International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
Since we assume, that $ and the parameters of orientation of all
images J, and thus also all vj, are known, the only unknown
parameters for the computation of G(x'y’) (equation 4) are the
parameters of the object surface model, the DTM heights Z,,
and Ap. Each considered object surface element can be
projected into the image space of each used image / using the
well known collinearity equations. At the resulting position
P, (x “y ) the image grey value gx. y ) can be resampled from
the recorded grey values. The g; are considered as observations
in a least-squares adjustment for the estimation of the
unknowns. The corresponding observation equations read:
, x ^ ^ ^ ; ^ :
v(x, py) = G (Zu, Ar ) = (x (Ze. ). (Zu. )) (5)
where w(x’,y’) residuals of observed grey value in image /
Ze. DTM-heights (k — column; / — row), unknown
A 2 reflectance coefficient, unknown
G model grey value
gi observed grey value in image j
After inserting equation (4) into equation (5) we obtain:
(6)
vj) UR Ves) Peeej(2n.7]]
(I-A) cosfi (241 )) = 8j (s (Zi, )»( Zk ))
Equation (6) is non-linear with regard to 2^ and for this
reason initial values have to be available for the unknown
object space parameters Z,, and 4, for carrying out the least-
squares adjustment.
3. MI-SFS INVESTIGATIONS
In order to investigate the proposed method with real
extraterrestrial imagery we have selected suitable overlapping
images from NASA's 1994 scientific lunar mission Clementine.
A detailed description of the Clementine mission is published in
(Nozette et al., 1994).
At the beginning of this section we investigate and discuss the
case of a one-image analysis by means of MI-SFS. After that,
we carry out the multiple-image analysis and determine the
radius of convergence of the method.
3.1 Input data
For the reconstruction of a surface by means of MI-SFS it is
necessary that following information and data is available:
e one or more digital images
e interior and exterior orientation of the images
e sun position during data acquisition for each image
e initial values for the unknowns (heights Z,, and Ar)
For our investigations we selected images from the
Ultraviolet/Visible (UV/Vis) digital frame camera, a medium
resolution camera based on CCD-technology. We chose two
images (figure 2) which were taken from different orbits. Image
no. 334 is an oblique image with an off nadir angle of
approximately 12.2 degrees. The second image no. 338 wag
recorded when the camera was tilted sidewards over the same
region with an off nadir angle of about 46.8 degrees. The two
images were recorded with a time difference of 20 hours. We
assume that during this period of time no changes happened in
the observed area. The mean geometric resolution of a pixel in
both images is about 180 m. In the overlapping part of the two
images an area with a size of 24.3 x 24.3 km? was chosen. The
altitude difference in this region is about 1.3 km. The selected
area of the moon is part of the "Northern Mare Orientale Basin"
(between 16.3? and 14.3? South and 87.3? and 90.9? West) and
is depicted as the white rectangles in the two images (figure 2).
The area is divided into 54 x 54 DTM grids with a mesh size of
450 m. Thus, in total there are 3025 DTM-heights. Each grid
mesh consisted of 3 x 3 object surface elements with a size of
150 x 150 m.
=
SU à di 8 5 Lu
Figure 2. Selected images: no. 334 (1.), no. 338 (r.)
3.2 One-image analysis
In the following, we carried out analyses with one image;
assuming Lambert (L) and Lommel-Seeliger reflectance (LS).
This means, that A, the weighting parameter for the ratio of the
two models, takes the zero and the value one,
respectively.
value
We introduce a manually measured DTM as initial-DTM. This
DTM was measured several times by different operators using a
digital photogrammetric workstation. For the unknown
reflectance coefficient 4, we use the mean grey value of the
input images as initial value.
The internal accuracy of the manually measured DTM is about
80 metres. However, the stereo configuration of the images was
not optimal and for this reason the measurement of the DTM
cannot be regarded as reference. Nevertheless, we compared the
obtained DTMs with the manually measured DTM to calculate
the mean offset Z, and the standard deviation rms (table 1).
These parameters include the inaccuracy of the initial-DTM.
For the interpretation of the accuracy parameters it should be
noted that the mean position change in the two images of about
one pixel (pixel size of 23 um) conforms with a height change
in the DTM of approximately 360 metres.
No.| Image | Model Absolute | lterations | Zo [m] | rms [m]
DTM-height | jas
wl 338 L corner noconv. | - 1
2 334 L corner no conv. -
3 338 LS corner | 13 14.7 |
4 3M ES | comer .] moconv | -
SS |. 338 | 1S | eoe do ule s 193 1
6 338 LS edge 14 8.9
830
Table 1. Results of the one-image analyses
With the assumption of a Lambert surface the calculations
diverge. Analysis no. 3 assuming a Lommel-Seeliger surface
converges after 13 iterations. The rms value lies below a hall
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