Utilizing Mars Digital Image Model (mdim) And Mars Orbiter Laser ...
Utilizing Mars Digital Image Model (MDIM) and Mars Orbiter Laser Altimeter (MOLA) data for
photogrammetric control. M. R. Rosiek, R. Kirk, T. Hare and E. Howington-Kraus United States Geological
Survey, Astrogeology Team, Flagstaff AZ 86001 (e-mail: mrosiek@usgs.gov).
Introduction: The USGS is producing digital
produced extremely high quality data for photogram-
elevation models (DEM) and topographic maps of
metry, the Viking Orbiter images will remain our best
Mars at scales of 1:250,000 to 1:1,000,000. The initial
source for local topographic mapping in the near term,
source material will be Viking Orbiter images [1], with
but two other image sets may become available later.
a later transition to Mars Global Surveyor (MGS) Mars
First, the narrow-angle Mars Orbiter Camera (MOC
Orbiter Camera (MOC) [2] when stereo coverage from
NA) is now imaging Mars at a minimum of 1.5-m/pixel
that source is available for topographic mapping. The
resolution. Because of the very small footprint of the
digital terrain models and topographic maps produced
NA images, repeat coverage from which a stereopair of
by this effort will support geologic mapping and geo-
two such images can be formed will be extremely rare.
physical studies. The maps will be based on the hori-
Overlap between a MOC NA image and high-
zontal and vertical control from Mars Orbiter Laser
resolution Viking images with usable stereo conver-
Altimeter (MOLA) [3]. Currently, the maps are based
gence will be much more common, and mapping with
on planetographic coordinates, but eventually planeto-
such mixed stereopairs may become important. Sec-
centric coordinates will be used.
ond, the HRSC has been proposed for reflight on the
Background: Topographic information is es-
European Mars Express mission to be launched in
sential to the understanding of many planetary surface
2003. Thus, HRSC images will not be available for
processes. MOLA is producing a global altimetric
several years at best. Both MOC and HRSC are
dataset with phenomenal absolute accuracy and excel-
pushbroom scanners, and an appropriate sensor model
lent vertical and along-track (north-south) spatial reso-
will need to be adapted or created before they can be
lution but a larger inter-track separation that limits the
used for stereomapping. For the latest on mapping with
overall resolution of gridded products. An analysis, as
MOC NA images see the paper “High Resolution Digi-
of April 2001, shows that the current MOLA dataset
tal Elevation Models of Mars from MOC Narrow An-
(~8100 orbits) has an average of one equator crossing
gle Stereoimages” that is presented in this workshop
every 1.3 km. Even if the orbits were uniformly spaced,
[4]
gaps larger than 1.3 km would be common, but they are
Control: There has been a substantial im-
not uniformly spaced; 1/2 to 1/3 of the orbits are clus-
provement in geodetic control available for topog-
tered on top of previous tracks. Assuming that about
raphic mapping. Past topographic maps were either
2/3 the total are more uniformly distributed, it is calcu-
based on small, local control networks or tied to the
lated that about 39% of the grid cells (at 1/32 deg or
USGS global three-dimensional control net [5]. A vari-
1.8 km) contain no track and have to be interpolated.
ety of problems subsequently were identified with this
Runs of four interpolated grid cells (7.4 km gaps be-
net, including an overall longitude difference of almost
tween actual MOLA data) are not rare; they make up
a quarter of a degree with respect to more recent and
several percent of the area near the equator. For geo-
better accepted nets [6, 7], widespread horizontal er-
logic mapping purposes, the 7.4-km width of these
rors (both random and patterned) of several kilometers,
gaps is a much better measure of the quality of the
and vertical errors of as much as several kilometers.
MOLA DEM than just its 1.8 km grid interval or the
Over the past two years, however, we have
average 1.3 km per track. Note also that by the end of
participated in a joint effort by groups at USGS,
the MGS extended mission a 1/64 deg grid will be re-
RAND, JPL, Goddard, DLR, and elsewhere to produce
leased and there will be about twice as many orbits in
a new generation Mars global geodetic control net that
it, so all the resolution figures will be cut in half, but
is substantially improved in accuracy and that is widely
gaps of several kilometers will still be present. Photo-
supported by all relevant experts. As the first step of
grammetric mapping from medium- to high-resolution
this project, which was funded by the Mars Data
images remains useful in the post-MOLA era, because
Analysis Program, we densified the RAND control
it can produce much more finely gridded DEM. These
network by adding images and point measurements
models can now be tied to data from MOLA so that
from the global image mosaic of Mars (the well-known
they partake of its absolute elevation accuracy. High
MDIM, distributed on six CD's in 1991) [8], tripling
resolution DEM produced in this way can be used to
the number of Viking images [9]. We also contributed
study various local geologic processes.
