elements are awakening today to exploit array algebra. The
reported speed of GLSR was over 100,000 posts/second.
By slight modifications, GLSR gets applicable for ortho
rectification or object reconstruction from multiple images
registered by GLSM at the typical resolution of 2x2 pixel
node spacing. The resulting high resolution DEM of
automated edit captures the visible portions of the terrain
and its occluding canopy features in the fashion of the
emerging SAR DEMs.
One of the first practical goals of ELSM and GLSR is the
automation of the validation and edit of the high density
DEMs and feature data bases of the new image mapping
systems enabled by GLSM and IFSAR technologies. The
tests showed the feasibility for merging data of varying
quality while assessing their consistency in real-time with
the full 3x3 LSM weight matrix in the global adjustment.
The main reason for the outliers is that different parts of
the terrain and its canopy layers are visible from different
sensor views. The percentage of the screened data, not
passing the automated edit, is in the order of 1-596 of the
raw data. The interactive edit can also be speeded up by the
fact that the outliers are clustered on local features such
that the new techniques of FELSM, ELSM, GLSR and
GLSM get applicable also in the local repair work.
ELSM can be expanded to 3-D and 4-D arrays and for
dissimilar sensor fusion with applications limited only by
the imagination of the users. An expansion of the single
model ELSM mode into entire strips or blocks of DEM
and image sequences is feasible in the theory of array
algebra. The orientation parameters form 5-D or 6-D
arrays and the coordinate parameteres are arranged into 3-D
or 4-D arrays. Some of the parameters can be eliminated
by the principle of differential photogrammetry and back-
substituted to the “absolute” bundle adjustment for image
or point variant self-calibration. The resulting quality of
the 2x2 pixel dense feature geometry is approaching that
of the photogeodetic control points.
The reported ELSM simulations pioneered some practical
uses of the nonlinear estimation theory of minimum
residuals and perturbation, published at the 1992 ISPRS.
The new general theory of nonlinear estimation recovers
the known solution algorithms as special cases. It uses
the high order partials of Taylor series in the linearized
solution of the normals minimizing any arbitrary power
(vs. the power=2 of least squares) of the residual object
function. The perturbation theory applies an entire grid of
initial values of the nonlinear parameters for a
simultaneous solution. The range and rate of the
convergence is improved by using the 3-D, 4-D etc. arrays
of high order partials and the estimate of the uncertainty
grid of the initial values. The direct (one iteration)
solution of large systems of nonlinear equations is getting
practically feasible but lots of experimentation is needed
to gain insights on these advanced concepts. The reported
technology driven work took the first steps on this fertile
new boundary of modern math and engineering sciences.
326
REFERENCES
Brown, D., 1994 New developments in photogeodesy.
PERS Vol. 60, No 7, pp. 877-8%4.
Fausett, D. and C. Fulton, 1994. Large least squares
problems involving Kronecker products. SIAM J. Matrix
Anal. Appl., 15, pp. 219-227.
Hermanson, G, J. Hinchman, U. Rauhala and W. Mueller,
1993. Comparison of two terrain extraction algorithms:
Hierarchical Relaxation Correlation and Global Least
Squares Matching. SPIE Proc. Vol. 1944, April, Orlando,
Holm, M., E. Parmes, K. Andersson and A. Vuorela,
1995. Nationwide automatic satellite image registration
system. SPIE Proc. Vol. 2486, pp. 156-167.
Kubik, K., 1992. Differential photogrammetry. ISPRS 29
B3, pp. 93-100.
Rauhala, U., 1974. Array Algebra with Applications in
Photogrammetry and Geodesy. Thesis at the Royal
Institute of Technology, Fot. Medd. VI:6, Stockholm.
Rauhala, U. 1976. A Review of Array Algebra. ISPRS
Comm. III, Helsinki and Fot. Medd. 2:38, Stockholm.
Rauhala, U., 1980. Introduction to array algebra. PERS
Vol. 46, No. 2, pp. 177-192.
Rauhala, U., 1986. Compiler positioning of array algebra
technology. ISPRS Comm.III Symposium, Vol 26-3/3.
Rauhala, U., 1989. Compiler Positioning System: An
array algebra formulation of digital photogrammetry.
PERS No 3, pp. 317-326.
Rauhala, U., 1992. Nonlinear array algebra in digital
photogrammetry. ISPRS Vol 29 B2 II.
Rauhala, U., 1995. Latest developments in array algebra.
Paper prepared for the SIAM Minisymposium on
Kronecker products, held in Charlotte, N.C., October 25.
Rauhala, U., D. Davis and K. Baker, 1989. Automated
DTM validation and progressive sampling algorithm of
finite element array relaxation. PERS No 4, pp. 449-465.
Rauhala, U. and W. Mueller, 1995. Feature Entity Least
Squares Matching (FELSM): A technique for the
automatic control of imagery. SPIE Vol 2486 pp. 61-72
Rosenholm, D. and K. Torlegard, 1988. Three
dimensional absolute orientation of stereo models using
Digital Elevation Models. PERS No 10, pp. 1385-1389.
Van Loan, C. and N. Pitsianais, 1992. Approximation
with Kronecker products. CTC92 TR 109, 20 pages.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996
KE?
ABS
Larg
regit
CD
quic.
sear
facil
a fur
agen
expe
An 1
lite n
spec
as m
surfa
need
poste
data
is wi
Data
inter
Thes
and a
Venu
NAS.
offer:
repor
acces
data-:
remo!
Euro}
organ
NAS,
Comp
Durin
plane
data :
volun
are at
meter.
three
sensoj
proce:
at the
the oj
resolu
create
usable
Storin
