° to 296.542°E. From the DTM and ortho-image shown in Fig. 6(a), (b) and (c), the dramatic height variation featuring ridges and steep valleys in the chaotic regions of the Candor Chasma and Coprates Labes is obvious. The assessment of the old version HRSC DTM revealed that the DTM accuracy is about −40 m (Table 7). Also, the distribution of points is shown in the accuracy map (Fig. 6(d)). From the rendered colour, it is noted that these points mainly located at or near the chaotic regions (outlined in Fig. 6(d)). This issue was addressed after surface matching. The accuracy of the matched DTM was upgraded to 2.314 m and the number of points with large height differences was reduced. Furthermore, the disparity between the MOLA, original and matched HRSC DTMs was investigated by inspecting various profiles. Four profiles across the area of h1984 DTM are shown in Fig. 7. The

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Fig. 4. (a) Colourised by height hill-shaded HRSC h1196 DTM, (b) associated hill-shaded MOLA DTM, (c) HRSC h1196 ortho-image, (d) accuracy map before surface matching and (e) after matching.

solid line, dash–dot line and dotted line represented the profiles derived from the MOLA, original and matched HRSC DTMs respectively. Along the profiles plotted, it is found that the discrepancies between MOLA and HRSC DTMs were improved after surface matching.

Table 5 Statistics of height differences for assessing h1196 DTM. HRSC DTM version

Status

HRSC points located in the MOLA buffer

Maximum (m)

Minimum (m)

Mean (m)

Std. dev. (m)

Old

Original Matched Original Matched

11 483 11 516 45 569 45 268

305.710 438.642 589.810 581.045

− 639.340 − 633.470 − 346.240 − 346.867

− 54.871 − 4.228 0.865 − 0.153

±63.470 ±62.428 ±42.627 ±42.853

New

4. Co-registration of HiRISE, HRSC and MOLA DTMs Since a successful co-registration of MOLA and HRSC DTMs over a factor of 15 in resolution using surface matching has been demonstrated, a data fusion with another Mars topography product, HiRISE stereo DTM, was attempted and is described in this section. However, as the area that any HiRISE DTM covers is small and also considering the 3 orders of magnitude difference in DTM resolution between MOLA (1 km) and HiRISE (1 m) DTMs, it would be difficult to apply the MOLA data as a reference in the surface matching. Therefore a hierarchical approach is here illustrated. The HRSC DTM was first employed as an intermediate dataset and it was matched to the MOLA DTM. The matched HRSC DTM was subsequently adopted as the reference surface in a surface matching with HiRISE DTM. The HRSC DTM could provide more terrain features than MOLA and is well co-registered with MOLA, hence it was suitable to replace MOLA in the case of fusion with a HiRISE DTM. As a result, a co-registration of all three DTMs was achieved.

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Fig. 5. (a) Colourised by height hill-shaded HRSC h1947 DTM, (b) associated hill-shaded MOLA DTM, (c) HRSC h1947 ortho-image, (d) accuracy map before matching and (e) after matching.

The USGS HiRISE DTM selected for this study consisted of bright gully deposits in a crater in the Centauri Montes region (Pelletier et al., 2008). The extent of the DTM was 38.317° to 38.455°S and 96.744° to 96.872°E (see Fig. 8). To cover the HiRISE DTM, the DTM covering HRSC orbital strip h2510 was proposed as the intermediate data. However, as the new DTM was not available on the ESA PSA at the time this experiment was conducted, the old version one obtained from the TMIS database was employed instead. A section at 37.718° to 39.118°S and 95.588° to 97.981°E of the h2510_0001 HRSC DTM was

Table 6 Statistics of height differences for assessing h1947 DTM. HRSC DTM version

Status

HRSC points located in the MOLA buffer

Maximum (m)

Minimum (m)

Mean (m)

Std. dev. (m)

