tanbul 2004
hotographic
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rameters f.
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system to
ze system by
med in two
n the terrain
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ie altimetric
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O referenced
the vector L
), p and Ka
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
The Eq. 2 can be expressed as the Eq. 2 and 3, where aj are the
2
matrix elements. The Eq. 3 and 4 are rigorous and not linear in
terms of all six parameters unknowns Xo, Y¢,Zo. ©, ©, K.
NOM aj (X- X9) t a4, (Y- Yo) * a4(Z- Z9) Q)
=< aj (X- X9) t aj (Y- Yo) * a33(Z- Z9)
y aj (X- X9) t a33(Y- Y3) * a32(Z- Z4) 2
-c ag(X- X9) * a (Y- Yo) +a33(Z-Zy)
24 Transformation of the DTEM from the fiducial system to
the digital image system
The coordinates of the DETM nodes are transformed from the
fiducial system to the digital image system through an affine
transformation.
2.5 Correspondence between the DTEM resolution and the
digital image
In the stage 2.4, the position of each DTEM cell referenced to
the fiducial system, is determined in the digital image system. As
the size of the DTEM cells are greater than the pixels of the
digital image, the cells must be divided in subcells whose heights
are unknown. The geometric correspondence between each
subcell of the DTEM and the digital image can be determined in
two ways: i) using the colinearity equations or, ii) using a
projective transformation. In the first one, it is needed to know the
coordinate Z of each subcell, which is given only for the cell
nodes of the DTEM. This means that it would be necessary to
generate a new DTEM to the resolution of the digital image. This
involves a great volume of calculation and information to store. In
the second way, it is not needed the coordinate Z of the subcell,
since each subcell is projected directly on the digital image,
considering each DTEM cell as a plane surface (Figure 3)
(Jauregui, 2000).
DTEM cell RES. Ann
+ Cell node
i
i
i
t
'
i
1
1
1
1
i
f
i
i
1
i
i
1
i
‘
!
DTEM subcell
Figure3. Projection and densification of the DTEM
The projective transformation of each DTEM subcell on the
digital image can be expressed in the Eq. 4.
x; = at à; Xi + a, Y; + a XiY;
y "bot bi Xt b; Y, t b XY, (4)
where x;y; = DTEM nodes coordinate referenced to the digital
image system |
X,,Y; =DTEM nodes coordinate referenced to the terrain
system
ag, 41, A> , a3, bg, by, ba, by - parameters of the projective
transformation.
The parameters of the projective transformation are determined
from the coordinates of all four nodes of each DETM cell. Then,
the coordinates Xi, Yi of each subcell node are transformed to the
digital image.
2.6 Determination of the grey levels of the color orthophoto
bands
The color image is separated into the red, green and blue bands.
For each band, the grey tone is assigned to each subcell of the
DTEM that has been projected on the digital image in the step 2.5.
In general, the DTEM subcells projected on the digital image do
not coincide precisely with any pixel. Commonly, it exists a .
partial overlapping on several pixels. For this reason it is
necessary to realize an interpolation of the grey tone, from the
pixel values of the digital image covered by the subcell, to obtain
the grey value of each subcell. The interpolation methods
commonly used are closest neighbour, proportional areas,
significant areas among others.
Image : D nere
Projected DTEM
subcell
|
Figure. 4. Projection of the DTEM subcell on the digital image
2.7 Determination of the horizontal parallaxes of the DTEM
nodes
The horizontal parallaxes of each DTEM node are determined in
the terrain system respect to the reference plane. The referenced
plane is the one that contains the minimal Z value of DTEM. With
these parallaxes and an appropriately photographic base the
coordinates of each DTEM node are transformed to the
stereomate system, involving only a scale factor along the
direction of the X axis in the two systems. The horizontal
parallaxes Px for each DTEM node are determined by the Eq. 5:
Px;= AH; B/ (Zp - AH) (5)
