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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
Extraction of topographic radiance image
accounting for variations both in relative albedo and
thermal inertia. a. Image V0881003RDR.QUB (Band 3), b.
Figure 1.
Image 10881002RDR.QUB (Band 9). c. Nighttime Image
101511006RDR.QUB (Band 9). d. "Magic airbrush" weighted
sum of a, b, c chosen to cancel variations of albedo and
thermal inertia. Images cover part of Gusev crater, with the
MER-A Spirit landing point to the left of the triangle of hills
in the top center.
thermal conductivity, p is the density and c, is the specific
heat. For Mars, / ranges from —50 for very fine dust, to ~300
for fine sand, to ~2000 for solid dense rock (cf. Jakosky and
Mellon, 2001; Mellon et al., 2000). A further condition for
the success of our analysis is that the influence of these
parameters on the observables is sufficiently distinct that
they can be disentangled. The VIS image, formed by
reflected sunlight, is sensitive to slope orientation as
described by the surface photometric function and is
proportional to albedo A, but is not affected by thermal
properties. The day IR image is formed by energy that has
been absorbed and reradiated. For small / this reradiation is
mostly instantaneous, and the day image has a Lambertian
orientation dependence and is proportional to (1-4); the
former is similar to the VIS image but the latter is of the
opposite sense. For finite /, the daytime temperature is
reduced by thermal conduction to the subsurface and retains
a "fading memory" of the past history of insolation.
Increasing / has the opposite effect on night temperatures,
raising them by conduction from below. Albedo and
orientation have weaker influences on the night temperature
through the total energy absorbed during the day. From this
description it is evident that the THEMIS observations have
distinct responses to orientation, A, and /, so that an
inversion for these parameters is likely to be robust.
2.3 A "Magic Airbrush"
Mathematically, it is a given that the full thermal model can
be linearized for small departures of orientation, albedo, and
thermal inertia from some mean values, but will such a linear
approximation be valid over a useful parameter space?
Theoretical considerations, preliminary investigations with
the numerical thermal code "KRC" (Kieffer et al., 1977), and
empirical results with THEMIS data suggest the answer is
yes. Work now underway with the KRC code will guide us
to a strategy for inverting the THEMIS data in the general
(nonlinear) case, provide error estimates for the recovered
parameters, and lead to an empirical "photometric function”
that describes how day IR radiance depends on east-west and
north-south slopes.
If py represents the visible-band photometric function of the
surface and pyr an effective photometric function for the
infrared emission, then the accuracy with which albedo
variations can be cancelled in a linear combination of the
visible image Ap, and the IR image (1-A4)prr depends on the
degree of resemblance between pe and pr. As described
above, pz will be nearly Lambertian for small /, whereas p;
835
Figure 2. MOLA-controlled photoclinometry to derive high
resolution DEM: a. "magic airbrush" as in Fig. 1d, b. MOLA
gridded topography, c. THEMIS-based photoclinometry
modeled DEM, d. model of relative albedo derived by
simulating the VIS image with the DEM and dividing out
topographic modulation.
for the martian surface at the phase angles of interest is
slightly less limb-darkened (Kirk et al., 2000b) and will
have only 70-80% the contrast of a Lambertian function. In
practice, we find that it is straightforward to determine an
empirical combination of the images that cancels both
albedo and thermal inertia variations and leaves only slope-
related effects as shown in Figure 1. The existence of such a
solution depends on the properties of the thermal model as
described above; the ease with which it is found is a result of
the extreme acuity with which the visual system can
distinguish intrinsic effects like albedo (which can affect
arbitrarily large patches of the surface in a similar way) from
topographic shading (in which dark and bright slopes are
typically paired within a small region). We use the informal
term "magic airbrush" for the empirical processing of
THEMIS images, because it leads to a product (Fig. 1d) that
resembles a shaded relief map yet is the result of
surprisingly simple image processing rather than the
painstaking efforts of an airbrush illustrator.
A further requisite for the production of "magic airbrush"
maps that requires mention is the accurate coregistration of
the component images. The VIS and IR images (Fig. 1a-c)
were aligned by resampling them to a common map
projection at a sample spacing of 80 m/pixel (a compromise
between the VIS and IR resolutions) and then interactively
adjusting the position of each dataset to register it to the
others and to a control base prepared from Mars Orbiter Laser
Altimeter (MOLA) gridded radius data (Smith et al., 2001).
We are currently developing tools for correcting the
positional errors in THEMIS data by rigorous least-squares
bundle adjustment (Archinal et al., 2004).
2.4 Quantitative Topography
The use of the "magic airbrush" images is not limited to
qualitative photointerpretation of the morphologic features
that they reveal by suppressing albedo variations. The
product can also be subjected to analysis by two-di-
mensional photoclinometry (Kirk, 1987; Kirk et al., 2003b;
http://astrogeology.usgs.gov/Teams/Geomatics/pc.html) to
produce a DEM with single-pixel resolution. Because of the
use of thermal infrared data, this may also be referred to as
"thermoclinometry," or "shape-from-heating." A weighted
combination of p, and p;& should properly be used to
interpret the weighted sum of VIS and IR images. Until the
form of ps is determined, we empirically resort to a
Lambertian function and adjust the contrast of the input
image to produce a DEM in which the heights of selected
features agree with an independent (but generally lower
resolution) source of topographic data such as MOLA (Smith
et al, 2001). Such "calibration" of the photoclinometric
