tient af
ion of the
sn nf X,
© used for
ji variate
m analysis
However,
wish ta
predictive
à) FESPONSE
ipn ky the
luste — the
jsinst the
ig bear in
hy desired
pah of à
couid use
hservation,
applied in
sper ations
shi, 15380)
hod ithree
t ahout 8%
lial value,
ed value cf
£P negative
hanged to a
to modify
3RNAL CASE
nf the HCY
‘amexork for
ered in this
true object
SY BERUREING
photographs
tpordinales
esirial and
, the effect
uded in the
à certain
e gained i5
e different
three dats
An effort was made to create the data sets in such a
way that they approach closely nr imitate quite
nearly the corresponding practical / live data. The
true object space coordinates were perturbed using
appropriate standard errors while assuming the usual
normal distribution. Al other input data were also
audified and/or perturked as necessary, The basic
information used in simulating the data sets is chown
in table !. The MEV Y-coordinates, used in deriving
the corrections to computed Y-coordinates of non-
control points, were perturbed for incorporating the
random errors that are characteristic of practical
data.
The magnitude of the standard error used is tabulated
in ites 4. The ‘Field Base' used in computing the
photographic coordinates were perturbed using values
of standard errors given against ilem 2 in the table.
As regards pholographit coordinates, three major
sources of systematic errors; the error in the
interior orientation parameters, the error due ic
Hils deforsalions, and error due to lens distortions,
were considered. — The corresponding sean values and
standard errors arg indicated in items i,2,and 4,
sing these, two values were simulated for each one
of the parameters & the first one was used to
incorporate the source of error, while the second one
wis used to counteract its effect, Bo, it is easy to
see that the resulting photographic coordinates
reflect the presence of uncospencated residual
systematic error effects, which is so characteristic
of a practical! live data. The equations used in
consideration of the radial and tangential lens
distortions as recommended and used by Merchant,
1972) and listed below, The data sets were used with
9 MCV control points, equally distributed, in all the
three planes,
Br zo» Hb r2 6K2rd + 63 ré) PRL
dyr = y Ui r2 € K2 r4 € K3 rh ) 5213.2]
iisiPirze3232i € 22x yM 16€ Pu.
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dut = 1 MPiny#P2 (r2 € 282 31H 1 foutu!
vee iti)
where, the subscripts — r and t refer to radial and
tangential distortion effects respectively. Finally,
the photoccordinates were perturbed far random
Beaturement errport using indicated standard errors,
401
The data were analyzed on an JEN compatible PC,
3, ANALYSES OF RESULTS
The results chtained by processing the various data
sets discussed in section 2 are summarized ang
presented in table 2. RE already stated, three data
sets were simulated and snalysed, For each dats set,
three cases Ze, Jh and Jc with different casple sizes
of 35, 7? and i were chosen, the first case Being a
representation of the theoretical class, and the last
one representative nf the typical pratiital cases in
industrial phetogramselry, The comparison between
the entries in items ! apd I gives the iagrovesent in
quality which can be directly attributed to the NOY
method. This improvesent expressed in percent 35
averaged and shown against item 7, À comparison of
the entries against itess 3 and 3 indicates the
improvement im bias. This again is expressed at
percentage and then chown az entries against iles 8,
bias reduction. Finally, a rosperisen of entries
against items © and & indirales the iaprovement in
the standard error, This isprovemeni is against
calculated as & percentage and chown ac entries again
item 9, Thus, a Summary of the isprovesents gained by
the use of the BOY method can be essily read by
locking at the entries against items 7,8 and 5,
Accordingly, il is essy to see that iaprovemenis of
the order of &0X te 70% are generally achieves,
However, it ic to be noted that 9? NOY control pointe
distributed in the three planes, were used in
achieving the stated improvement.
5. CONCLUSIONS
The conclusions are cusmarizes ss folioss,
|j, The NOY technique is easily adaptable to the case
of close-range photogrammetry.
2, The reductions in AHS, Bias and Variante ere very
substantial and hence worth the trouble,
i, For the practical realisation of the method, it
is essential for anyone io be able to invert the
Variance matrix &
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
