X 
2T, 3 
38 = aj = ssin(y) [r31, 732; 733] y 
x] 
oT, 
S az = S|[rzi, 722,723] | Y (12) 
y Z 
[X 
9T, m aj £g [-71, —T712, —r13] Y 
Dry Z 
2T, zi 
ds = d4-—sÍ[nuniz713]| Y 
8 Z | 
X 
2T, 
= = e mmermslY 
3 Z 
2T 
2 = = 1 
dz, 7s 
2 
Üy; 
= 
i7 = 
mu 
42 7 "n 
where r;; are the elements of the rotation matrix R4 in equa- 
tion 9. 
4. APPLICATIONS 
There are several practical applications for multiple image 
matching. We focus on aerotriangulation and describe briefly 
the simultaneous adjustment of surface patches within a 
block. Aerotriangulation consists of several tasks, for ex- 
ample point preparation, point transfer, measuring, adjust- 
ment, and analysis. Oviously, multiple image matching is 
related to transferring and measuring points. However, we 
may combine the matching process for individual points 
with the blockadjustment. For the following discussion we 
assume that good approximations for all tie points are avail- 
able. How to determine good approximations automatically 
is a problem in its own right and is not treated here. 
4.1. Automatic Aerotriangulation 
The model derived in 3.1. is suitable for an automatic aero- 
triangulation. The parameters in the observation equations 
(6) comprise the exterior orientation elements of the im- 
ages whose patches are involved in the reconstruction of 
the surface patch S, and the elevations and gray levels of 
S. Assuming a surface patch size of m x m grid cells that 
corresponds approximately to the pixel size of the images 
we obtain a total pm? observation equations for p image 
patches. Suppose we now move to the next surface patch 
and repeat the same procedure. Some of the images involved 
in the previous patch participate also in the new patch. We 
note that the images involved in both patches relate the new 
set of observation equations with the previous one. Obvi- 
ously, adding more and more surface patches which partially 
share the same images is analogous to measuring points on 
photographs forming a block. 
Suppose we have a block of three strips with four pho- 
tographs per strip and regularly distributed surface patches 
such that on every image at least nine surface patches are 
258 
visible. This would lead to approximately 40 surface patches. 
We further assume that the size of every surface patch is 
13x13. The number of unknowns to be determined is 12 x 6 
exterior orientation elements plus 40 x 13 x 13 elevations and 
40 x 13 x 13 gray values for the 40 surface patches. Thus, 
the total number of unknowns is 13592 and the number of 
observation equations is 4 x 40 x 13 x 13 — 27040, assuming 
that a surface patch shows on four photographs. 
As shown in Agouris and Schenk (1992) the structure of the 
normal equation matrix is such that the unknown gray val- 
ues can easily be eliminated. Thus, the size of the reduced 
normal equations would be 6832 in our example. This is 
still a large system considering the small block. A reason- 
able alternative then is to determine the surface patches 
independently and to introduce them later in the aerotrian- 
gulation. In this case, the model described in 3.2. should 
be used. 
5. REFERENCES 
Ackermann, F. 1984. High Precision Digital Image Correla- 
tion. Institute of Photogrammetry, TU Stuttgart, Vol. 9, p. 
231-243. 
Agouris, P., T. Schenk 1992. Multiple Image Matching. In- 
ternational Archives of Photogrammetry & Remote Sensing, 
ISPRS XVII Congress, Washington, D.C.. 
Ebner, H., Ch. Heipke, 1988. Integration of Digital Image 
Matching and Object Surface Reconstruction. International 
Archives of Photogrammetry & Remote Sensing, ISPRS XVI 
Congress, Vol. 27, Part B 11, pp III-534 - III-545. 
Forstner, W., 1984. Quality Assessment of Object Location 
and Point Transfer Using Digital Image Correlation Tech- 
niques. International Archives of Photogrammetry & Re- 
mote Sensing, ISPRS XV Congress, Vol. 25, Part A3a, pp 
197-219. 
Grün, A., E. Baltsavias, 1988. Geometrically Constrained 
Multiphoto Matching. Photogrammetric Engineering & Re- 
mote Sensing, Vol. 54, No. 5, pp. 633-641. 
Helava, U., 1988. Object-Space Least-Squares Correlation. 
Photogrammetric Engineering & Remote Sensing, Vol. 54, 
No. 6, pp. 711-714. 
Wrobel, B., 1988. Facets Stereo Vision (Fast Vision) - A 
new Approach to Computer Stereo Vision and to Digital 
Photogrammetry. Proc. Intercomm. Conference of ISPRS 
on Fast Processing of Photogr. Data, Interlaken, pp. 231- 
258. 
  
  
  
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