substantially improved estimates of the image coordi-
With the loss of the Mars 96 mission, whose
nates of all three U.S. Mars landers used in the net
High Resolution Stereo Camera (HRSC) would have
[10]. The RAND net is two-dimensional, that is, it uses
1
Utilizing MDIM and MOLA data for photogrammetric control. M. R. Rosiek, R. Kirk, T. Hare and E. Howington-Kraus
near-vertical images and must have the elevations of
The MOLA team used positive east longitude
control points specified as input. In 1999, the majority
and planetocentric latitude values for the altimetry
of control points were given elevations interpolated
data. This system is not directly supported by commer-
from MOLA data [11] and a new control net was de-
cial photogrammetric and geographic information
veloped. MDIM 2.0 has been produced [12] based on
software. The coordinate values are converted to
that control net. A further revision to the geodetic con-
coordinates based on planetographic values. Since the
trol net will take place with MDIM 2.1. This product
MOLA data are so widely available and many products
will be based on additional horizontal and vertical con-
are based on this data, there is a need to consider which
trol from the MOLA data [13]. Thus, excellent data are
coordinate system to use in the production of map
available currently and in the future for both horizontal
products. The USGS has requested approval from
and vertical control of special-scale maps. One diffi-
NASA to move to positive east longitude, planetocen-
culty is to use data based on different control.
tric latitude coordinate system for cartographic prod-
Geodetic Parameters: Another complication
ucts.
is the change and refinement in geodetic parameters for
Photogrammetry: The photogrammetric
Mars. A reference surface for a planet is defined by the
triangulation and DEM extraction will be carried out
semi-major and semi-minor axis. The origin for longi-
on a LH Systems DPW 790 digital photogrammetric
tude on Mars is based on defining a location for the
workstation (BAE Systems SOCET SET software)
prime meridian located at Airy-0. For MDIM 2.0,
[16]. We have augmented the SOCET SET software
MDIM 2.1 and the MOLA data these data are different.
supplied with this system with interface routines to
The MOLA and MOC data have helped define im-
Integrated Software for Imagers and Spectrometers
proved values for Mars. The most recent values are:
(ISIS) system [17] for importing and exporting plane-
semi-major axis is 3396.19 km; the semi-minor axis is
tary data. When importing images into the photogram-
3376.2 km; and the prime meridian is based on W0 =
metric workstation the camera positions and angles are
176.630° [14]. In the future, data will be provided
converted from the J2000.0 inertial coordinate system
based on these parameters. At present, it is necessary to
into a Mars fixed and centered coordinate system. In-
determine which geodetic parameters were used to
put parameters into this conversion process include the
produce the data and to determine the appropriate pa-
geodetic parameters for semi-major and semi-minor
rameters for the product being produced.
axis, W0, W_dot, and the observation time. The final
Coordinate System: There are two coordi-
coordinate system is a planetographic latitude with
nate systems for Mars that were defined and approved
longitude values positive west. The commercial sys-
by the International Astronomical Union (IAU) [16].
tems are primarily used for earth-based projects and the
One combines longitude measured positive east with
coordinate system must be compatible with the ex-
latitude measured from the equatorial plane to a point
pected input of the commercial software.
through the center of the planet, planetocentric latitude.
The quality of stereomapping depends on the
This is a right-handed spherical-polar coordinate sys-
resolution and geometry of images available and varies
tem. The other system uses longitude measured in such
widely over Mars; understanding the availability of
a direction that the sub-Earth longitude increases with
data is crucial to planning this task. A Viking Orbiter
time; for Mars, this means positive west. The second
Image Database is available to help select images for
system uses planetographic latitude, which is measured
topographic mapping [18]. This database contains a
as an angle between the local vertical at a point and the
subset of geometric metadata from the most up-to-date
equatorial plane. Because the shape of Mars is flat-
records at the USGS, Flagstaff. We have written cus-
tened relative to a sphere, the planetographic latitude of
tomized software to analyze and display selected as-
any point is greater in magnitude than the correspond-
pects of these data. This provides an indication of the
ing planetocentric latitude (except at the equator and
stereo quality for a given area and helps in selecting the
poles, where the two types of latitude are equal). The
images to use for topographic mapping.
