Figure 2: Valve seat via mirror reflection 
  
  
  
  
  
origin 
  
  
Figure 3: Plane 
  
  
X Tu 
XTU 
  
ol 
  
  
A 
  
  
  
Figure 4: Geometry of reflected point 
If points on a circle are observed in a mirror then Equation 
3 may be rewritten as follows, 
nt. s 
I -e- acr = ? 
p| = (8) 
  
In this case c' is the reflected position of the actual circle 
center c, and n' is the reflected image of the circle normal 
vector, n. Note that since ¢’ and n' are functions of c, 
n, and the mirror parameters, we are able to caarry the 
parameters of the actual (unreflected) features in the ad- 
justment. This has the virtue that both direct and reflected 
observations of the same feature may be used, even in the 
same photograph. One cautionary note should be made for 
the circle condition equations. If the ray corresponding to 
the observation is nearly parallel with the circle plane (i.e. 
you are looking nearly edgewise at the circle), then the so- 
lution becomes ill-conditioned and numerically unstable. 
Such observations may actually provide a great deal of in- 
formation, and it seems that a better solution would be 
to develop an alternative condition equation rather than 
eliminate that observation. 
3 RESULTS 
Table 1 shows some recent results comparing pho- 
togrammetrically determined dimensions against dimen- 
sions taken manually. These results do not seem consistent 
with the known capabilities of close-range photogramme- 
try. We feel that the cause of these discrepancies can be 
traced to several sources. First, the descriptions of some 
of the quantities to be measured are ambiguous, second, 
some of the physical features to be measured do not have 
uniquely defined edges and faces, and third, illumination 
inconsistency and specular reflections lead to uncertain in- 
terpretation by the operator about the location of some of 
the features. We have developed a number of strategies to 
address these difficulties. 
46 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996 
  
Feature | F 
B1 
B2 | 
B3 | 
B4 | 
B11 ; 
B12 
B14 | 
R3 
R4 ( 
  
  
  
  
Table 
4 CON( 
Our results t« 
tations. One 
tuted in the n 
manual measu 
one from the 
that problems 
”communicati 
we plan to h: 
a coordinate 
check. Never 
made by the 
gineering at t 
requirements : 
internal surfa 
togrammetry 
internal condit 
manual measu 
cal because of 
Reference 
[1] Benes, M 
Mirror, P 
[2] Bethel, J 
Photograi 
Photograi 
ing, p. 89 
[3] Kratky, V 
of Limbs : 
ciety of P 
[4] Mulawa, ! 
Treatmen 
Commissi 
[5] Mulawa, ! 
Treatmen 
University 
[6] Sayed, A 
Exploitati 
Thesis, P1 
[7] Torlegard, 
Analytical