scanline. These look angles are also supplied with the
image and remain constant during the acquisition of
one scene (CNES and SPOT IMAGE, 1988). The rela-
tionship between the look direction vector [u v w] and
three dimensional coordinates on the ground [X Y Z]
is then given as :
o un
X-X
= x1 Y-Y
= R, R
á Z-Z7
ue
(3)
with [X, Y. Zl the position coordinates of the satellite
at moment t and À a scale factor. Replacing R,.R, by M,
equation (3) gives rise to two collinearity equations :
m,, (X - X) +m, YY) t2 (Z-2Z)
m. (X-X) td Y-Y) + Ms (Z-Z)
u=w
is nu (X - X) + ma (Y- Y Tm, G- Z)
m. (X - X) * m (Y - Y ) + Mas (Z - Z)
(4)
with my,--mM33 the components of matrix M. Six pa-
rameters in the right hand side of (4) remain un-
known (Z4, £j £4 0 $ x) and are determined accurately
in the adjustment phase by applying a general least
squares technique using reference points (see
Salamonowicz, 1986; Westin, 1990). Once this is done,
a relationship between the pixels in the raw image and
the cartographic reference plane is established. In
order to fulfil somehow the epipolar constraint, an in-
termediate reference system is introduced, which is
S1
Intermediate Reference System
Final Cartographic Heference System
Fig.2 : Parallax Calculation
474
the final cartographic plane rotated in such a way that
the parallax displacement is more or less confined to
the x-direction (fig.2). Leclerc (1989) proposes following
method for the calculation of the rotation angle y:
tan, sin Qr - Ya)
sin À =
2 2 4
tan B+ tan B,- 2 tan tan cos Qo)
Hd (5
with p; the incidence angle and y, the orientation
angle of image i. Both raw stereoimages are resampled
in the intermediate cartographic reference system with
the above described method, thus leaving only relief
displacements unaltered.
3. IMAGE MATCHING TECHNIQUE
The area based matching algorithm is based on a cross-
correlation technique and was found to be efficient
both in terms of accuracy and computation time. The
cross-correlation between an N x M array of pixel grey-
values surrounding pixel i of line j in the target image
(fig.3) and an N x M array surrounding pixel i^ of line
j in the search image is calculated to determine if (i,j)
and (i’,j’) are conjugate match points. For Ti and Sy
defined as the greyvalue for pixel ij and i'j' in the tar-
get and search image respectively, the correlation coef-
ficient is calculated as (e.g. Ungar et al, 1988) :
2
2 Org
T. —
roi ro
IT S SS with
L
Org = > > Em StR ] -(NMTS)
k=X i=1
K 2 —
7
Or = > [ Tai | -NMT)
k=-Kl=-
p"
L —
Ogg = > = [ S Aki I -(NMS)
=-K1
x
r=
ll
(6)
with S and T the mean grayvalue of the search and
target array respectively.
K = (N+1)/2 and L = (M+1)/2.
For a target array centred along a particular pixel, a
search array seeks a conjugate point by moving over a
predefined search space (fig.3). The maximum correla-
tion coefficient of all searches refers to the correspond-
ing point. The overall accuracy is increased by calculat-
ing the corresponding points at subpixel accuracy
using a suitable interpolation method in the neigh-
bourhood of the maximum (Rosenholm, 1985).
