Poli, Daniela 
  
Ground control points (GCPs) were acquired from a 1:50000 digital topographic map. 29 points were measured in the 
map, manually measured in the left image and transferred to the other one with semi-automatic least squares matching 
(Fig. 4). The program SPOTCHECK«- (version 3.2) developed by Kratky was used for the bundle adjustment. For a 
description of the model see Kratky (1989). The program was tested with different number of GCPs and with linear and 
quadratic functions to model the attitude changes, taking into account that the minimum number of needed full control 
points is 4 for the linear model and 6 for the quadratic one. Optimal results were obtained using 10 GCPs and quadratic 
attitude rates. In this case, the RMS errors of the remaining 19 check points were: 5.2 m in X, 4.4 m in Y and 11.1 m in 
Z. The strict sensor model was then approximated with polynomial mapping functions (PMFs), that describe direct 
projection equations from ground space to image space and vice versa and from one image space to the other. PMFs 
consist of 3rd-4th order polynomials with 11 - 16 terms, that are estimated with least square adjustment. The advantage 
of PMFs is that they are almost equally accurate as the strict model, but they are much faster. These functions will be 
further used to impose geometric constraints during the matching: they define quasi-epipolar lines along which the 
corresponding points are searched. The processing steps for MOMS sensor modelling and subsequent matching were 
similar to the ones described in Baltsavias and Stallmann (1996). 
  
Figure 4. Identification of GCPs (white dot at image center) in the images and in the map. 
For cloud-top heights, an accuracy from 100 to 500 m is required, thus coarse resolution images could suffice. Thus, we 
resampled the high resolution MOMS images to 288 m, estimated the cloud heights from these and the original images 
and compared the results, using the estimated heights from the original images as reference data. For matching, pyramid 
levels 6 to 4 were used (1152 to 288 m footprint), with the original images being level 0. An interest operator (Forstner 
and Giilch, 1987) was used to detect points on the fifth level of channel 6 that had better image quality. About 9000 
interest points were found, projected on level 6 and matched with the PMFs. The points were then sequentially projected 
on levels 5 and 4 and matched with the help of the corresponding PMFs. 
The algorithm for matching had to take into account the low texture of the clouds, the discontinuous, sometimes 
transparent or semi-transparent cloud form, and the cloud movement during the time interval between the acquisition of 
the images. These problems were reduced, by using least squares matching with the above mentioned geometric 
constraints (Baltsavias, 1991) and different geometric transformations for each level. On the highest level, shifts and a 
7x7 pixel patch size and on the fifth level shifts and a rotation and a 9x9 patch size were used. On level 4, the matching 
algorithm was run in 6 versions, with three transformations (conformal/ rotations/ shifts) and with/without radiometric 
adjustment at each iteration. A quality analysis on the matching statistics and on the coordinates was made. At first, 
absolute and relative tests were applied on the matching statistics of each point (number of iterations, correlation 
coefficient, sigma 0 and shift/rotation/scale) to delete blunders, then points with height outside the known 350 - 8150 m 
range were deleted. Overall, about 25-30% of the points were rejected. The estimated ground coordinates were 
controlled by semi-automated, manually controlled least squares matching of 55 reference points (well defined and 
distributed) in order to choose the best matching configuration for level 4. The difference in the versions with/without 
radiometric adjustment was not large, with the first one being generally slightly better. Table 1 shows statistics of the 
height differences (mean with sign, maximum absolute, RMS) between reference data and the three matching versions of 
level 4 using radiometric adjustment at each iteration. The heights were compared before and after applying the two 
quality analysis tests. As Table 1 shows, although the tests improve the error statistics, many very big blunders, often in 
clusters, remain in the data, distort the error statistics and do not allow a comparison of the 3 geometric transformations 
used in matching. Thus, a last comparison was obtained by using the points after the two tests and after manually 
eliminating points with AZ bigger than 1100 m. For a base/height ratio of 0.77, an expected mean matching error of 1 
  
1164 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000.