maximum difference between the two types of latitude
Photoclinometry: Photoclinometry (PC, or
on Mars is about 0.3 degree or 20 km, at 45 degrees
more descriptively, shape-from-shading) is another
North and South. [15]
method that is used for producing high-resolution to-
Historically, maps produced by the USGS
pographic data. Numerous approaches to PC have been
have used the West positive longitude, planetographic
developed; we will use the method of Kirk [19], which
latitude systems. To adapt commercial photogrammet-
constructs a full two-dimensional digital elevation
ric and geographic information software to this system
model (DEM) from an image. In essence, a finite-
meant negating the longitude values since earth coordi-
element model of the surface shape is set up and itera-
nates are positive east longitude and geographic lati-
tively adjusted until a shaded "image" calculated from
tudes.
it agrees with the real image, in a least-squares sense.
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Utilizing MDIM and MOLA data for photogrammetric control. M. R. Rosiek, R. Kirk, T. Hare and E. Howington-Kraus
Because PC directly determines slopes and then inte-
to be projected into a planetographic system since the
grates slopes to get elevations, the accuracy of relative
commercial photogrammetric software expects geo-
elevations between points varies with separation. PC
graphic coordinates as inputs. The digital terrain model
provides excellent topographic detail at the single-pixel
and orthographic image mosaics produced by the pho-
scale, which stereomatching cannot do, but is subject to
togrammetric workstation will then be projected in
increasing distortions over larger horizontal distances.
planetocentric coordinate system.
One effective way to use PC is as a form of
To obtain vertical control, the MOLA data are
“smart interpolation”, to add pixel-scale detail to a
used as a surface to interpolate an elevation value for
preexisting stereo dataset while retaining the absolute
the estimated horizontal coordinates values. These es-
accuracy of the later. If the broad-scale distortions can
timated horizontal and vertical coordinates are used in
be tolerated, PC can also produce useful topographic
the triangulation solution solved for on the commercial
models where stereo coverage is nonexistent or ex-
photogrammetric workstation. The triangulation solu-
tremely poor.
tion is a weighted solution and all parameters are used
Methodology: When producing a map prod-
in the solution. By adjusting the weights, different pa-
uct it is necessary to determine the geodetic parameters
rameters are solved for and some are held constant.
and coordinate system for the input data (images, ele-
The camera angles are allowed to be adjusted the most,
vation data) and the desired geodetic parameters and
since their estimates are the least reliable. The horizon-
coordinates system for output map product. The input
tal coordinate estimates are allowed to adjust some-
data will have to projected to a common coordinate
what, since they are based on the MDIM and that
system, which might not be the coordinate system of
product is not a true orthoimage the horizontal coordi-
the final map product. This means the final data pro-
nates need to be adjusted for the difference in eleva-
duced might have to be projected to the final coordi-
tion. The vertical coordinate estimates are allowed to
nate system.
adjust slightly, since the estimates for the horizontal
To use MOLA data in map production the
coordinates can be off and the values are interpolated
data has to be projected to a common coordinate sys-
from an interpolated surface based on the MOLA data.
tem. Since the commercial photogrammetry software
This triangulation solution is iterated, as better esti-
expects data in geographic coordinates, all base prod-
mates, for the horizontal coordinates are obtained new
ucts are projected into this system. The longitude val-
estimates for the vertical coordinates are obtained, this
ues are projected to have the prime meridian based on
iteration continues until a stable solution is obtained.
W0 = 176.630°. Future releases of MOLA data will use
The triangulation solution provides better es-
this value, so a check is made of which W0 was used to
timates for the camera angles. Based on these angles a
produce the MOLA data. This projection is carried out
digital terrain model can be obtained by extracting ter-
using the ArcView software by ESRI. The values used
rain values from stereo models. The digital terrain
for the semi-major and semi-minor axis of the planet
model provides the base data needed to produce con-
are dependent upon which MDIM is being used.
tours, orthoimages, and shaded relief images that are
MDIM 2.0 is based upon 1991 geodetic pa-
used to produce maps used by the geological mappers
rameters (a=3396.0 km, b=3376.8 km). The images
and scientist.
used in MDIM 2.0 were projected to fit a reference
References
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Utilizing MDIM and MOLA data for photogrammetric control. M. R. Rosiek, R. Kirk, T. Hare and E. Howington-Kraus
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