e Feature point tracking by multi-criterions
After the numerically distinctive points, associated with their
descriptions, are extracted from the first frame of each test
fields, we used image track algorithm to seek conjugate points
in the following images with a multi-criterion method. The first
criterion is maximum parallax constraint for determining the
search range. A horizontal parallax of about 10 pixels (because
we knew the resample rate of the image sequences) and a
vertical parallax of about 3 pixels are recommended. The
second criterion is a correlation coefficient maximum between
window patches around the point pairs. The black crosses in
Figure 8 show the tracked feature points in the 28" image. The
black cross in the magnified window illustrates the location
accuracy of the tracked point.
* Refining the conjugate points by LSM
The feature points used for the epipolar image generation had
better be subpixel accuracy because even though the error
introduced into the slopes of the conjugate lines by the pixel
inaccuracy is small, the magnitude of the inaccuracy can be
magnified when interpolating gray values along the conjugate
lines (Luhmann and Altrogge, 1986; Tang and Heipke, 1996).
Thus, we further refine the conjugate points by least square
matching-LSM (Ackermann, 1983). The number of conjugate
points, which can be extracted from the image sequences
decreases with the distance from the first frame. Close to the
first frame (e.g., the second frame), we can identified over one
hundred conjugate points; at the last frame, we could only get
about 30 good conjugate points. Basically, this operation
guaranteed that all of the conjugate points were with high-
quality, and that at least 8 conjugate points can be extracted.
e Rectifying the original images
Based on extracted distinctive feature points, the implied
relationship between the original and normal images can be
established using Equation 9. Least square estimation is
employed to solve the 8 implicit parameters. With the implicit
parameters, the original image sequence can be rectified into
the normal image sequences by Algorithm 1.
* Epipolar-plane image (EPI) generation
In terms of the method of EPI generation (The details of
generation of EPIs was described in Zhou et al., (1999)), the
EPIs for the three test fields were obtained from the rectified
image sequences. We randomly selected one EPIs from each
test field, as displayed in Figures 9b through 11b. To compare
the differences of EPIs, the corresponding original EPIs
constructed by the original image sequences are displayed in
Figures 9a through 11a.
» DEM generation
The ground coordinates (X, Y, Z) are uniquely determined by
the slope and the intercept of the trajectories in the EPIs (Zhou
et al., 1999). The DEMs of the three test fields were generated
by the rectified EPIs and displayed in Figures 12b through 14b.
To compare the differences, the original DEMs generated by
the original EPIs are displayed in Figures 12a through 14a.
3.2 Analyses of the experimental results
e Analyses of EPI
The EPI principle demonstrates that all trajectories in the EPIs
should be straight lines if we successfully rectified the original
(distorted) image sequences into normal (rectified). This
criterion can be used to evaluate our algorithm by comparing
the original EPIs with the rectified EPIs.
The first experimental field (Berlin city test field): In Figure
9a, trajectory 2 (a wide white bar) first shows a curve at the top,
and then splits into two curves at 2/3 heights from the EPI's
bottom. The rectified EPI shows this trajectory is indeed a
straight line.
The second experimental field (Schónefeld test field): The
rectification effects in the second test field are more obvious
(see Figures 10). For example, trajectories 1 thru 6 in Figure
10a are segments in the original EPIs. The rectified EPIs
(Figure 10b) show almost all of these trajectories are straight
lines, and are neither broken nor disappear.
The third experimental field (Werder test field): Some of
trajectories in the rectified EPI and corresponding trajectories in
the original EPI are labeled. The rectification effects get very
obvious in the third test field. For example, trajectory 1 in
Figure 11a only appears in the middle of original EPI, while the
rectified trajectory is a continuous straight line (see Figure
11b).
e DEM analysis
In order to evaluate the accuracy of the DEM, we chose the first
and 108th images to construct a stereo pair of images, and then
produced a DEM using VirtuoZo v2.0 softcopy
photogrammetric system (Supersoft Inc.). 15 ground control
points (non targeted photogrammetric points) were measured
from a 1:2000 scale map. The generation of three DEMs was a
highly labor-intensive and time-consuming using VirtuoZo. A
lot of human's edit is needed. The DEMS for the three test fields
are shown in Figures 12c thru 14c. In each test field, we
measured X,Y,Z coordinates for over 500 points. The variances
between the before and after rectified DEM's are listed in Table
1. Accuracy of the rectified DEM's was increased up to 30% in
X, 40% in Y and 35% in the Z direct
Table 1. DEM accuracy evaluation. The increment rate is
computed by "ate = (variance, — variance, )/ before
Test Accuracy Improvement Rate (%) | Checked
Field X Y Z points
31.9 328 37.0 580
2 44.2 42.3 48.5 990
3 27.7 30.7 44.4 1500
4. CONCLUSIONS
A method for automatically rectifying distorted aerial image
sequences for Urban 3D mapping using EPI analysis technique
has been described in this paper. The apparent advantages of
this method are:
(1) The relationship between the original and the normal
images is described by the implicit instead of explicit
parameters. Thus the computing time consumes less than those
of which use the explicit parameters to describe the
relationship.
(2) The whole rectification process is linear and, therefore,
simpler.
(3) The mathematical model does not need the orientation
parameters of the cameras. It is a convenient and practical
solution for a number of applications, such as mobile mapping
technology.
The algorithm developed here has been demonstrated to be
useful in an EPI analysis applied to aerial image sequences.
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