eigh-
j lies
ins
s our
ents.
Je es-
ram-
self-
g and
ng for
(3a)
nated
; and
'ative
jated
, the
a used
nd in
itude
prime
ers.
In order to be feasible, height Z; at the center
of each ground resolution X;,Y; is described by
patchwise continuous bilinear models:
when performing experiments with respect to
the model integrating image matching and 3D
positioning. Our national 40 x 40m? digital ter-
(Xm+1 7 Xi)(Ynii - Y)
Zi = Zn nT
(Ani mm Xo Yui - Ya) ;
(en c - X
+
(Xi TES X mn) (Yn+1 = Y)
Zm41,n
(X rl =. E) Ts Ya)
(Xi - X205 = Va)
Zm,n m+1,n
(Xm+1 T Xm)(Ya+ı = Y.) io = Xm)(Yn41 — 7} Tiki (4)
Heights oo nma Emi ahs Born ee Vr Lem ie vite
at nodes of a square grid are treated as primary
unknown parameters in the combined Eqs.(3b,4).
In fact, …Zm,n stand for the digital elevation
model (DEM) we are interested in. So, we con-
duct iterative digital image matching by mini-
mizing the weighted sum of squares of gray-value
residuals and, simultaneously, arrive at object-
space 3D point determination. For theories in a
stricter sense that gray-value ”truth” with each
ground resolution is also asked for, readers can
refer to among others Ebner and Heipke(1988)
and Wrobel(1991).
A stereoscopic SPOT image pair is selected for
studying our models, see Table 1.
As far as the model for space resection with
Eqs. (1,2) is concerned, we summarize accuracy
results at 25 independent check points in Ta-
ble 2. The number for dynamic sensor stations
varies from 3 to 5. Ground control coordinates
have throughout +50m a priori standard devia-
tions while 6 additional self-calibrating parame-
ters are treated as free parameters. Better accu-
racies result when 4 sensor stations are chosen, a
plot of which is shown in Fig.1. We also see that
cross-track accuracy in Y is better than along-
track accuracy in X. This confirms the fact that
SPOT imagery shows better cross-track geomet-
ric quality. When two ground control points lie
between two adjacent sensor stations a solution
for space resection can converge regulaily, i.e.
nonlinear Eqs. (1,2) are fulfilled in about 7 iter-
ations to within 1.0 x 107*?[mm] .
. Space resection for SPOT stereo images yields
the orientation parameters p/, p" and a for use
in Eqs.(3b,4). The parameters are held fixed
rain model (DTM) is derived from conventional
aerial photographies using analytical plotters.
Use of the DTM is made to interpolate heights
for 20x 20m? or 50x 50m? grids. They represent
reference heights adopted in comparison with
heights estimated form SPOT sub-images, see
upper left quadrants in Fig.2a. Table 3 reveals
typical results on generation of digital elevation
models. In general, the nonlinear functional re-
lationship Eqs.(3b,4) can be satisfied at 9596 to
within 0.1 digital counts in 10 iterations. We
notice that the integrated approach works for
spaceborne images but weight constraints have
to be imposed on the estimated height parame-
ters. Extensive cases are still being studied. In
3. EXPERIMENTS WITH SPOT IMAGERY particular, it is required to construct more reli-
able reference DEMs for accuracy analyses.
After geometric relationship between object-space
elements and picture elements is reconstructed
in a convergent solution, direct by-products out
of the integrated approach are orthographic im-
ages. Fig.2a illustrates digital orthographic im-
ages. Their difference image and its histogram
are shown in Fig.2b from which it is evident that
the mean of differences in gray values is near
zero and the distribution nearly Gaussian.
4. DISCUSSIONS
For SPOT imagery, our mathematical models
used in space resection and in the integrated ap-
proach to image matching and 3D positioning
are documented. In the course of our experi-
ments, piecewise continuous linear modeling for
time-dependent position and attitude parame-
ters appears quite realistic when we consider the
fact that SPOT stereo images of about 4? field of
view have in our case 0.65 as a base-to-height ra-
tio. SPOT scene CCTs contain orbital informa-
tion, see CNES and SPOT Image(1988), which
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