The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
Figure 3. Matching of conjugate linear features in overlapping 
strips 
3.2 Similarity Measure 
So far, a semi-automated approach for the extraction of linear 
features from overlapping strips was presented. The extracted 
primitives are then matched using their respective attributes. In 
this section, the similarity measure, which incorporates the 
matched primitives together with the established transformation 
function to mathematically describe their correspondence, is 
introduced. The formulation of the similarity measure depends 
on the representation scheme for the involved primitives. In this 
work, a linear feature will be represented by its end points. It 
should be noted that the points representing corresponding 
linear features are not necessarily conjugate to each other. In 
this research, a point-based similarity measure, which can deal 
with non-conjugate points, is proposed. More specifically, a 
rigid body transformation (Equation 2) will be used to relate the 
observed strip coordinates (X s ,Y S ,Z S ) to the adjusted strip 
coordinates ( X c ,Y C ,Z C )• Such a transformation will 
¿A *A 
minimize the inconsistency among overlapping strips. The 
adjusted strip coordinates together with the parameters of the 
transformation function for the involved strips will be estimated 
through a Least Squares Adjustment (LSA) procedure. 
X' 
~X T ' 
X " 
= 
+ R o>,t,K 
Y s 
_ Z s_ 
Z T 
Z s 
L ò a J 
In order to compensate for the fact that the observed points 
along corresponding lines in overlapping strips are not 
conjugate, one can manipulate the variance-covariance matrices 
%xyz (Equation 3) for such points. First, a local orthogonal 
coordinate system UVW is defined with the U axis aligned 
along the line direction (Figure 4). The rotation matrix R, which 
is used to establish the relationship between the UVW 
coordinate system and the XYZ coordinate system (Equation 4), 
is defined by the line direction. Then, using the law of error 
propagation, the variances of the line end points in the local 
coordinate system are derived from the variance-covariance 
matrix in the data coordinate system (Equation 5). A large 
number N is added to the variance along the line direction U 
(Equation 6). Finally, the variance-covariance matrix X xyz in 
the original coordinate system can be derived according to 
Equation 7. 
Figure 4. Variance-covariance expansion along the line 
direction 
¿Lxyz 
= R 
* M 
°XY 
a XZ 
(3) 
2 
a YX 
(Ty 
&YZ 
°ZX 
°ZY 
V 2 Z 
'X' 
(4) 
Y =RY 
Luuvw Lux 
R T 
N00 
0 0 0 
0 0 0 
(5) 
(6) 
* < 7 > 
In summary, the proposed strip adjustment procedure proceeds 
as follows: 
(1) Using the developed interface, the user defines the areas of 
interest in the intensity images of some strips. The areas of 
interest are then automatically identified in all other strips 
where the linear features are extracted and matched. The 
corresponding linear features are represented by their end 
points, which might not be conjugate. The points 
representing corresponding linear features, however, will 
be assigned the same identification code. 
(2) For each of the points representing the extracted linear 
features, one can write the observation equations similar to 
those in equation (2). Six transformation parameters (three 
shifts and three rotations) are used for each of the involved 
strips. To compensate for the fact that the utilized points 
along corresponding lines are not conjugate, their 
variances should be expanded along the line direction. The 
modified variances of the points in the local coordinate 
systems associated with the linear features are calculated 
according to equation (6). The modified variances in the 
strip coordinate system are then derived using equation (7). 
The variance expansion should be carried out for all the 
points sharing the same identification code except one. The 
point without variance expansion will be used to define the 
adjusted coordinates of that point along the linear feature 
in question. Maintaining the variance for that point is 
necessary since the variance-expansion process only 
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