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In the second method of
3-dimensional coordinates from a stereo pair
the following procedure has to be followed.
extracting
$- RESULTS
3
Some times is called 'the one step orientation',
Reference points used in this experiment are
(i) The orientation elements of each image have classified, according to thier identification
to be determined by applying the space resection qualities, into two groups. The first group, is
equations:
r11(Xs-Xg) tr21(Ys-Yg) *r31(Zs-zg)
a Laert and
r13(Xs-Xg)+r23(Ys-Yg)+r33(Zs-Zg)
r12(Xs-Xg)+r22(Ys-Yg)+r32(Zs-zg)
LV SO tre marin rire LEE
r13(Xs-Xg)+r23(Ys-Yg)+r33(Zs-Zg)
where; (X,Y), (Xg,Yg,Zg) are the image and
ground coordinates of any control
point, (Xp,Yp,C) are the interior orientation
elements of the image and (Xs,¥s,Zs,R) are the
exterior orientation elements of the same image.
It is obvious that the rotation matrix R is an
orthogonal and is defined by three independent
parameters. Thus, a total number of
9-orientation elements will define the attitude
for each image.
(ii) The oriented (rotated) image coordinates of
any point (X* v* (7j then, computed as:
X X+Xp
y? d Ro |Y*Yp
C^. c
(iii) Ground coordinates of any reference point
(Xg,Yg,29) can be computed using the following
equations:-
13 > 125 4(X 70°) Ros fX /62)3 Xs" -
Xs" /[x" /C" -x' /c* ],
Xa = [Xs” - X’*{Zg-Zs’}/C’] and
Yg z [Ys" - Y'*[29-2s')C*].
( ^ and " refer to image number one and image
number two respectively.)
To correct computed heights (Z-coordinates)
from the effects of applying approximate scale
factor and from parallaxes, a polynomial in the
form :
dZ = al + ax + 835. .Yt a4. 74 a5. X*X*24
a6.X.Y: is used. Another form of the heights
correction polynomial where observational
errors in X-direction are considerd, is also
tested. This polynomial is in the form:
dZ=al * a2. X" + a3. X" 4 a4. DX' 4 a5. DX"-
where, (dz) is the error in computed height,
{X%,%") „are: "Che rotated image coordinates and
(0X" ,DX") are the residuals in image
coordinates. The signs ^" and "" refer to image
number one and image number two respectively.
This last polynomial can not be applied, in
practice, since the computation of residuals in
image coordinates require the availability of
ground coordinates. So, this polynomial is
applied only to test the effects of
observational errors on the computed heights.
the formed from a 23 well-identified points. The
second patch is formed by adding another 9
points, of moderate identification quality, to
the first group making a totoal of 32 reference
points.
The stereomodel was formed, first, by
conventional anylytical relative orientation
procedure. A modified method for analytical
relative orientation, then, was applied. In this
modified approach, the base components ,By and
Bz, are represented by second-order polynomials
in order to take into accuonts changes with
time. Table (1). shows the: root mean squares
values of the computed Y-parallax in each case.
Table (1). Root Mean Squares in Y-Parallax at Check points after
Applying the Conventional and The Modified Relative
Orientation Methods.
Root Mean Squares in Y-Parallax (um)
Number of Check Points
Conventional Relative Modified Relative
Orientation Orientation
id 37 50.5 12.2
23 39.9 3.0
Computed model coordinates are fitted into
ground coordinates using three-dimensional
affine and polynomials transformations.
Residuals and their root mean squares values, of
coordinates of check points, are computed and
shown in Table (2).
Table (2). Root Mean Squares Values of Residuals at Reference
Points After Fitting Model Coordinates Into Ground
Coordinates Using Three-dimensional Affine and Second
Order Polynomials Transformations.
Root Mean Squares (meter)
Number of -
Reference Affine Transformation Second-order Polynomials
Points
Rx Ry Rz Rx Ry Rz
37 55 58 19 38 39 =
23 40 47 17. 24 29
287
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