-B3, 2012
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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B3, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
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Figure 6: Optimal penalty functions (75; and P»;) for the Cones
image (solid lines) and in the presence of AWGN (dotted lines).
The degenerated images are shown in Fig. 8 top row. The eval-
uation methodology remains as with the first experiments. This
experiment is aimed at answering the following questions: Are
the penalty functions robust towards a variety of different im-
age interferences and which performs best? How robust is the
parametrization across these interferences? Is the choice of penalty
function and parametrization the same as for the non-degenerated
images? The errors curves for the four types of simulated de-
generation are shown in Fig. 7. Fixed penalty functions degrade
quickly for census and rank, as the constant values are now trained
to the type and amount of noise in the image. Adaptive functions
are able to cope with the noise and radiometric changes. As with
non-degenerated images, P»; and P»; perform best and in many
cases similar. For rank, P»; outperforms 7^», except for salt-and-
pepper noise. For census, the two functions perform equally ex-
cept for salt-and-pepper noise where the P^; significantly outper-
forms the linear function. The variance based approach is always
outperformed by the other adaptive approaches. For qualitative
evaluation the resulting disparity maps are shown in Fig. 8.
Comparing configurations across the different types of degener-
ation shows that good configurations coincide (data not shown).
As before, good configurations from one image to the next can
often be found within a 0.5 percentage points error margin. How-
ever, comparing good configurations to configurations from the
non degenerated images shows that now higher dynamic range
and higher penalties are chosen. For example, the best param-
eter set from the original Cones image for P»; is (P, — 11,
Po min = 17, 7 = 35,0 0.5) resulting in 5.23 95 erroneous
disparities. For the AWGN case it is {P, = 20, Pa min = 24,
y = T0, œ = 0.5} and for the salt-and-pepper case (P1 = 14,
P2,min = 24, y = 40,a = 0.5} resulting on the original image
in 6.27 % and 5.37 %, respectively. For comparison, the opti-
mal penalty functions for the AWGN case have been included
in Fig. 6. Consequently, proper selection and parametrization of
penalty functions can make disparity estimation robust to high
levels of interferences with only minimal performance decrease
in ideal cases. However, it also shows that for high-end applica-
tions targeting highest quality disparity maps sophisticated image
preprocessing is required.
3.3 Real World Images
For real world image data the lack of ground truth makes it ex-
tremely difficult to setup automated parametrization. However,
optical inspection using real world data from (Ess et al., 2007)
was performed with the parametrizations obtained from the non-
degenerated and degenerated images. Special attention has been
paid to planar, little textured areas, edges, and small structures
(e. g. lamp posts). Generally, better results were obtained when
using the configurations from the degenerated images. This is in
accordance with the argumentation from above.
f | Cones Teddy Venus Tsukuba
Census Transform
Pe. 15383% 104094 253% 8.35 %
PB, (523% 9.03% 1.92 % 7.45 %
Pi | 543% 930% 2.06% 7:55.95
P. 532395 10.79% 255% 8.54 %
Rank Transform
Pe | 746% 1244% 4.20% 9.32 %
17299. 11179» 3.15% 8.58 96
Pi 737% 11.76% 4137 9.06 %
Pov 749% 1257% 416% 9.41 %
Table 1: Errors in non-occluded areas with a threshold of 1 dis-
parity obtained with optimally parametrized penalty functions.
f | Baseline AWGN Salt Shadow Gamma
Census Transform
P 538% 26.35% 7.63 96 786% 5.41 %
P 523% 18.01 95 8.277 96 727% 527%
P5 543% 18.94 % 7.40 % 7.26%. 530%
P. 528% 30.70 % 8.40 % 816% 545%
Rank Transform
P 746% 40.64% 10.9970 10.2790 7.60%
P 729% 32.6176 11.74% 727% 7.41%
P; 749% 4061% 11.11% 994% 7.47 %
Py 737% 45.84% 119% 1054% 7.61%
Table 2: Errors in non-occluded areas with a threshold of 1 dis-
parity obtained with optimally parametrized penalty functions on
the cones image under various types of degeneration.
4 CONCLUSIONS AND FUTURE WORK
In conclusion, the choice of penalty function and its parametriza-
tion has significant influence on the performance of SGM, es-
pecially under difficult imaging conditions (e. g. noise, expo-
sure differences). While for highly structured images taken un-
der near ideal conditions constant penalty functions (P5) per-
form well, they tend to become overfitted to the particular imag-
ing conditions and performance is not stable over different con-
ditions. Among the adaptive functions, the linear (P»;) and in-
versely proportional (P,;) functions significantly outperform the
variance based approach. They are also robust to interferences
in the images making adaptive penalty terms mandatory for ro-
bust disparity estimation. Even then, the quality of the dispar-
ity map significantly depends on a suitable penalty function for
SGM. Using inversely proportional penalty functions, as origi-
nally proposed with SGM, does not result in any performance
improvement compared to linear dependencies, which is of inter-
est for computationally limited implementations. Nevertheless,
thorough parametrization according to the employed matching
cost function is essential. Since parametrization using difficult
images results in more robust parameter sets real world systems
should parametrized under these conditions. For all penalty func-
tions, employing census transform instead of rank transform ex-
hibits better disparity maps with less edge blurring because cen-
sus transform retains spatial information. Future work includes
testing the penalty functions for other types of matching cost
functions, e. g. mutual information.
ACKNOWLEDGEMENTS
This work has been supported in part by the Hans.-L.-Merkle
Stiftung (Stifterverband fiir die deutsche Wissenschaft).
