FEATURE
luclear Power
ers, and verniers. The
asurement techniques
mination hazard from
lve components. Per-
it for radiation expo-
form these tasks. Be-
manual measurement
rammetry offered the
e and proximity com-
ice only photographs
ve location, with the
a clean environment,
osure. Likewise, the
manual measurement
activity involved with
distance of about one
g photogrammetry is
e made at a later time
plant to disassemble
provide a permanent,
ater inspections to de-
There have also been
ability of the manual
letry does not neces-
s offer the possibility
icate or repeated sets
liscrepancies or unex-
s also been suggested
may potentially pro-
ier spheres, i.e. topo-
ient, etc., photogram-
d as preferable in cost
techniques.
rements for this pur-
es (0.15 mm). From
ave been reported as
| the range of 1 part
a distance of one me-
5 mm which is about
us it seems plausible
for the proposed task.
nmetric problems, the
discrete, well-defined
roblem, however, the
; as distance between
e on a beveled valve
nd themselves well to
1a 1996
traditional "pointwise" photogrammetric processing, and
moreover there may be photo interpretation problems in
locating the feature to be measured in cases of low con-
trast, poor illumination, specular reflections, or poor view-
ing angles.
Thus there is promise in this technique, but there are
also some potential difficulties which may limit the accu-
racies attainable, compared to other point oriented mea-
surement tasks.
2 FEATURE MODELING
In this application, as in many such instances in close-
range photogrammetry, there is a distinct shortage of well-
defined image points which would be usable for pass points
or control points for spatial triangulation. On the other
hand, there are numerous linear features which are visible
in the images. In our case these linear features are either
straight lines, circles, or low degree curves, all arbitrarily
oriented in space. Photogrammetric condition equations
for such linear features have been developed by Mulawa
(1988, 1989) and applied by Sayed (1990).
In our case, these linear features are often the items
of most interest in the dimensional analysis of motor-
operated valves. One of the characteristics of observing
linear features is that, for monoscopic measurements, one
cannot obtain conjugate observations of the same point on
the feature. There are generally no distinguishing or iden-
tifying characteristics of any single point on the feature.
Fortunately with the above mentioned condition equations
it is only necessary that an observed image point be on the
feature, there is no requirement for conjugate points. In
the case of straight linear features, the following condition
equation would be written for each observation on each
photograph.
Ps pj "p:
pean Alp See) (1)
lez do le,
In this equation p is the object space vector defined by
the observed image point, b is a vector defining the ob-
ject space components of the line of interest, and lc is the
vector from the exposure station, l, to the point, c, on
the line and closest to the origin. In the case of circular
linear features, the following condition equation would be
written for each observation on each photograph.
t
|a-4- 4-2, = (2)
pn
where l is the exposure station as before, c is the point at
the center of the circle, n is the normal vector to the circle
plane, p is the object space vector of the observed point,
and r is the circle radius. A sample photograph showing
a valve seat with the gate removed is shown in Figure 1.
As evident in this photograph, the difficulty caused by the
lack of well defined points is compounded by the unfavor-
able viewing angle. This viewing geometry is forced by
the construction of the valve itself, not permitting views
of the features of interest without substantial obliquity.
In order to see these features more clearly, it was decided
to introduce a first surface mirror into the valve. It can
be positioned for optimum viewing of the upstream valve
45
Figure 1: Valve seat
seat, then re-positioned for optimum viewing of the down-
stream valve seat. This is shown in Figure 2. To incor-
porate photogrammetric observations of reflected features
into the bundle adjustment, a number of new capabili-
ties had to be incorporated. (1) Equations were written
to allow points on the mirror surface itself to be used to
estimate the parameters of the reflecting plane. (2) Equa-
tions 1 and 2 were extended to permit observation of a
reflected feature, carrying the parameters of the actual
feature plus the mirror plane parameters. Previously pub-
lished work which has included the photogrammetric pro-
cessing of mirror reflected objects includes Benes (1969),
Kratky (1974), and Torlegard (1975). The geometry which
is necessary to develop the reflection equation is shown in
Figures 3 and 4. The equation of the plane is,
x’u=d (3)
where x is any point in the plane, u is a unit vector
normal to the plane, and d is the distance from the origin
to the plane in the direction of u. From Figure 4, where
x4 is the point and x» is the reflected position,
x = X1 — [1 tu) u— du| (4)
and,
x =X1+ (d-xz'u)u (5)
xo will be located at just twice the displacement from x;
to x,
X =x; +2 (d—x;'u) u (6)
By taking differences of Equation 6 between two points
and their reflected images, we obtain a means to write an
expression for a reflected vector,
V9 —V1-— (2vifu) u (7)
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
