International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999 
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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. 
3. CORRELATION COEFFICIENT 
The correlation coefficient R is defined as 
[x\xi] 
a/ £ 1 
[xix\] 
\e\ 
[X2X2) 
(-1 <p< 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 
occurred. 
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 
(2) 
with 
P 
1-/7 
(3) 
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 
InSAR DEM.