In: Wagner W., Szekely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
185 
Figure 5 Relative performance of the different sub-pixel 
approaches for the control set expressed as the mean deviation 
of the matching positions from that of the same resolution 
original image 
rj c/3 
S g 
B ï 
-Ö w 
U 
DO 
Bi-cubic 
(correlation) 
Gaussian 
Parabollic 
Bi-cubic 
(intensity) 
No- 
Interpolation 
Sub-pixel precision (fraction of a pixel) 
Figure 6 Relative performance of the different sub-pixel 
approaches expressed as the mean deviation of the matching 
positions from that of the same resolution original image 
(averaged from the three mass movement types investigated) 
4. DISCUSSION 
The results show that intensity interpolation outperforms all the 
other algorithms of similarity interpolation. There can be two 
explanations to this. Firstly, in correlation interpolation the 
positions of the correlation values on which the interpolation is 
based, and which are computed based on coarse resolution 
images, influence the position of the recomputed correlation 
peak. Secondly, the number of pixels in an entity is higher when 
intensity interpolation is applied leading to the suppression of 
noise. Fewer numbers of pixels in an entity makes the entity 
more susceptible to chance-based, i.e. erroneous matching 
results. This explains the increased difference between intensity 
interpolation and similarity interpolation at very detailed levels 
of sub-pixel precision. 
The bi-cubic interpolation scheme that was used for the 
intensity interpolation is known to replicate the reference data 
better than most interpolation schemes (Keys 1981), and it is 
known to approximate the sine interpolation that is ideal in 
image interpolation (Dodgson 1992). This has led to the fact 
that the images re-interpolated from coarser resolutions were 
found to have high correlation with the aerial images of 
corresponding original resolution. For example, when the down- 
sampled rockglacier image of resolutions 0.4m, 0.8m, 1.6m, 
3.2m and 6.4m were re-interpolated to a resolution of 0.2m (1/2 
to 1/32 of a pixel respectively) their global correlation 
coefficients with the reference image of 0.2m resolution were 
0.98, 0.96, 0.93, 0.90 and 0.86 respectively. Although the 
images deteriorate due to resampling noise, they still remain 
well-correlated with the reference image due to the good 
performance of the interpolation algorithm. Correlation is, in 
fact, one of the quality measures of image interpolation 
(Lehmann et al. 1999). 
The same interpolation algorithm, bi-cubic, performed best in 
the similarity interpolation approach although not as good as in 
the intensity interpolation. The better performance in 
comparison to the Gaussian and parabola fitting is partially 
ascribed to the reasons explained above. In addition to that, 
parabola fitting is reported in many occasions to have a 
systematic bias known as “pixel locking”, which forces the 
estimated sub-pixel locations to approach integer values 
(Nobach and Honkanen 2005; Prasad et al. 1992). The presence 
of a systematic bias is testified by the fact that both parabola 
and Gaussian fitting could not fully substitute the same 
resolution original images in the case of the control set unlike 
the other two algorithms (Figure 5). Although reports from PIV 
state that Gaussian peak finding does not have that kind of bias 
and performs better (Westerweel 1993; Willert and Gharib 
1991), it performed no better than parabola fitting in the present 
study. We believe the underlying reason is the fact that the 
cross-correlation surfaces of the mass movements cannot be 
perfectly modelled by either parabolic or Gaussian functions. 
The image resolutions used in the present study are not so high 
to be compared to that of particle images used in mechanics 
which is high enough to be approximated by, for example, 
Gaussian. Besides, noise that is present in the images due to 
temporal surface changes and other sources contribute to the 
deviation of the correlation shape from both Gaussian and 
parabolic. 
Finally, two important points regarding the size of the matching 
entities: Firstly, in this study the absolute metric size of the 
matching entities was kept constant across image resolutions. 
This means that the number of pixels in each entity varies with 
the pixel resolution, leading to a variable signal-to-noise ratio. 
This was done for the sake of comparison. In reality, the size of 
matching entities will vary with the resolution of the image pair 
to keep a good signal-to-noise ratio. Secondly, the size of the 
matching entities was kept the same for the entire scene. In 
reality matching entities vary in size. 
5. CONCLUSIONS 
This study has clarified a number of questions around the 
relation between accuracy and pixel or sub-pixel resolution 
when matching terrain displacements such as glacier flow, land 
sliding or permafrost creep from repeat optical images by using 
pixel-precision correlation measures, here namely the 
normalized cross correlation (NCC). That way the study 
contributes, on the one hand, to better exploiting the 
unexploited archives of repeat remotely sensed images that exist 
over actual or potential earth surface mass movements, and on 
the other hand, to better meeting the increasing needs to 
quantify and monitor mass movements, in particular when they 
are accompanied by adverse effects. 
This study has in particular evaluated the performance of two 
different approaches to sub-pixel precision in NCC for 
displacement measurement based on repeat images. When sub 
pixel accuracy is aimed for, interpolating image intensities to a