7.2 Irregular boundary
The irregular boundary of the photographed area, or
the existence of lakes or large water bonds, or the
intentional extension of one strip, or more, to
cover a ground control point outside the boundary,
or any other reason might give rise to a situation
whereby the numbers of models in adjacent strips
are not the same, and/or the starting models in
them might not coincide. The change in M would
take place in the structure of the correlation
submatrix b(k, k+1). The key to define this
structure is to find the order of the first and
last models (0) in a line L(k) and the order of
the joined with them first and last models (B,Y) in
the following line L(k+1); and the number of models
joined with each. It should be noted that 0 and/or
DB is the first model in its line, also Ww and/or Y
is the last. The order of these models (d,B),
(W,Y) gives the start and end non-zero basic
covariance matrix m of one diagonal (if they fall
on one diagonal) or two boundary diagonals
respectively (if they fall on different diagonals).
The number and location of non-zero diagonals of
b(k,k+1) are then identified as in the two
illustrated cases by figure 15.
The resulting pattern of M for any combination of
irregularities with different p$, q$ could be
constructed by integrating the appropriate basic
concepts.
7.3 Irregular scale and orientation of photography
The irregular scale and/or orientation of photo-
graphy could arise when different date photography
are used for aerial triangulation. This might
result in a model being connected with several
other models by varying numbers of tie points. In
this case a search routine should be employed
(Julia, 86) to identify the points common to
particular models, and which models are connected
by one and the same point. The minimum bandwidth
strategy for ordering the models might be suitable
for this situation.
8. CONCLUSION
The established patterns of M and the numerical
examples make it possible to conclude the following
remarks and recommendations:
(1) The sparsity and structure of the coefficient
matrix M has the property of regular band pattern,
where the non-zero basic matrices m lie within a
diagonal band W. The decomposition of M can be
performed within this band.
(2) The storage of the matrix M is most suitably
accomplished by diagonal storage. The storage space
of the non-zero envelop is the most economical.
This storage system is most suitable for solution
by Gauss elimination.
(3) The storage of M with its full half bandwidth
W would require extra storage facilities from 5%-
25%,
(4) If the solution is sought by partitioning, the
best candidate for a partitioned unit is the sub-
matrix b. The half bandwidth of M in this case is
D, with 25$-70$ additional storage requirement.
(5) The ordering of the models has a prime influence
on the size of M. The number of F.I. « s? g? for
ordering across - strip, down-strip respectively.
(6) The conditions for economical ordering depend
on p$,q$,8 and g..These conditions could be set in
the computer program to resequence the models.
Together with a suitable computer graphics facility
manipulation of the ordering for least size of M
could be achieved.
249
(7) The rise in the p$, q$ increases the number of
models. The increase is almost linear with every
20% step increment of p & gq (g=20% = g=40%).
(8) The inclusion of the corss models, if they are
possible to be constructed, almost doubles the
number of the constructed models and quadrable the
size of M.
(9) The inclusion of the cross models is antici-
pated to strengthen the solution. The significance
of the improvement yet to be established versus the
cost of additional observations and increase in
storage and computation time. In this case the
economy in storage and computation of M composed of
models' transofrmation parameters against coordi-
nates of the points should be investigated.
(10) For very large M,perdherals are recommended to
be used with micro computers to transfer to and
from the core the active part of M necessary for
forward reduction or back substitution of one step
at a time.
9. REFERENCES
(1) Cuthill, E., 1972. Several strategies for
reducing the bandwidth of matrices. In: D.J.Rose
and R.A. Willoughby (Eds.), Sparce Matrices and
Their Applications. Plenum Press, New York,
pp. 157-166.
(2) Jennings, A., 1977 Matrix Computations for
Engineers and Scientists, John Wiley & Sons,
London, pp.145-181.
(3) Julia, J.E., 1984. A general rigorous method
for block adjustment with models in mini and micro
computers. In: Int. Arch. Photogramm. Remote
Sensing., Rio De Janiero - Brazil. Vol. III, Part A
3a, pp.473-480.
(4) Julia, J.E., 1986. Development with the COBLO
block adjustment program. Photogrammetric Record
12(68): 219-226.
(5) Klein, H., 1988. Block adjustment on personal
computers. In: Int. Arch. Photogramm. Remote
Sensing., Kyoto - Japan. Vol. 27, Part B-11,
pp. 111 588 = ITT 598.
(6) Kruck. E., 1984. Ordering and solution of
large normal equation systems for simultaneous
geodetic and photogrammetric adjustment. In: Int.
Arch. Photogramm. Remote Sensing., Rio De Janeiro-
Brazil, Vol. III, Part A-3a, pp. 578-589.
(7) Lukas, J.R., 1984. Photogrammetric densifica-
tion of control in Ada County, Idaho: data
processing and results. Photogrammetric Engineer-
ing and Remote Sensing, 50(5): 569-575.
(8) shan, J., 1988. On the optimal sorting in
combined bundle adjustment. In: Int. Arch.
Photogramm. Remote Sensing., Kyoto-Japan. Vol.27,
Part B-3, pp.744-754.
(9) Stark, W., Steidler, F., 1983. Sparce matrix
algorithms applied to DEM generation. Bulletin
Geodesique, 57(1):43-61.
(10) Wang, K.W. 1980. Manual of Photogrammetry,
Fourth Edition. American Society of Photogrammetry,
Va., pp.94-96.
Errata to Table 1
Ordering (282) for p-80$, q-60$, (4C)
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