ncies be- 
and those 
  
alibration 
real time, 
ans of a 
formance 
equipped 
pairs and 
ution. 
n stereo- 
on at the 
matic re- 
"to solve 
ithms do 
d; there- 
ase, give 
s and, in 
collima- 
, all the 
who lo- 
error of 
operator, 
xel reso- 
n. À tar- 
a search 
d on the 
d in this 
images, 
an avoid 
in ANS 
lected. 
If a is a geometric shift equal to a fraction of the pixel (in 
the search area)and b and c are the density gain and 
shift in the target area, an equation for each pixel can be 
written as: 
b - g,(x) + c = g (x+a) (1) 
If the image is b/w, a system of 81 equations of this type 
can be written in the three unknowns a, b and c. If the 
image is coloured, 81 equations for each RGB colour 
have to be written. The geometrical shift a is the only 
unknown used, including its r.m.s.e. The solution is 
computed by using the least square method. 
In numerous experimental tests it has been proved that 
this sub-pixel matching gives an accuracy of positioning 
that is 0.1+0.2 pixel: therefore the values of p, (and p, if 
a bi-dimensional matching is carried out) can be deter- 
mined with an accuracy that is similar to that of an 
analytical plotter, even in the case where a poor image 
resolution of 600 dpi is used. 
3.2 DEM automatic extraction 
A very useful feature of a digital restitution unit is the 
possibility of automatic data capture for a DEM grid. 
When using oriented images, this topic can be achieved 
using the VLL (Vertical Line Locus) correlation algorithm. 
A number n of equidistant horizontal planes, spaced at a 
given AZ, are defined for each point of the regular grid 
centred on an approximate value Zo: (for ex. the height of 
the previous determined point). Each point P(X,Y,Z;) is 
then projected by means of collinearity equations and 
homologous windows are defined in each image. A cor- 
relation coefficient for each pair of windows is then com- 
puted. The Z value corresponding to the maximum 
measure of correlation represents a more approximate 
value of the unknown height. 
The shape of the windows has been defined as follows: 
25 x 25 pixels on both images, where different weights 
are given to each pixel depending on its position. 
  
  
25 15 
  
  
  
  
15 
  
  
  
25 
Figure 4 - Weighted window 
If the resolution is 600 dpi, the total window size is about 
1 mm? on the image. This window has been subdivided 
in three different frames: the weight of the pixels in the 
innermost frame (5 x 5 = 25 pixels) has been fixed = 16, 
in the second frame (15 x 15 - 25 = 200 pixels) the w = 2 
and in the external frame (25 x 25 - 225 = 400 pixels) the 
w = 1. This means that each of the three frames have an 
equivalent total weight (see fig. 5). 
The Z co-ordinate corresponding to the highest correla- 
tion coefficient is assumed as the new approximate 
height Zo». The same number n of horizontal planes, but 
now spaced at AZ/2 are centred up and down the new 
value of Zoo. An iterative procedure is performed until the 
distance between the horizontal planes reaches a pre- 
fixed value Ah. The last so found Z is assumed as the 
height of the X,Y point. 
If the highest correlation coefficient of the last iteration is 
not acceptable (for ex. r < 0.7 for b/w images or r < 
0.7x0.7x0.7=0.35 for colour images), the software asks 
the operator to confirm the solution. In both cases a sub- 
pixel correlation is finally made, following the procedure 
described in 3.1, in order to refine the height measure- 
ment. 
  
  
  
  
Cs PE “max Z 
: AZI2 e E Um 
: RC 
M AZ/4 = Ah 
Zo: 
MÀ. res 
Figure 5 - VLL iterative process: 
9 surfaces - 3 iterations 
  
4. PRACTICAL RESULTS 
4.1 Primary data calibration 
A calibration grid, obtained using a contact copy on film 
from a high precision glass plate, has been used for 
calibrating the UMAX PS2400X scanner. 
The grid of 10 x 10 square meshes, 20 mm x 20 mm 
each, has been checked on an analytical plotter, in order 
to define any deformations due to film shrinkage. The 
values of the newly measured co-ordinates have been 
used as "true" co-ordinates for calibration. 
The grid has been scanned several times, in order to 
check the repeatability of the scanner. The results have 
shown that: 
e the scanner must be “heated” for at least 1 hour 
before using it for scanning. In fact, during the first 
hour the geometric changes are not negligible: differ- 
ences are of more than 2+3 pixels (~ 1/10 mm) along 
the side of the grid (200 mm) in the X direction, i.e. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996