International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
This means that corresponding points are searched in areas only 
where points have been found before due to good texture (Tang, 
Heipke, 1996). 
To further refine the result Multi Image Least Squares 
Matching (MILSM) is carried out following the approach of 
Krupnik (1994). In this method the tie points are matched in all 
images simultaneously. Because it is the most accurate 
matching technique available it is possible to further refine the 
result of the feature based matching. In our implementation we 
can decide whether to apply MILSM or not for each pyramid 
level. To save computing time it is advisable to carry out 
MILSM only on the last level, which represents the original 
resolution. In this approach the affine transformation 
parameters between areas defined around the matching location 
called image patches are determined in an arbitrary number of 
images. In order to avoid a datum defect, one image patch has 
to be fixed serving as reference for the other patches. The least 
squares adjustment can be described by 
  
eo . A : 
= ==2dp + dG - (gf Po ) — G,) 
op e el ! 
where v denotes the residuals, G the theoretical grey values 
computed as mean value from all image patches at (r, c), g(p) 
the grey values of the image patches, p the affine 
transformation parameters between the image patches, dG the 
unknown differences to the initial value for the theoretical grey 
values, dp the unknown corrections for the parameters and the 
subscript 0 stands for initial values of the unknowns. One such 
equation can be set up for every pixel of the reference patch 
transformed into every available image. The discretisation of 
equation (5) leads to the following linear system: 
v= —g;(r,c)dâ, ip! (r.c)dà5 
-g,(r.c)dà; - g; (r.c)dà; 
-g. (r,c)da; = g. (r. c) da; (6) 
«dG(r,c) -g' (r.c) G, (r.c) 
yz dG (r.c) -g'(r.c)* G,(r.c) 
where i denotes the number of the image patch, r the row— and 
c the column coordinates of the image patch. The used symbols 
are described in the following: 
grey value of image patch i (i ^ 7, ..., n) atr, c 
( x > . 
g'(r,c) grey value of fixed reference image patch 0 at r, c 
g. grey value gradient of image patch i w.r.t. r 
eg“ grey value gradient of image patch i w.r.t. c 
G,(r,c) initial value of theoretical grey value at r,c 
daj,,da, ^ unknown shift parameters between image patch i 
and reference image patch 0 
da;,...,da, unknown rotation and shear parameters between 
image patch i and reference image patch 0 
dG(r,c) unknown change of theoretical grey value at r, c 
It is also possible to choose whether to use all six unknown 
parameters daj,...,da; for the MILSM or only the two shift 
parameters da, , da; . 
Finally, model points are derived via forward intersection of the 
image coordinates of the tie points. They serve as an 
approximation for the reduction of the search space on the next 
lower pyramid level instead of the MOLA points. The MOLA 
DTM is used only on the first pyramid level. The application 
flow of the matching is shown in Figure 3. 
  
input 
observed ; ; 
; interior 
exterior ; : 
: orientation 
orientation 
area of interest 
= whole image 
level = 
start level 
feature extraction 
in area of interest 
Y 
pairwise feature based 
matching in all combinations 
Ÿ 
| tuple generation using RANSAC | 
forward intersection 
geometric consistency check 
back projection of all 
3D-points from forward Least Squares Matching 
intersection (optional) 
  
    
   
  
  
   
     
MOLA DTM 
(optional) 
   
images and 
image pyramids 
  
  
    
   
  
  
  
Y 
  
  
  
  
  
  
  
  
  
   
   
    
  
area of interest = 
related image chips 
  
    
    
  
  
  
  
  
  
  
  
     
X 
forward intersection 
level = level <= intermediate 
level - 1 level 
  
  
  
  
  
  
  
4 yes no 
level = original 
level 
no yes coordinates 
  
  
of tie points, 
  
  
  
Figure 3: Application flow of the matching. 
3. RESULTS 
In this section, first the used HRSC imagery will be described. 
In the second part the results of the matching will be presented 
and discussed on the basis of the orbits 18, 22 and 68. 
3.1 Data 
For the evaluation of the matched tie points, imagery of the 
orbits 18, 22 and 68 have been chosen which have been 
received in the early phase of the Mars Express mission. 
Besides the HRSC imagery, the observations of the exterior 
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