d
h area for one
s expected, Q
ed as a CAD model
sts of a cube (size of
rossed red lines. The
f the images has been
| 8um (or 0.8 pixels)
(pixel size is about
cube using three
; technique (LSM)
orward resection and
tes were compared.
LSM Defocus Cross Correlation
6.2 cm 6 cm 7.8 cm
Table 1. Comparison of RMS values of the points’
ground coordinates.
The defocusing algorithm and the LSM technique gave the best
results (almost of the same accuracy) while the cross
correlation algorithm gave the worst solution (table 1), as it was
expected.
The coordinates of the matching points given from the
defocusing algorithm (using different zoom factors) and the
cross correlation technique were compared to the ones provided
from the LSM technique. It has been assumed that the LSM
technique is giving the best results. The results of the
comparison are illustrated in table 2.
Defocusing Cross
Zoom x 1 Zoom x 4 correlation
Mean error
(pixels) 0.54 0.42 0.63
Standard
deviation 0.41 0.37 0.38
(pixels)
Table 2. Comparison of the mean errors and standard
deviations of the defocusing and cross correlation
solutions vs. LSM
(c)
Defocus
LSM (noise) (noise) Corel (noise)
vs. LSM (original) |vs. LSM vs. LSM
Mean error
(pixels) 0.42 0.54 1.61
Standard
deviation
(pixels) 0.54 0.41 1.78
Table 3. Comparison of the mean errors and standard
deviations of the LSM, defocusing and cross
correlation solutions vs. the original LSM solution.
In order to check the robustness of the algorithm gaussian noise
was added to the images (fig. 3). All three procedures were
used to provide new conjugate points coordinates. These
coordinates were compared with those calculated using the
LSM on the original images (no noise). Table 3 illustrates the
results of these comparisons. It is obvious that the defocusing
algorithm is giving very good results providing sub-pixel
accuracy and seems that it is not affected by the random noise.
5. REAL DATA
In real life applications several tests have been applied on
various epipolar stereo-pair images. In most of the cases the
algorithm succeeds in the determination of the conjugate
points. In fig. 4 an example of a true and a false match is
illustrated. It is obvious that the detail image 4d is presenting
many edges parallel to the x-axis, thus, high texture occurs,
while the image 4c is presenting low texture, and appears to be
more blurred, leading to the minimum value of Q factor.
The defocusing algorithm has also been used successfully to
determine conjugate points in aerial applications (fig. 5). The
diagrams (c and d) of figure 5 illustrate the locus of the
matched point on the epipolar images.
(b)
(d)
Fig. 4. Close range application of the defocusing algorithm. Correct match with a Q factor of 16925 (c), false match
with a Q factor of 17725 (d).
6. CONCLUSIONS - DISCUSSION - EXTENSION
There are many advantages, when the above-mentioned
defocus technique is used to produce automatically the
restitution of the 3D object that is displayed 3-dimensional on
the user screen.
Simplicity and almost real-time response of the automatic
procedure are the main advantages. The algorithm consists
only of simple image processing procedures that have already
been implemented into most CPU and graphics chipsets, fact
that makes them really fast and accurate.
Accuracy is another great advantage. Using the defocusing
algorithm the mean errors of the conjugate points’ location and
their standard deviation values were better than those obtained
T7
