Applications to Lunar Remote Sensing - 3D Computer Vision: Efficient Methods and Applications - page 338

tion of the PSF radius σ . A similar method is used by Baumgardner et al. ( 2000 )to
estimate the PSF for ground-based Mercury images, using the limb of the planetary
disk as a reference. Then the PSF-dependent intensity error term proposed by Joshi
and Chaudhuri ( 2004 ) is used:

I uv −

R(ρ,p uv ,q uv ) 2

e i = G σ ∗ (8.7)

u,v

(Joshi and Chaudhuri, 2004 ). The uniform surface albedo ρ and approximate val-
ues for the surface gradients p uv in the east-west direction are estimated using the
method described in Sect. 3.2.2.1 , obtained there under the assumption of zero val-
ues of the surface gradients q uv in the north-south direction. The surface profile z uv
is computed such that the integrability error term ( 3.25 ) is minimised.
To obtain a DEM of the dome in the southern part of the crater Petavius shown in
Fig. 8.25 , Lena et al. ( 2006 ) employ the ratio-based photoclinometry approach de-
scribed in Sect. 3.3.2 , relying on the image shown in Fig. 8.25 b and a further image
acquired under lower solar illumination. The albedo map ρ uv determined according
to ( 3.49 ) was then inserted into the single-image shape from shading scheme de-
scribed in Sect. 3.2.2 , making use of the integrability constraint ( 3.25 ). The surface
gradients p uv determined by ratio-based photoclinometry based on ( 3.48 )wereused
as initial values for the iterative update rule ( 3.30 ).
The image scale in kilometres per pixel is determined for the telescopic images
relying on craters of known diameters. The dome diameter D is measured in pixels,
where for non-circular domes the geometric mean of the major and the minor axis
is used. The height h of a dome is obtained by measuring the depth difference in
the reconstructed three-dimensional profile between the dome summit and the sur-
rounding surface, taking into account the curvature of the lunar surface. The average
flank slope ζ is then obtained by

arctan 2 h ζ =

D .

(8.8)

The dome volume V is computed by integrating the DEM over an area correspond-
ing to a circular region of diameter D around the dome centre. If only a part of the
dome can be reconstructed, as is the case for a few domes in the Milichius field due
to shadows cast on the dome surfaces by nearby hills, rotational symmetry is as-
sumed, such that the volume can be estimated based on the rotational body formed
by a cross section through the dome centre.
DEMs obtained by Wöhler et al. ( 2006b ) for the regarded lunar domes are shown
in Fig. 8.26 , illustrating the rich variety of three-dimensional shapes occurring in the
examined four lunar dome fields. For example, dome C1 near Cauchy is remarkably
low but clearly effusive due to its summit pit. The nearby domes C2 and C3, tra-
ditionally known as Cauchy ω and τ , are steeper but quite different in shape, since
C2 clearly displays a flattened top with a summit pit while C3 is of more conical
shape. The large edifices A2 and A3, traditionally designated Arago α and β ,are
somewhat irregularly shaped, while dome A1 next to A2, situated near a mare ridge,
is of regular conical shape. The domes near Hortensius have large and deep summit