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to solve is first to find a suited radiometric transformation
between the orthoimages to eliminate systematic differences
in the intensities which result from physical aspects of im-
age formation. Secondly, if the systematic effects are elim-
inated, the resulting differences in the intensities can be
tested. Those pixels where significant differences are indi-
cated can be grouped together (applying region growing and
closing to fill small gaps), so that the location of this dis-
crepant regions in the orthoimages and with them in the
DTM is found. Assumed to be given two digital (aerial)
intensity images together with the complete interior and ex-
terior orientation, and a digital terrain model. The first we
do is to compute orthophotos from each of the two images
individually thereby taking the same regular lattice. In con-
sequence the geometrical prerequisites for comparing pixels
are fulfilled. The differential resampling is done for each or-
thophoto pixel individually by computing the corresponding
position in the aerial image and resampling with the sinc-
function. That this involves great expense is quite clear.
But for the experimental investigations we want to avoid
approximations in this first step.
The procedures which we explore for localization of discrep-
ancies consist of radiometric transformation models between
the stereo orthoimages and thresholding. The intensities of
the orthoimages 1 and 2 are denoted by O,(r,c) and O,(r, c),
respectively. For model A we assume linear regression with
radiometric scale and shift parameter according to
^
A: Oi(r,c) + e(r, c) 2 àOx(r, c) b.
The adjustment with two parameters allows to compensate
only global differences between the intensities if the images.
This model does not differ from a direct subtraction proce-
dure significantly.
For model B we assume that the intensity differences between
the stereo orthophotos can be described by a finite element
(FE) model, which we formulate by
B: Oi(r,c) F&(r,c) = Ô(r,c)
Ox(r,c)-Fer,c) - Ót(r,c
The adjusted *parameters" Ó(r,c) differ from orthoimage
O, by the estimated residuals, which reflect noise if model B
is true. The grid spacing of the adjusted difference surface
C(m,n) between O; and O, is a multiple of the grid spac-
ing of the orthophoto lattice. The finite elements of C are
facets with bilinear surfaces, i. e., all orthoimage pixels {7,¢)
contribute according to their weights in the bilinear interpo-
lation operator a(r,c, m,n) to the determination of C. The
individual facets are connected to the neighbouring facets by
joint edges and identical node values Ó(i, k). In comparison
with model A the FE-model is more flexible because the sur-
face C is able to follow the differences between O; and O, up
to a certain degree. The formulation of radiometric surface
models has e. g. also been proposed by Wrobel (1988) in the
context of DTM reconstruction and orthophoto generation
from digital imagery.
For the third procedure no explicit model for parameter esti-
mation has to be formulated. The idea behind is quite differ-
ent from A and B. We propose working with image pyramids
(r,c) + a(r,c,m,n) C(m,n) .
235
applied to the orthophotos. In consequence the construction
of orthophoto pyramids is the first step. For that purpose
the images are smoothed with a Gaussian filter with radius 1
and resampled to obtain the next level of the pyramid. The
resampling operation reduces the number of pixels by the
factor 2 x 2 to 1 which fits to the Gaussian diameter of 2
pixels. In this way the pyramid is generated. We count the
levels from the bottom to the top, i. e. level 0 of the pyramid
bears the original image and level n is the coarsest represen-
tation level for the image information. To get an idea on a
variety of applications which use image pyramids refer e. g.
to Ackermann and Hahn (1991) and Rosenfeld (1984).
From each of the stereo orthophotos an image pyramid can
be constructed. Computing the differences between the pyra-
mids for all levels gives a difference orthophoto pyramid
(DOP). On the coarser levels of this DOP low frequent infor-
mation is represented which matches with global differences
between the orthophotos. Because inconsistencies between
the DTM and the real world geometry are of local nature
(if not, then this DTM appears not to be a suited model
to represent the surfaces of the corresponding world), this
local differences will be mixed with the global ones. So it
suggests itself to eliminate the coarse level differences from
the information of the next refinement level. This procedure
we formulate by
C calculate DOP; for all levels i
eliminate DOP, from the current level k — 1:
DOP, _, = DOP;., —- DOP,
By this technique we get a bandpass copy of the intensity
differences between the stereo orthophotos. Depending on
the spatial extend, the discrepancies are expected to be in-
dicated mainly on the first few levels of the bandpass copy.
For all three models A,B,C the stochastic component, i. e.
the noise in the orthoimage intensities, is assumed to be
white Gaussian noise.
In the models À and B the error terms e and the difference
surface Ó, in model C the elements of the bandpass DOP
are tested and thesholded. As described before it will be
more convenient to visualize the discrepant regions rather
than individual pixels. Therefore region growing should be
applied as a final step.
3 EXPERIMENTS AND
RESULTS
For the experimental investigations we pick up an image pair,
which was used by Hahn and Fórstner (1988) to assess the
quality of matching procedures applied for DTM reconstruc-
tion. Though the radiometric differences in the intensities
are considerable, as is convincingly shown in figure 1, with
the matching algorithms a DTM precision of better than 0.2
?6 of the flying height À was obtained in this project. For
two other projects with less demanding surface geometry the
precision was around 0.1 96 of h. For presentation of the
results we chose two characteristic examples for each of the
three procedures A,B,C described above. More examples are
collected in Raifler (1991).
