International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
motion might reach tens of pixels. Therefore, it is important 
to adjust the research area size to the expected maximum 
offset, or, if one can model the movement, to provide the 
correlation process with the estimated offset value. In the 
latter case, the research window may remain small, because 
the estimated position of the homologous points in the 
secondary image is accurate enough. 
2.4 Conversion into latitude and 
longitude and geo-coding 
Now that we have computed the offsets in line AL and in 
columns AC in the reference image, for a given set of points 
(usually a regular grid of points), we must convert them into 
ALat and ALon on the ground, or their equivalent AX and AY 
if we use a map projection. At this stage, we must be careful 
not to simply multiply the offset by the average satellite 
image pixel size (2.5m in the case of SPOTS THR), because 
the pixel size is variable inside the image, in particular in 
mountainous areas. To be precise, we proceed the following 
way 
* Project the reference point on the ground 
* Project the secondary point on the ground 
* . Deduce by difference the horizontal displacements ALat 
and ALon. The difference in altitude is only due to the 
local glacier slope. 
At this stage, we have converted the initial offset grids, in 
pixel unit and in reference image geometry, into offsets in 
meter or degrees, in the two directions North and East. A 
final transformation, using the geometrical model of the 
reference image, allows the geocoding of the two offset grids. 
We now have 2 grids of offsets, one in the North/South 
direction, and the other in the East/West one, directly 
interpretable: they are hopefully null (or almost null) outside 
the glaciers and they represent absolute motion on the 
glaciers. 
From those grids, we can extract profiles of highest velocity 
fields, or simply read displacement of reference geographical 
points. We may separately consider the two directions, or 
compute the total horizontal displacement: 
AHorizontal- JAY?-AY? 
25 Measurement accuracy 
The different errors which might affect the process are 
+ Global image geometrical distortion residuals 
° Local geometrical residuals, due to local DEM error 
+ Local offset computation errors, on the glaciers 
themselves. 
We can give an upper bound to the first error, computing the 
residuals outside the glaciers. Average residual is null (we 
refined the image geometrical models in order to minimize 
the residuals, by bundle block adjustment, which usually 
presents a null residual average), and standard deviation 
provides us with an information about the quality of this 
process. However, due to the low gain of the images, glaciers 
correlate much better than general landscape: the rms error 
on the glaciers is expected to be lower than the one outside 
the glaciers. 
The second error mainly depends on the stereoscopic baseline 
between the two acquisitions. The closest the two local 
832 
acquisition angles, the less sensible the results to relief errors. 
Even if an accurate DEM is not available everywhere on the 
60km x 60km SPOTS scene, one should try to have a good 
DEM at least on the glaciers themselves. 
The third error is mainly due the radiometric dissemblance 
between the two images, provided the resampling processes 
are all performed with an adequate filter, like the apodized 
cardinal sine  (Carfantan, 2001). This radiometric 
dissemblance may be related to surface changes between the 
two acquisitions, or may be a consequence of different 
acquisition incidence angles. In the case of time interval, one 
must not forget that, even if the images are acquired at the 
same hour of the day, different sun angles will lead to 
different shadows. This is particularly true in mountainous 
areas, but in our case, we found it more visible outside the 
glaciers than on the glaciers themselves, because glaciers 
were not on the areas of steepest slopes in the image. 
Quantifying this error is possible: computing the glacier 
motion on a given profile (for example on the steepest slope 
line), and then on a different one, close to the first one, can 
provide a good approximation of the accuracy. 
3 TEST CASE: THE ALPS, SUMMER 2003 
Glaciers of the Mont Blanc range have been selected for a 
first application of the methodology. The two main glaciers 
in this area are the “Mer de glace” and the “Argentière”. 
They are well known, easily accessible and we have a good 
knowledge of their past velocities. A field campaign has 
taken place last summer, at about the same time as SPOTS 
images were acquired. Ground truth could therefore be 
gathered, which allowed us to validate our methodology. 
3.1 Images 
Four images were acquired by SPOTS (Figure 2) on this 
region in the summer 2003, forming the following two pairs: 
° 19 July / 19 August: incidence angles -23.6° and -15.2°, 
31 days interval 
+ . 23 August / 18 September: same local acquisition angle: 
16°, 26 days interval ( one SPOTS orbital cycle) 
  
6 42' 6 48' 6 54' Ot 7 06' 
  
16 00' 46 00 
45 48 
  
  
6 42 648 6 54 7 00 7 06 
Figure 2: SPOTS image on the Mont Blanc range (detail, 
geo-referenced). Lig and Col represent image direction. 
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