merged solution of the object space were negligible. Their
outliers were clearly visible in the residual analysis. The
merged solution can be converted into "raw edited" shift
values of new GLSM processes to produce the "refined
edited" merge. The resulting solution can then feed the
reference-to-reference image registrations, thereby coupling
all 2p images with the tie points of about 2x2 pixel
spacing. The resulting dense tie, feature and DEM point
mensuration of automated edit enables the system concept
of multi-ray image mapping, (Rauhala, 1986, 1989).
A practical ELSM operations strategy was developed
through thousands of tests with various factors affecting
the quality and speed of convergence of the ELSM
orientation solution. The solution speed in fitting the 4-D
parameter array to the LSM estimates of local dh,dx,dy
values was so high that it could match the LSM speed of
10,000 tie points/sec in a SUN Sparc 5 computer. Thus,
all input DEM posts could be afforded in the orientation
solution, making it as robust as possible against the
outliers. The solution typically converged in 3-7 iterations
and 2-6 seconds of user time. Three slave DEMs and a
Ground Truth reference DEM of about 200x200 posts
were oriented and merged in both test areas.
The ELSM algorithm was debugged using a simulated
reference 256x256 DEM of 2-D sine curve. An initial
sequential (vs. simultaneous merge) baseline of GLSR
was used to create the regridded slave DEMs of known bi-
linear address polynomials from the simulated reference
DEM. They were recovered (within the computer round-off
error) by ELSM in 3-4 iterations. Shifts or translations up
to 10 posts and shift variations of 5-10 posts due to the
higher order terms were recoved without resorting to the
pyramidal pull-in process. The convergence and range of
pull-in were improved by allowing the high order terms to
adjust beyond n1=n2=2. The bi-quadratic case of n1=n2=3
was an optimal model of the real test data with large blobs
of locally diverged spots at the deep SAR shadows. Since
the LSM weight matrix is divided by the large residual
error of such blobs, their effect on the global solution was
found negligible.
Practical insights were gained in using the minimum
residual estimation theory of nonlinear array algebra
beyond least squares. Also explored was the use of the
nonlinear perturbation theory (use of multiple initial
values for each parameter) by including the high order
partials in the linearized normals of LSM, (Rauhala,
1992). An improved convergence was noticed with the
simulated error free data. The outliers of the real data made
some LSM sample normals (weight matrix) negative
definite opening new possibilities for automated edit of
the nonlinear ELSM, FELSM and GLSM technologies.
The discussed initial test provided insights on the DEM
shape matching and merge problem, showing the
robustness of ELSM even with the very poor test cases.
The dissimilar merge of IFSAR data and GLSM DEMs
produced from the stereo SAR and/or EO is getting
feasible. The goal of such tests is to reduce or automate
the cumbersome manual DEM validation and fill-in. The
stereo SAR and IFSAR DEM techniques often lack the
capability of manual mensuration and fill-in, making the
full automation a high priority in the future production of
high density DEMs or Digital Elevation Canopy Model
(DECM). The envisioned merge of dissimilar stereo
models allows the manual edit performed in the existing
EO workstations. The dissimilar merge can be expanded to
3-D and 4-D medical images or to a compression of digital
video and other image sequences.
Some interesting questions and problems for further
testing and development of ELSM are: How many models
are typically needed before the plateau of diminishing
returns is reached? The answer can be found in practical
tests using IFSAR DEMS and by developing the chaining
processes of GLSM, FELSM, ELSM and GLSR with the
expanded ELSM strip and block triangulation of entire
DEM sequences of a systematic overlap pattern. The
ELSM strip adjustment (with a 5-D array of orientation
parameters and a 3-D array of the merged elevation
parameters) is also applicable for the "fast" image space
bundle adjustment of image sequences in the fashion of
differential photogrammetry, (Kubik, 1992). These new
technologies open a new era of multi-ray softcopy
workstations replacing the traditional feature and sparse
DEM data base collection with the system concept of
automated and user friendly image mapping. Their control
networks can be established in an integration of some
photogeodetic GPS ideas of (Brown, 1994) into the data
base of control features and site models of FELSM,
(Holm et.al., 1995), (Rauhala and Mueller, 1995). In the
transition period, the DECM of GLSM can support the
more traditional feature extraction by FELSM.
4. DESIGN AND RESULTS OF GLSR
The estimation of the orientation and elevation parameters
of the merged grid is split into two phases. ELSM of the
first phase couples the tie point mensuration into a real-
time adjustment of the orientation (and deformation)
parameters. The second phase of GLSR considers these
parameters known by mapping the input DEMS into the
output space. The resulting horizontal locations form
irregular grids which have to be merged into a single
unknown regular grid by GLSR. The unknown elevation
values at the merged grid are estimated in GLSR while
automating the edit of the input data. An automated
blunder elimination is feasible at post locations having
two or more observations in their close neighborhood.
The results of the GLSR prototype prove that GLSR is
practically feasible. The speed of 100,000 posts in a
second was reached in the initial sequential algorithm
where each input DEM was transformed and regridded to
support the debugging and testing of the ELSM program.
GLSR is an evolutionary “fast transform” product of array
algebra. Some starting ideas of array algebra are today
getting the attention of applied mathematics and
engineering, (Fausett and Fulton, 1994), (Van Loan and
Pitsianais, 1992), (Rauhala, 1974, 1976, 1980, 1986,
1992, 1995). Array algebra is an expansion of the
Kronecker or tensor products to more general R-products
and estimation theory of general “fast” matrix and tensor
324
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996
as
mM DD (4 pd mm 9 (5 e
CS) "in MN
= BD a
