In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
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2.3 The sub-pixel precision approaches 
2.3.1 Intensity interpolation 
The coarse resolution images within the above-computed 
resolution pyramids were back-interpolated to different finer 
resolutions using the MATLAB-based ‘imresize’ module. Again 
the bi-cubic interpolation was used for the same reason. After 
such back-interpolation, the NCC algorithm was applied using 
the same templates and search windows as used in the original 
reference image pairs. The interpolation is done on the fly for 
each reference template and search window, and not for the 
entire image before the matching process. This was done due to 
memory restriction by MATLAB. 
2.3.2 Similarity interpolation 
Bi-cubic interpolation. To find the sub-pixel position, one can 
interpolate the cross-correlation surface to higher resolution 
using two dimensional bi-cubic interpolation algorithms. The 
algorithm uses a two-dimensional cubic convolution of the 
correlation coefficients to the resampled grid. The peak is then 
relocated. 
Curve fitting. As an alternative to peak interpolation, one can 
also create a continuous function that optimally fits the 
correlation coefficient data and compute the precise location of 
the peak from the maximum of the function. The challenge is 
that no single function can usually perfectly describe the cross 
correlation surface. However, the fact that the correlation 
surface around its peak often approaches a bell shape can be 
exploited. Therefore, two dimensional polynomial functions can 
approximate the surface. A number of interpolation models 
have been tested in empirical and theoretical researches, 
particularly in particle image velocimetry (PIV), though with 
varying successes (Nobach and Honkanen 2005; Westerweel 
1993; Willert and Gharib 1991). Some of the well performing 
ones will be tested here for mass movement analysis. These are 
parabola fitting and Gaussian fitting, as these have shown 
successes especially in PIV. 
In parabola fitting, the shape of the correlation surface is 
assumed to fit two separable orthogonal parabolic curves. The 
location of the ‘actual’ peak is computed by independently 
fitting one dimensional quadratic function and computing the 
location of the peak (Nobach and Honkanen 2005; Westerweel 
1993). 
In Gaussian fitting, the bell shape of the correlation surface is 
assumed to fit a 2D Gaussian function (Nobach and Honkanen 
2005; Westerweel 1993; Willert and Gharib 1991). It is 
assumed that the two dimensions are separable and orthogonal. 
Thus, the sub-pixel peak location is calculated separately for the 
two directions by fitting a second-order polynomial to the 
logarithm of the maximum sample and the direct neighbours. 
2.4 Evaluation of different levels of sub-pixel detail 
Section 2.3 evaluates which sub-pixel approach performs best in 
improving the precision and accuracy of NCC-based image 
matching. It is also important to know how far sub-pixel 
interpolation of coarse resolution image intensities or the 
correlation surface is able to substitute pixel-level matching of 
images of the corresponding but original resolution. In other 
words, what is the sub-pixel detail at which the interpolation to 
achieve sub-pixel precision can no longer sufficiently substitute 
image of that resolution. The approach used here to resolve this 
issue is to compute the sub-pixel precision matching at different 
levels of the image pyramid and evaluate its performance in 
reference to the pixel-level matching of images with the same 
but original resolution. This issue becomes clearer with an 
example. Suppose we want to know the performance of sub 
pixel precision matching at the level of half a pixel. This can be 
achieved by taking an image of, for instance, 8m resolution, 
compute the sub-pixel precision matching to 4m and compare 
the latter sub-pixel performance to the performance of pixel- 
level matching of an image with 4m original resolution. Or else, 
take a 4m resolution image, compute its sub-pixel resolution 
matching to 2m and compare the performance of the latter in 
relation to a 2m resolution original image, and so forth 
including the entire pre-processed image pyramid and all 
resolution steps included in it. 
2.5 Performance evaluation 
As indicator of accuracy, we used the shift in matching position 
instead of the often-used difference in displacement magnitude. 
The matching positions obtained during the correlation of the 
original images were considered as references. All the matching 
positions at the different coarser or back-interpolated 
resolutions were compared to these reference positions. The 
magnitude of this offset (deviation) is here used as measure for 
the accuracy of the image and algorithm used. The deviation 
between the matching position of the interpolated image and 
that of the same resolution original image is used to assess the 
relative performance of the sup-pixel approaches. 
3. RESULTS 
3.1 Displacements of the different mass movement types 
Table 2 summarises displacement statistics for the three mass 
movements investigated. The results are produced from the 
analyses of the original ortho-images after filtering all the 
mismatches. One can well see that the glacier moves very fast 
as compared to the rockglacier and the even slower moving 
rockslide. Figure 1 and Figure 2 present the displacement 
vectors of the three mass movements. Image matching showed 
that all the areas in the scene show non-zero displacements due 
to the presence of systematic image (co-)registration error. 
However, after filtering of the vectors based on the estimated 
overall image (co-)registration error of one pixel, thresholding 
of the correlation coefficients and excluding upslope 
movements, only the remaining vectors presented in the figures 
are considered to be valid and useful as reference. 
3.2 Accuracy of the sub-pixel algorithms 
Figure 3 and Figure 4 depict the mean deviation of the matching 
positions against the sub-pixel precisions of each of the sub 
pixel approaches for the control set and the three mass 
movements respectively. The magnitudes of Figure 4 are 
created by averaging the values obtained for the three mass 
movement types as the trend is very similar for all the three. 
Both figures show that interpolation of the image intensity 
before matching results in the best matching accuracy. If one 
looks at the interpolation of the correlation surface, the bi-cubic 
approach follows the intensity interpolation. The curve fitting 
using parabola and Gaussian models perform only better than 
bi-cubic interpolations to one half of the original pixel size.