International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004
Kix
E, = (<[M,]+ /[M,] yoE- 29,
AZ T4.
xX, =X
E, = (y[M,|+ f[M;] Y -Y. |=9
Lu bs
where,
M,
M «| M,
M,
Since these equations are nonlinear with respect to ground
coordinates, they have to be linearised by Taylor series
expansion, which has the differentials of three unknowns (X,,
Yı, Zu). Two equations are obtained for each point in one image
and another two equations for its conjugate point in the other
image. The correction to the initial approximate values of (X;,
Y, Z4) can be determined by solving these four equations.
Solution is iterated till they satisfy the collinearity equation to
the desired accuracy. Thus ground coordinates are computed
corresponding to each conjugate point identified in the previous
step. The initial approximation to the ground coordinates is
obtained through the intersection method.
4.3 Processing Steps Involved for Geomatica (PC/
Geomatics, 2001):
4.3.1 Project Creation and Data Input: A project file has
been created by giving the GCP information (geographic
lat/long coordinates in this case) and the output projection
(UTM, Datum: WGS-84 and Zone: 31 for Montmirail and
Zone: 55 S for Melbourne). Since PCI Geomatica supports the
DIMAP format of SPOT-5, both images have been directly
imported into PCI compatible format (.pix) in the project.
4.3.2 GCPs and Tie Points Identification: Next step in the
DEM generation is GCPs (Ground Control Points) and Tie
Points identification. The corner coordinates and the center
pixel coordinates as given in the header file of both the stereo
datasets have been used as ground control points. Out of the
required 10. GCPs, 6 GCPs have been considered as stereo
GCPs (ie., same ground point location in the both images).
GCPs and stereo GCPs are collected in order to reference the
images to the ground. We have also introduced the Z value at
the two stereo points by interactively viewing the given
BDTOPO DEM in another viewer.
Further 30 tie points are collected manually by identifying the
same feature in both the images. Tie Points are collected to
improve the image matching between the two stereo images.
4.3.3 Model Calculations and Epipolar Image Generation:
The geometric model used inside the software is a rigorous
parametric model. This model is based on principles relating to
orbitography, photogrammetry, geodesy, and cartography. It
further reflects the physical reality of the complete viewing
geometry, and corrects distortions that occur in the imaging
process due to the platform, sensor, earth, and cartographic
projection. This model has been successfully applied with a few
GCPs.
The rigorous models (both collinearity and coplanarity
equations) are computed for both the images by using a
minimum of six ground control points (GCPs), a pair of quasi-
epipolar images are generated from the images in order to retain
elevation parallax in only one direction. Here we used 10 GCPs
and 30 Tie points for the model calculations. The overall rms
error in this case was 1.89 pixels in the epipolar direction.
4.3.04 DEM Generation: An automated image-matching
procedure is then used to produce the DEM through a
comparison of the respective gray values of these images. This
procedure utilizes a hierarchical sub-pixel normalized cross-
correlation matching method to find the corresponding pixels in
the left and right quasi-epipolar images. The difference in
location between the images gives the disparity, or parallax,
arising from the terrain relief, which is then converted to
absolute elevation values above the local mean sea level datum
using a 3D space-intersection solution.
The basic principle for DEM generation in PCI Geomatica is
based on image matching. The image matching system operates
on a reference and a search window. For each position in the
search window, a match value is computed from gray level
values in the reference window. The match value is computed
with the mean normalized cross-correlation coefficient and the
sum of mean normalized absolute difference. The correlation
window size varies from low resolution (8 pixels) to 32 pixels at
the full resolution. Elevation points are extracted at every pixel
for the complete stereo pair. The 3-D intersection is performed
using the above computed geometric model to convert the pixel
coordinates in both images determined in the image matching of
the stereo pair to the three dimensional data.
The output elevations are not computed for the pixels where the
image matching fails to find the corresponding pixel in the
reference image, resulting into some failure areas. In case of
small and scattered failures the software does interpolate and
compute most probable values for them.
4.4 Projection & Datum Issues: The DEM (PCIDEM) thus
generated is in UTM projection and for comparison with respect
to the BDTOPO DEM, it is necessary to re-project the output
DEM (PCIDEM ) into Lambert-II NTF (Nouvelle Triangulation
de la France) projection with Clarke 1880 IGN ellipsoid
considering Paris as the prime meridian. This re-projection has
been done directly in Erdas /magine using parametric rules
considering 7 parameters. The parameters are dx, dy, dz, rw, rj,
rk and ds. dx, dy and dz are the translations to WGS84. rw, rj
and rk are the omega, phi, kappa rotations to WGS84, in
radians. The term ds reflects the scale change to WGS 84. The
rms error during this re-projection was 0.0021 meters.
Altimetric datum transfer has not been attempted.
4.5 DEM Interpolation Using Imagine: The DEM surface
from the output points of Saphire software has been created
using the interpolation technique in Erdas /magine. Erdas
Imagine uses multisurface function interpolation technique with
least square prediction. The multisurface technique also
provides the most accurate results for editing DEMs that have
been generated through automatic extraction.
5. DEM EVALUATION & RESULTS
5.1 Montmirail Data Set: Three major comparisons have been
done to validate the accuracy of the DEMs. These are:
l. Comparison of Reference DEM Datasets (BDTOPO
DEM w.r.t. the Laser DEM)
2. Comparison of Saphire DEM with Reference DEM
data sets
3. Comparison of PCIDEM and Reference BDTOPO
DEM
Finally detailed comparison profiles along a diagonal have been
plotted using the different results available.
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