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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004
e Use the parallel projection parameters for the original and
normalized scenes to transform the grey values from the
original scenes into the resampled scenes according to
epipolar geometry.
3. DEM GENERATION
So far, the original scenes have been resampled according to
epipolar geometry. The resampled scenes exhibit two main
properties. First, conjugate points are located along the same
rows. Second, the x-parallax between conjugate points is
proportional to the height of the corresponding object point. The
following subsections briefly discuss the utilization of the
normalized imagery for DEM generation. The generation
process involves four steps: primitive extraction, primitive
matching, space intersection, and interpolation.
3.1 Primitive Extraction
At this stage, a decision has to be made regarding the primitives
to be matched in the normalized scenes. Possible matching
primitives include distinct points, linear features, and/or
homogeneous regions. The choice of the matching primitives is
crucial for ensuring the utmost reliability of the outcome from
the DEM generation process. In this research, point features are
chosen. This choice is motivated by the fact that the parallel
projection model, which will be used for space intersection, can
only deal with point primitives.
Forstner interest operator (Forstner, 1986) is used to extract
distinct points from the imagery. The operator identifies points
with unique grey value distribution at their vicinity (e.g., corner
points and blob centres), thus reducing possible matching
ambiguities (refer to Figures 5 and 6 for a sample of the
extracted points). The next section discusses the matching
procedure of these points.
3.2 Primitive Matching
The outcome from the interest operator is a list of distinct points
in the left and right scenes. This section deals with the
identification of conjugate points,. which is known as the
matching/correspondence problem. The solution to this problem
can be realized through defining the location and the size of the
search space as well as establishing matching criteria for
evaluating the degree of similarity between conjugate points.
3.2.1 Centre of Search Space
The search space outlines the area where conjugate points to the
selected matching: primitives are expected. For normalized
scenes, conjugate points should lie along the same rows. The
relative location between conjugate points along the epipolar
lines as described by the x-parallax depends on the height of the
corresponding object point. An approximate value for the x-
parallax can be derived by knowing the average height
associated with the area under consideration.
3.2.2 Size of the Search Space
For normalized imagery, the size of the search space in the right
scene across the epipolar lines should be exactly equal to the
size of the template centred at the matching primitive in the left
scene. In other words, the search is done in one direction along
the epipolar lines as represented by the rows of the normalized
scenes. However, since there is no guarantee that the y-parallax
between conjugate points in the normalized scenes is exactly
zero, the size of the search space across the rows is selected to
be slightly larger than the size of the template.
395
On the other hand, the size of the search space along the rows
depends on the height variation within the imaged area. Rugged
terrain would require a wider search space compared to tha
associated with relatively flat terrain.
o
c
t
3.2.3 Matching Criteria
The matching criteria deal with establishing a quantitative
measure that describes the degree of similarity between a
template in the left scene and a matching window, of the same
size, within the search space in the right scene. Either
correlation coefficient or least squares matching could be used
to derive such a similarity measure. Since the involved imagery
is captured by the same platform within a short time period, one
should not expect significant variation in the appearance of
conjugate features in the acquired scenes. Therefore, we used
the correlation coefficient for deriving the similarity measure
between selected features in the left scene and hypothesized
matching candidates in the right scene. The centre of the
matching window that yields the highest correlation coefficient,
which is larger than a predefined threshold (e.g., 0.7), is chosen
as the initial match of the selected point in the left scene.
To eliminate possible mismatches, initially matched points
undergo a consistency check using neighbouring matches. More
specifically, the x-parallax (P,) value of a matched point is
compared to those associated with the surrounding matched
points. For a given point, the mean and standard deviation of the
x-parallax values of the neighbouring points (i.e., # and o,
respectively) are computed. Then, if the x-parallax for that point
is significantly different from those associated with
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T
highlighted as a mismatch and is eliminated.
neighbouring points (e.g., the point is
3.3 Space Intersection
Following the matching process, conjugate points undergo an
intersection procedure to derive the ground coordinates of the
corresponding object points. The parallel projection formulas
(Equations 2) are used for such computation. For a conjugate
pair in the left and right scenes, one can formulate four
equations with three unknowns (X, Y, Z - the ground coordinates
of the corresponding object point). These coordinates can be
derived through a least-squares adjustment procedure.
3.4 Interpolation
So far, the ground coordinates of matched interest points, which
passed the consistency check, are derived through space
intersection. These points are irregularly distributed and are not
dense enough to represent the object space. Therefore, they
need to be interpolated. In this research, Kriging is used to
interpolate the resulting object space points into regular grid.
The Kriging methodology derives an estimate of the elevation at
a given point as a weighted average of the heights at
neighbouring points. However, the weights are stochastically
derived based on the statistical properties of the surface as
described by the elevations at the matched interest points
(Allard, 1998).
So far, we outlined a comprehensive methodology for DEM
generation from high-resolution satellite scenes using an
approximate model.. The reliability of the matching process is
enhanced by utilizing scenes that are resampled according to
epipolar geometry. The following sections deal with
experimental results from real datasets to evaluate the validity
and the performance of the developed methodology.