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Fusion of sensor data, knowledge sources and algorithms for extraction and classification of topographic objects
Baltsavias, Emmanuel P.

International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999
errors). Height measurement fails for various reasons all over
the DEM (e.g. temporal (radiometric or geometric) changes or
sensor noise), therefore all resulting random errors will be
summarized in a statistic error. The definition of blunders is
adopted from the common multi-measurement case (e.g. wrong
determination of ground control points). Note that blunders and
systematic errors have (statistically) the same effect, as they
cause an offset in the expectation values of the observations.
The correlation coefficient R is defined as
a/ £ 1
(-1 Several authors give surveys of InSAR and stereo-optical DEM
errors. Grim (1986), who refers to the Baarda error model, gives
a detailed error description for photogrammetric sensor
modelling. Zebker et al. (1994) gave an evaluation of ERS
topographic map accuracy, dividing errors according to their
effects in statistic and systematic errors.
Each error type will occur in both InSAR and stereo-optical
DEMs. In contrast to systematic errors and blunders, statistic
errors of phase and parallax measurements occur locally, but
may turn affected regions unusable. Typical reasons for statistic
errors in spacebome DEM generation are temporal changes
between both passes. As the InSAR procedure is very sensitive
to a change of backscatter geometry, the errors in InSAR DEMs
increase with the repeat pass time interval. Additional problems
with the handling of mountainous terrain lead, in comparison to
optical sensors, to a generally less robust performance.
The presentation of erroneous heights is different in both
DEMs. The stereo-optical DEM is affected by spikes, which
make the DEM appear rugged. These spikes originate from the
mismatching of conjugate points in the stereo pair. The
resulting parallax causes a wrong height estimation, i.e. the
point lies above or below the terrain (Fig. 4). The localization of
these errors seems to be much easier than the error detection in
the InSAR DEM. Although residues in the interferogram appear
as phase jumps higher than 7t, these values are either not used or
replaced by surrounding phase estimates, depending on the
phase unwrapping algorithm. For this study, the least squares
(LS) unwrapping algorithm (Ghiglia and Romero, 1994) has
been applied, which estimates heights by integrating the phase
vector gradient field under a smooth solution constraint, thus
suppressing residuals and yielding a global solution. Although
this algorithm performs robustly in comparison to the tree
algorithm (Goldstein et al., 1988), errors are still localized in
areas of low correlation in the LS DEM (Zebker and Lu, 1998).
As stated above, interferometric and stereo DEM generation
requires the correct identification of the same point in both
images, in order to measure the phase difference or the parallax.
Unlike systematic errors, which can be reduced by suitable
choice of parameters, the reduction of statistic errors is the
challenging act for the fusion process. The next section shows
the meaning of the correlation coefficient for both techniques. It
will be used as an indicator of the presence and extent of noise
and consequently of the statistic error of each measurement.
where E{Xi} denotes the expectation value of the statistic
variable Xi, hence E{(Xi) 2 } is the variance and E{X1X2} the
covariance of XI and X2. Note that coherence denotes the
absolute value of p in interferometry.
The correlation coefficient between two images is used in both
techniques, but has for each technique a different meaning. In
the stereo-optical case, points are matched by maximising the
correlation coefficient within the correlation window.
Therefore, the correlation coefficient of each DEM point shows
the maximum correlation value occurring during the matching
process. Therefore, low correlation indicates not necessarily a
point error, but points, where matching problems may have
Low correlation of grey values results from radiometric
differences between the images, due to multitemporal and
across track data acquisition (case of SPOT stereo viewing),
sensor noise or atmospheric effects due to scattering and
absorption, etc. Therefore, a low correlation coefficient will
occur randomly all over a DEM, wherever differences between
the stereo images exist (Fig. 3). Image pre-processing, like
filtering and introduction of geometric and radiometric
constraints are highly needed in the multitemporal case in order
to reduce the effects of radiometric differences on the matching
algorithm (Baltsavias and Stallmann, 1993).
In the InSAR case, a high coherence indicates those areas,
where phase estimation for DEM generation is reasonable. Even
more, the cross-correlation would give an estimate of the height
error, if it was known precisely, as
a = K
a: height error
K: constant term
E: signal to noise ratio
Note that only a correlation estimate is computed within an
estimator window from the flattened interferogram (Small et al.,
1995). Therefore, the estimated height error is dependent on the
size of the estimator window (Prati et al., 1994). Still, the
correlation coefficient can be used as a confidence map of the