Old

Original Matched Original Matched

27 026 26 898 189 938 189 802

372.900 353.431 279.760 274.233

− 468.630 − 254.366 − 200.080 − 200.187

− 20.475 − 0.158 3.255 0.114

±51.180 ±42.302 ±31.159 ±30.977

New

inputted in the first round of co-registration of MOLA and HRSC DTMs (Fig. 9). Once the matching was finished, the quality assessment of the original and matched HRSC DTM was carried out. It is shown that the accuracy was significantly upgraded from −42.622 m to 5.859 m (Table 8). Moreover, the regions with large disparity between the original HRSC DTM and MOLA points were improved effectively after matching (Fig. 10). Subsequently a second round of co-registration of the HRSC matched to the MOLA and HiRISE DTMs was performed. Compared with the matched HRSC DTM, the HiRISE DTM only covered a small area (Fig. 9). Therefore a relatively larger DTM than the HiRISE DTM was extracted from the matched HRSC DTM and employed as the reference surface in the matching. Although the resolution of the adopted HRSC DTM (200 m) was better than the MOLA (1 km), the large resolution differences between HRSC and HiRISE (a factor of ≈200 in this case) might still cause problem during surface matching. Based on an assessment of the number of points in the DTM employed in a matching (Section 2.1), it was proposed to match the HRSC DTM re-sampled to 75 m and the HiRISE DTM downsampled to 50 m to address this issue.

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Fig. 6. (a) Colourised by height hill-shaded HRSC h1984 DTM, (b) associated hill-shaded MOLA DTM, (c) HRSC h1984 ortho-image, (d) accuracy map before matching and (e) after matching.

The mean height difference between the original HRISE and HRSC DTM was −34.707 m. After the surface matching was finished, the difference was reduced to − 5.236 m, indicating the HiRISE DTM fitted closer to HRSC DTM after matching. In addition, three profiles across the area of the HiRISE DTM are shown in Fig. 11 to demonstrate the matching results, in which the solid line, dotted line, dash–dot and dashed line represent the profiles derived from the HRSC, original

HiRISE, matched HiRISE and MOLA DTMs respectively. From the profiles it is observed that the alignment of the matched HiRISE and HRSC DTMs was improved. As the HRSC DTM has been matched to the MOLA, the co-registration of the three DTM was achieved. 5. Discussion 5.1. Co-registration of MOLA and HRSC DTMs

Table 7 Statistics of height differences for assessing h1984 DTM. HRSC DTM version

Status

HRSC points located in the MOLA buffer

Maximum (m)

Minimum (m)

Mean (m)

Std. dev. (m)

Old

Original Matched Original Matched

30 773 30 808 123 114 123 187

544.670 732.967 445.010 469.738

− 734.690 − 940.126 − 944.310 − 897.661

− 40.441 2.314 0.728 0.216

± 112.253 ±70.773 ±48.272 ±41.312

New

From the assessment conducted in Section 3, it was shown that the accuracy of the new HRSC DTMs could be improved by a factor of 7 to 50 compared with the old HRSC DTMs. This improvement is mainly due to the implementation of photogrammetric bundle adjustment. However in the case of the orbital h1947 DTM, it was noted that the accuracy of the matched old DTM (−0.158 m) was better than the new DTM (3.255 m) (Table 6), which might imply that surface matching could be adopted as a tool for upgrading the old HRSC DTM.

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Fig. 7. Profiles across the MOLA (solid), original (dash–dot) and matched HRSC (dotted) DTMs.

To further examine this option, the accuracy maps of the matched old h1947 DTM and the new DTM are shown (Fig. 12(a) and (b)). It is found that some points with obvious height disparity still remained on the edge of the crater located in the top and middle of the old DTM after surface matching (outlined in the figures). However, these points were improved in the new HRSC DTM.

Although surface matching did not completely upgrade an old HRSC DTM in the case of h1947 DTM, the feasibility of improving new HRSC DTMs was also demonstrated. Fig. 12(c) and (d) shows the accuracy maps of the new version of the original and matched HRSC h1984 DTM. Comparing the regions outlined in the figures, the points with noticeable height differences in Fig. 12(c) were improved after

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Fig. 8. Colourised by height hill-shaded HiRISE Gullies DTM and ortho-image. Note that the height value in HiRISE DTM is relative to the MOLA-adopted areoid.

