ELSM. The adjusted orientation and deformation 
parameters of the ELSM solution act as "fast address 
generators" in mapping the input DEMs into the common 
output space. GLSR treats the transformed elevations at 
the arbitrary horizontal locations of the unknown merged 
DEM grid as the observables of a simultaneous but fast 
least squares adjustment of finite elements, (Rauhala, 
1986), (Rauhala et. al, 1989). The continuity or 
regularization constraints contribute to an automated fill- 
in, smoothing and editing of raw DEM data. 
  
  
    
DEM i 
iz 1.2, ..D 
or ientati on End ELSM 
golynom. | iter ations 
y 
reshape slv. 
windows i 
1 
LSM tie pts Fu cODiure | | derenœ 
of DEM i | update | Windows 
1 
tri angul at ed 
pd ynom corr. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Figurel showing the flow chart of the ELSM and GLSR 
2. DESIGN OF ELSM 
This section discusses DEM tie point mensuration 
technique of ELSM and the associated real-time 
orientation. The orientation solution is updated after each 
iteration of the LSM tie point measurements in all 
overlapping DEMs, thereby feeding the initial values of 
the next iteration as shown in the flow chart of Iigure 1. 
All points of a given DEM share a set of "entity 
orientation” parameters mapping the input DEM arrays 
into a common reference datum. This is different from the 
traditional image-to-image registration model or a regular 
tie point mensuration where each match location also 
depends on its point variant object space coordinates. For 
instance, GLSM has typically 512x512 or over 250,000 
point variant shift and illumination bias parameters (total 
of over 750,000) to cover a 1kx1k reference image area at 
2x2 pixel node spacing. ELSM employs only few 
orientation (and shear error) parameters in object space. 
This is achieved as a modification of the fast image space 
bundle adjustment and automated feature recognition, 
called FELSM, where the linear features act as the tie and 
control entities, (Rauhala and Mueller, 1995): 
Least Squares Matching (LSM) produces estimates (and 
their 3x3 weight matrix) for three small parameter 
corrections dh,dx,dy at the "tie point" locations of a 
regular sampling grid on the overlap area. At each sample 
location, a window of 3x3-7x7 slave array values are 
matched with the DEM reference window to derive the 
“observed” LSM values of dh, dy and dx. 
* The spacing of the LSM tie point grid is typically 
sparser than the used window size. Thus, not all DEM 
values are used in the least squares estimation of the 
corrections to the orientation polynomials. The LSM 
starts by evaluating the predicted values dx9, dy? of the 
horizontal shifts of the orientation polynomials. The 
predicted or reshaped elevation values g(xdx9,y--dy?) of 
the slave window are interpolated in the slave DEM and 
comected by the vertical orientation polynomial dh(x,y). 
The differences of predicted “slave” DEM values, g, from 
reference values f(x,y) are used in LSM to get small local 
corrections dh,dx,dy and their 3x3 weight matrix (normal 
matrix scaled by the locally minimized square sum of 
residuals of LSM). 
e The local normals of LSM can be considered as a 
(weighted) observation equation in the adjustment of small 
corrections for the global orientation model used in 
predicting the values of g. These two adjustment processes 
can be combined to express the observed differences g-f 
directly with the unknown orientation polynomials, 
resulting in the nonlinear ELSM observation equations 
dh(x,y) + g[x + dx(x,y) , y + dy(x,y)] = f(x,y) + ix 
Each 2-D global shift function dx,dy and the linear vertical 
bias dh is given an array polynomial of n1,n2 terms. The 
polynomial parameters have the separable array structure 
df(x,y) = [Lx,x2, ..xnl-1] A [1,y,y2....yn2- lt 
1. h, NN, fi. 1 
= sS xi! ay y! 
ij 
Q) 
+ yet S xi! Binz : 
1 
= Ex" a, + YLX a, - 
1 
1 
Variables x,y are the horizontal geographic coordinates of 
the output space (merged DEM). 
* There are some practical benefits of choosing three 
separable sets of 2-D polynomial coefficients A in (2) as 
the global modeling parameters of ELSM. One is their 
convenient and compact arrangement into a 3-D n,,n,3 
array for a given DEM. The orientation parameters of p 
overlapping DEMs form the 4-D array A of dimensions 
nl,n2,3,p. This arraying of parameters is not only 
convenient but results in computational savings in their 
least squares fitting to gridded observed values. Another 
practical benefit of the separable model is that the 
evaluation of these "address generator" polynomials at a 
grid of x,y variables is "fast". The recursive evaluation of 
322 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996 
  
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