e ww. 
mm XM 
Kw 
M 
If the matching process is formulated in object space 
(fig. 2.2), the grid is established there and trans- 
formations Ti, are set up between an image i and the 
object space o. Transformations between two images i,j 
can be derived from 
T; = To 9 Li = Tio . Tis! (1) 
  
object 
Fig. 2.2 Object based image matching transformations. 
The grid is established in object space, the inverse trans- 
formations T and 7 are the projections into the 
image planes. 
There is a number of advantages in object based image 
matching: 
- symmetry between all images (no master and slave 
images exist), 
- epipolar constraints are given implicitly, even for 
more than two images, 
- more than two images and different spectral bands 
can be introduced, 
- point determination, DTM generation, and ortho- 
image computation are included in the approach. 
2.3 3-line cameras and object based image matching 
The transformations Ti, are inverse to the well known 
collinearity equations: 
For line imagery, these equations have another meaning. 
The image coordinate x, can’t be calculated, it is con- 
stant and equivalent to the distance between the sensor 
and the principal point in image space. The elements of 
exterior orientation have to be expressed as time de- 
pendent functions. Instead of calculating the image co- 
ordinate x, at a given moment t, we must calculate the 
moment t from equation (2a) using xy — constant. In 
general this calculation must be carried out iteratively. 
Afterwards yy is computed from equation (2b) with the 
value of t calculated from (2a). 
image strip 
a 
= UE ERE. time 
flightpath 7 2775 NN 
  
Fig. 2.3 Projection of a DTM mesh to an image strip. 
3. THE MATCHING ALGORITHM 
In this chapter the developed object based image mat- 
ching algorithm for line imagery is described. It based 
on work by Heipke /1990/ and Müller /1991/. First we 
introduce a model for the object space, the flight path 
and the imaging process. Then we describe the least 
squares adjustment to compute values for the indepen- 
dent unknowns of our approach. At last we show how 
the necessary initial values for the unknowns can be 
calculated using a pyramid structure. 
o Tu) X= Xo) + ru) (¥ = Yo) + rst) (Z — Ze(t)) (2a) 
  
  
77 Te()) QC- X0) ra()) (V= Yo) + 70) (Z = Zol0) 
y, = = ¢ 120 X= XoO)+ raft) (V = Yo(0) * «(0 (2 - Z0) — Qb) 
nal) (X = Xo(0)) + ra(t) (Y = Yo(0)) + rs(0) (Z = Zo(0)) 
289