Fig. 9. Colourised by height hill-shaded HRSC h2510 DTM and ortho-image. The extent of HiRISE DTM is outlined in the white rectangle.

surface matching. Also the accuracy was upgraded from 0.728 m to 0.216 m (Table 7). The same findings were observed in the other two experiments in Section 3. Hence, it is here suggested that surface matching should be considered as a standard procedure for the postprocessing of HRSC DTMs. No matter whether the bundle adjustment has yet performed or not, the processed HRSC DTM should be matched with the MOLA DTM to obtain a more accurate product. Once the matching was finished, the alignment of the two DTMs is also improved. 5.2. Co-registration of MOLA, HRSC and HiRISE DTMs As explained by R. Kirk (personal communication, 1st of December 2008), the HiRISE DTM applied in Section 4 was adjusted to match MOLA directly. However the MOLA representation of the crater was extremely limited; it showed a depression but no sharp rim and it was not clear the extent of the deeper parts of the crater. As a result it was difficult to identify corresponding feature points between HiRISE and MOLA DTMs. Moreover, a sparse coverage of MOLA height point over this region led to insufficient vertical constraints on the adjustments of HiRISE DTM. These limitations affected the absolute accuracy of the USGS's HiRISE DTMs.

The hierarchical approach proposed in Section 4 addressed this issue. A HRSC DTM was adopted as an intermediate DTM for coregistration of MOLA and HiRISE DTMs. As the HRSC DTM (h2510) covered a much larger area including flat areas outside the crater (refer to Fig. 9), so it should be matched much more accurately to MOLA than USGS's HiRISE DTM could be. From the accuracy map shown in Fig. 10, it was found that the HRSC DTM matched to the MOLA DTM successfully. Subsequently, it is more effective to match the HiRISE to the matched HRSC than directly to MOLA DTM. The fine fit of the profiles across the three DTMs (Fig. 11) demonstrated the feasibility of the hierarchical approach, although the resolution of the HRSC DTM employed was relatively low compared with the normal new HRSC

Table 8 Statistics of height differences for assessing h1984 DTM. Status

HRSC points located in the MOLA buffer

Maximum (m)

Minimum (m)

Mean (m)

Std. dev. (m)

Original Matched

11 074 11 010

732.530 432.468

− 913.960 − 422.325

− 42.622 5.859

± 198.983 ±60.119

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Fig. 10. Accuracy map of h2510 DTM before (left) and after (right) surface matching.

Fig. 11. Profiles across the MOLA (dashed), HRSC (solid), original (dotted) and matched HiRISE (dash–dot) DTMs.

531

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Fig. 12. Accuracy maps of the matched old h1947 DTM (a), the new h1947 DTM (b), original new h1984 DTM (c) and matched new h1984 DTM (d).

DTM. More experiments will be performed and assessed as and when more HiRISE DTMs and new archival HRSC DTMs are released. 6. Conclusions After a series of experiments, a robust tool applying surface matching has been developed to realise the automated co-registration of Mars DTMs. The positive results demonstrate that the surface matching tool can be an effective method for aligning MOLA, HRSC and HiRISE Mars DTMs. By reviewing the assessments and experiments reported in this paper, we can summarise that the surface matching tool developed here has the following advantages: (A) It is capable of improving the accuracy of HRSC DTMs, irrespective of whether the DTMs are derived from the PSA or are only available in TMIS or elsewhere; (B) The matching tool is applicable to HRSC DTMs representing various terrain features;

(C) The hierarchical approach applied to the co-registration of HiRISE and MOLA DTMs with the surface matching tool appears feasible; (D) The implementation of a Mars DTM co-registration system was performed in a fully automated manner. Owing to these features, when Mars DTMs are derived from multiple sources, the surface matching tool is recommended to be applied to these data before they are used further. Moreover, it is suggested that surface matching should be considered as an additional step of any workflow for Mars DTM creation. Once this task is accomplished, Mars DTMs of various sources were all well coaligned based on the same MOLA DTM. This achievement is of great potential value for the observation and analysis of multi-resolution Mars DTMs. Since the automated co-registration of multiple-source Mars DTMs is demonstrated, the co-registration of any other planetary topography products using the surface matching tool will be conducted in future research.

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