wal Sl n 
x 
iT 
The results contained in case L may be stu- 
died to help us get ‘some insight into the geome- 
trical nature of the problem of variance reduc- 
tion. We proceed to tabulate the results of bi 
values for the various variations in case L. 
These arp -D.195, -0,174%, -0,1568, -0.13%, = 
0.128, -0.117, -0,107, -0,098 k -0.098 correspo- 
nding to the use of points 41, 42, ...,47 as the 
HCV parameters. These values were computed spe- 
cifically for point 12 only, situated in plane 
i, in all 9 cases.For this particular location, 
the covariance between the Y-coordinate of the 
point and the MCV parameter in each case is 
negative, and hence also the computed values nf 
B obtained by use of eg.3.4. It could be that, 
if this simplifying assumption were not made and 
the covariance and hence the bi value computed 
seperately for each plane and used on a plane hy 
plane basis ,then we should have obtained grea- 
ter variance reduction for points in planes 7 kk 
3 also, Inspection of cases M k M shows that 
this is indeed true. It might also be interes- 
ting to compare how the hi values change when 
one switches from the individual control va- 
riates of case L to MEY control variates of 
case H.Thus, the bi values of case H are: 
-0.248. —0.02748. -0.168, 0.118, -0.075, 0.013, 
20,097, 0,094, Obviously, inspection reveals that 
there is nn apparent relationship between the 
two sets nf values. Another point of interest 
may lie in comparison of residul systematic 
errors in cases À vs H. These values for points 
in planes 1, 2 and 3 are 0.043, 0.019, 0,021 for 
case A and 0.02, -0.004 and -0.044 for case H. 
Bhvinusly, with this limited amount of data, no 
specific conclusions may be drawn. Further dats 
analyses would be necessary. 
83. Is the use of complete three dimensional 
coordinates for the MCV parameters preferred 
over use of Y-roordinate only?. Comparison of 
results tabulated against cases H and 1 reveal 
that it is advisible to use only the Y-coordi- 
nate information, Further, from the computatin- 
nal point of view it should be easily possible 
to invert the B matrix. This would be the case 
when all used Y- coordinates are unegual and 
considerably different in value from each other. 
84, Which location in the control field is 
preferred for the selected MCV  parameters?, To 
arrive at an answer to this question, It is 
necessary to lock at the variations between the 
various results grouped under case L. It was 
noted that this variation did not exceed 9.1 
mme%? for any of the cases. Accordingly, it 
should be inferred that the location of the  MLV 
parameter in the control field need not be res- 
tricted. 
85. In data reduction, how many MEY parameters 
should one use?. To suggest an answer to this 
question, it is necessary to compare results 
given in cases L, K, 3 and H. The variances at 
mid-plane location for these cases in order are 
8,1, 2.8, 3.4 and 0.48 matt2 respectively. It 
may be noted that the variance reduction is by 
a factor of 10 when the  MCV parameters are 
increased from ! to 8. The results for other 
Cases can be obtained by interpolation. 
CONCLUSIONS 
The inferences arrived at in the previous 
section may now be summerized in a nutshell. 
1. The MCV technique is a powerful tool which 
is quite readily applicable in terrestrial and 
close range photogrammetry. 
2. Considering some possible variations given 
earlier the mathematical structure represented 
by eg.3.6 a & b is to be preferred. 
3. Using just the known Y-coordinates for MCV 
para- meters is better than using all the three 
dimensional coordinates for the MCV parameters. 
4. fs only the Y-coordinates are effective MCV 
parameters there is no preferred location for 
such points. 
5. The MCV control points should all lie in 
diff- erent XY planes or stated in another equi- 
valent way, the Y-coordiate of any MCV point 
should not be equal to Y-coordinate of any other 
HCY point. 
4. As a thumb rule, it may be stated that 
the variance reduction nf approximately 10X per. 
MCV parameter used may be expected. 
7. Further data analyses would be desirable in 
confirming the above conclusions. 
ACKNDHLEDGEMENTS 
The author wishes to thank praof.5.V.ü0tieno, 
Dean, Faculty of engineering,the members of the 
Dean's committee and Dr. F.W.0.Aduol, chairman, 
department of surveying and photogrammetry, at 
university of Nairobi, Kenya. Also, thanks are 
due to miss Shilpa Magaraja for the neat produc- 
tion nf the manuscript. 
REFERENCES 
References from BOOKS: 
Kobayashi, H.,1981.Modelling and analysis: An 
intro- duction to System performance Evaluation 
Methodology.  Addison-wesiey Publishing,Reading, 
Massachusetts, USA. 
BShannon,R.E.,1975. Systems Simulation, Prenti- 
ce-Hall,Inc., Mew Jersy, USA, 
References from GREY LITERATURE: 
Nagaraja, H.N., 1990. Application of Monte 
Carlo Analyses in Terrestrial and Close-Range 
Photngrammetry,IGPRS Commission V Symposium: 
Cinse-Range Photogrammetry Meets Machine Vision, 
Zurich, 
Nagaraja, H.N., 19971. Variance Reduction and 
Its Application in close range photogramsetry. 
Technical Papers 1991 ACSM-ASPRS Annual DConven- 
tion, Baltimore, USA, 
Torlegard,6.K.,19781. Accuracy improvement in 
Close Range Photogrammetry, Instut fur Photogra- 
mmetrie, Hunichen.