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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