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Christian Piechullek
Between the individual original film images distinct dif-
ferences in contrast and brightness are noticeable (see
again figure 5). These differences are larger than effects
Which can be explained with respect to different view-
points in conjunction with commonly used reflectance
models such as the Lambert or the Lommel-Seeli ger law,
and they can significantly influence the MI-SFS results
(see discussion on radiometric manipulations in chapter
3). The most probable cause for these differences lies in
the photographic processing applied to the analogue pho-
tographs. Unfortunately, we had no knowledge of this
process. Therefore, we had to approximate the related
effects mathematically in an image pre-processing step.
First, an average albedo value was estimated from the
digital images by considering the analytically measured
DTM as constant within our MI-SFS algorithm. The de-
termined albedo, together with the analytically measured
DTM, was then used to generate synthetic images. These
images were subsequently compared to their real counterparts in order to determine the parameters of a linear grey-
value transformation for each image by a least-squares fit, and this linear transformation was then applied to the real
images. Polynomials of higher order were also tested, but they did not improve the results in terms of the least-squares
fit. Finally, these images were filtered using a Gaussian lowpass in order to reduce any image noise.
Figure 6: Perspective view of the reference DTM
4.2 Surface reconstruction
The images thus pre-processed were used in the described MI-SFS approach. Experiments were conducted with a
varying number of images, each time using either the Lambert law or the Lommel-Seeliger law with a horizontal plane
at an average height within the test area as initial DTM. The rationale for the selection of the initial values comes from
our long term strategy in which a rough DTM is assumed to be available prior to employing MI-SFS. Convergence of
the iterative computations was postulated when each change in height from one iteration to the next was below 0.1 m.
The results were then compared to the reference DTM. In this comparison the two parameters Z, (offset) and m (scale
factor) of a linear transformation were computed, and the root mean square error s(AZ) and the maximum absolute
deviation AZ mx of the two surfaces after applying this transformation was determined (see table 1).
The results can be summarised as follows:
- When comparing the results of the multi image processing given in table 1 it becomes clear that the reflectance pro-
perties of the investigated surface are better approximated by the Lambert law. Therefore, the results of the Lom-
mel-Seeliger runs with the individual images are omitted from the table.
- The accuracy of the obtained results in terms of s(AZ) amounts to 0.43 m. This value still contains the accuracy of
the reference DTM (0.32 m), and is equivalent to 0.3%o of the flying height. Considering the poor image texture, this
result can be said to fulfil the expectations.
Image number(s) Z.[m] M AZ Im] s(AZ) [m]
| Lambert reflectance model
30,31, 32 -0.10 1.01 1.49 0.43
30 0.09 0.74 4.74 1772
be 31 0.36 0.75 15.87 2.49
32 0.57 0.33 19.84 3.83
Lommel-Seeliger reflectance model
30,31, 32 0.40 0.85 | 3.84 | 1.36
Table 1: Results of the practical test
Some small deviations remain after the computations. For this result no single source of error can be given. Possible
explanations relate to the object surface characteristics: there is obviously no guarantee that (1) the employed Lambert
law is valid throughout the whole surface, and (2) that the albedo is in fact spatially constant. From our experience
With the different reflectance laws small deviations from the Lambert law do not influence the results in the observed
extend. Thus, local albedo variations seem to be the most probable reason for the small observed deviations.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 729
