(8)
(9)
(10)
(11)
(13)
Vg = vector of right camera exterior
orientation observation residuals;
V - vector of object coordinate observation
residuals;
B, = matrix of left camera exterior
orientation partial derivatives;
Bj, = matrix of right camera exterior
orientation partíal derivatives;
B - matrix of point coordinate partial
derivatives,
A, = vector of left camera exterior
orientation parameter corrections,
À pn = vector of right camera exterior
orientation parameter corrections,
A = vector of point coordinate corrections;
e = discrepancy vector of plate observations;
C, = discrepancy vector of left camera
exterior orientation parameters;
C p = discrepancy vector of right camera
exterior orientation parameters,
C = discrepancy vector of object coordinates.
The normal equation matrix structure for this model is
shown in figure 3.
Figure 3 Normal equation structure of the camera
parameter portion of the modified collinearity equation
bundle adjustment of stereopairs.
Each left camera of a stereopair is represented by a 6x6
symmetric sub-matrix generated by the conventional
collinearity equations. The relationship between the left
and right cameras is represented by one 6x6 symmetric
sub-matrix and two 6sx6 sub-matrix generated by the
modified collinearity equations for the right cameras. The
number of camera parameters is reduced to 6s +6
compared to the conventional model however this model's
degrees of freedom is the same as the conventional model.
Object space orientation and position of the right cameras
of each stereopair can be computed from the following
relationships by back substitution after the adjustment is
completed from:
29
= RpAXE
RRB AXE (14)
i = Fi,
Xp = vector of right camera coordinates;
ip = rotation matrix of right camera in
object coordinates,
AXF = vector of objectiright camera
coordinate differences in right
camera coordinates;
Ry, = rotation matrix of right camera in
left camera coordinates
Il
2 5
X - B/X, (15)
= AUX,
X, = vector of left camera coordinates
X = vector of object coordinates
A,
= rotation matrix of left camera in
object coordinates
TEST DATA
Four stereopairs were taken of a simple object. All points
on the object were coordinated by theodolite intersection
to a precision of +0.1mm in each of the three coordinate
axes. Two stereopairs had horizontal camera bases and
two vertical. A total of 19 points were observed on all
images with an ADAM Technology MPS-2 Micro
Photogrammetric System.
The photographs were taken by two Canon AE-1 Program
cameras mounted on a bar with a nominal base of 0.200m.
The object filled the image frame at a distance of
approximately 1 metre giving a base:height of 1:5. The
MPS-2 and both cameras were calibrated by the ADAM
software prior to the observations being made.
Approximations of the camera parameters for each
stereopair were obtained from the ADAM software. Refined
approximations using all stereopairs were obtained from a
simple bundle adjustment using unweighted plate
observations. A self-calibrating bundle adjustment (Fraser
1982) showed that gross image correction parameters Af
(camera principal distance correction) and K, (first radial
lens distortion coefficient) were statistically not significant in
the plate observations.
This data was processed by three adjustment models:
a. a CONVENTIONAL bundle adjustment;
b. the CONSTRAINED bundle adjustment and;
c. the MODIFIED collinearity equation model.
Termination of each adjustment was controlled by either
the change in the reference variance or magnitude of
parameter corrections reaching specified limits. Tables 1
and 2 give the results of the three adjustments with the
object points treated as control (Table 1) and as unknown
(Table 2). The precision of the quoted results reflects the