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ELSM AND GLSR TECHNIQUES OF ARRAY ALGEBRA 
IN SHAPE MATCHING AND MERGE OF MULTIPLE DEMs 
Urho A. Rauhala 
GDE Systems Inc 
P.O.Box 509008, MZ 6100-D 
San Diego, CA 92150-9008, U.S.A. 
Intercommission Working Group II/III 
KEY WORDS: Matching, Rectification, Reconstruction, Registration, Triangulation, Array Algebra Estimation 
ABSTRACT: 
Two techniques of array algebra are introduced. The first technique, Entity Least Squares Matching (ELSM), automates 
tie point mensuration by using fast array algebra polynomials for real-time registration of overlapping Digital Elevation 
Models (DEMs). The dense raw DEMs (produced by interferometric SAR, automated stereo image matching, medical 
imaging etc.) may contain several blunders and missing data. ELSM is designed as a real-time measuring and adjustment 
system: 1) The LSM tie point matching of small windows gets speeds of over 10,000 automated transfers/sec among 4 
overlapping DEMs. It is robust against blunders because the parameters of its entity model are point invariant, 2) The 
global entity model is given the structure of Kronecker or R-products for their "fast" solution and evaluation by array 
algebra, 3) Every post can be considered as a tie point in a new vertical model, strip or block adjustment of array algebra 
with an automated blunder elimination, and 4) The technique can be expanded into data fusion and compression of 3-D 
and 4-D arrays in medical and video images. The second technique of Global Least Squares Rectification (GLSR) is 
introduced for rigorous merging and regridding in output space. It uses the refined ELSM or other orientation data, 
forming the geometric data base for automated site modeling and scene simulation. A similar process is applicable for 
multi-image ortho rectification or least squares object reconstruction. The merged DEM has a better quality and resolution 
than the raw input DEM arrays oriented by ELSM. The fast GLSR solution of array algebra eliminates most blunders of 
the raw input data. An experimental prototype achieved speeds of over 100,000 merged DEM posts/second. 
À controlled experiment in a GLSM study of automated 
1. INTRODUCTION low density (macro) DEM extraction with four experienced 
cartographers illustrated this problem of canopy layers, 
Current automated photogrammetric and SAR mapping (Hermanson et.al, 1993). The human eye-brain stereo 
techniques can produce high resolution DEM arrays at mensuration process failed to estimate a unique elevation 
high through-put rates. But this is true only for the raw value for the terrain surface at over 5% of the posts. The 
(unedited) data, often requiring some refined orientation — techniques of ELSM and GLSR reduce the problem into 
and “feathering” to merge overlapping DEMs into an automated weeding of outliers and undesired layers on 
seamless mosaicks of a reference datum. The reported the more uniquely defined (but more spurious) surface of 
automated rates of Global Least Squares Matching the visible parts of terrain and its occluding top portion of 
(GLSM) with optical and SAR stereo images are getting the canopy layer. The automated edit and merge constraint 
over 10,000 match points/sec in modem computers, of multiple overlapping DEM arrays consists of the fact 
(Rauhala, 1992), (Hermanson et.al., 1993). Similar raw that the same (interpolated) elevation should be achieved 
DEM collection rates are available from interferometric ~~ within the limits of random errors after the elimination of 
SAR (IFSAR) sensors. a systematic orientation or deformation error. A 
significant residual error is caused by a) an outlier, b) a 
The bottleneck of the overall DEM production is its valid change of the terrain and its top canopy, or c) an 
validation and manual edit. This is especially true for the ~~ ambiguous elevation at the horizontal post location. Use 
new flood of high density micro DEM or automated of three or more overlapping DEM arrays can also 
feature mensuration of the often poorly visible or defined eliminate the blunder if the other data sets agree within the 
layers of the terrain surface and its canopy. The visible limits of random errors. 
parts of these layers are captured by the typical 2x2 pixel : 
point density of GLSM. The problem is worse with The automated edit and merge problem is made more 
IFSAR DEMs capturing some canopy while penetrating ~~ challenging by requiring simultaneous refinement for the 
the other. As the elevation variations of this micro Orientation parameters and a removal of the systematic 
topography start approaching the measuring error, some deformations of the data. The merged output DEM is 
new automated techniques are required to classify the ^ required to be a seamless mosaick over a large area of 
measurements according to these surface layers. The amay interest. The process is split into two phases. The 
algebra based "fast" technologies offer new enabling mensuration of “tie points” by an automated matching of 
capabilities for this task. the local terrain shape from all overlapping DEMs is made 
using the LSM technique and its entity adjustment or 
global edit model. Therefore, the technique is called 
321 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996