Figure 4: Tie-point detection results showing 15 best (left) and 5 best (right) point candidates. 
3. TIE-POINT MATCHING 
3.1. HFVM Method 
In a next step the corresponding points of the detected 
tie-point candidates have to be found in the overlapping 
areas of the other image(s). Therefore, an automatic 
matching tool, the so-called Hierarchical Feature Vector 
Matching (HFVM) is applied, which has been developed 
by Paar et al. (1991, 1992). The HFVM method integrates 
particular derivatives of a SAR image, so-called features. 
While conventional matching techniques usually exploit 
just one local image property (e.g. grey level, edge, 
corner, local phase), the HFVM tool analyses a 
combination of several local features in connection with a 
hierarchical image representation. This allows to consider 
SAR specific image properties on the one hand and to 
correspond with the tiepoint candidate detection on the 
other hand, as similar or same filters and features can be 
applied within the tie-point detection and the tie-point 
matching procedure, respectively. By the large variety of 
features particular disadvantages can be equalised. 
The principle of the HFVM method can be summarised as 
follows: 
e A set of feature images for both the reference and the 
search image is CertEd. The features are derived from 
local properties in the surrounding of each pixel. The 
contents of these feature images describe a feature 
vector for each pixel location in both images. 
For each pixel of the reference image its feature vector 
is compared to the feature vectors in the expected 
search range in the search image. Using the Euclidean 
distance, the minimum distance vector defined the 
corresponding pixel. 
The columns and row disparity images are smoothed 
using median filters. Then, errors are removed and 
undefined disparities interpolated. This is done from the 
lowest to the highest necessary resolution, using the 
low resolution results as prediction. 
318 
HFVM provides a dense disparity map which gives 
access to the disparity of every pixel of the input image. 
HFVM allows fast and robust matching together with a 
large variety of choices in terms of accuracy, resolution, 
consistency checks, an computational effort. Originally, 
HFVM has been developed to compute dense disparity 
maps for optical stereo images including rugged terrain. It 
is a general method also suitable for SAR imagery. In fact 
this algorithm is shown to be just as efficient as methods 
being specifically suited for SAR imagery corrupted with 
speckle noise (Gelautz et al., 1996). 
For the matching of tie-point candidates the HFVM 
method has been slightly adapted as follows: 
Only the surrounding of a TPC has to be considered 
in the matching process. Thereby, potential pixel 
disparities due to terrain relief should be taken into 
account. 
SAR mapping mechanisms based on initial imaging 
parameters are used to map the reference area of 
interest to the search image. 
Backward matching from search to reference image is 
used and the pixel difference between reference TPC 
and ,back-matched" TPC serves as a quality measure 
in order to accept or reject the correlated result. 
3.2. Tie-point Matching Example 
The performance of the HFVM algorithm is analysed for 
those points being provided by the automatic tie-point 
detection procedure, i.e. the detection results presented 
in Figure 4. Figure 5 shows the reference image chip 
together with the respective area of the search image. For 
the matching of the TPCs a backward correlation was 
performed with a maximum mismatch distance of 1 and 
1.5 pixels, respectively. Figure 6 presents the reference 
image chip with those areas exceeding this backward 
matching limits shown in white. It can be seen that for 
SAR images the areas fulfilling the specified backward 
matching criteria are rather limited. Obviously for less 
than 50% of the entire area the backward matching is 
accurate within 1 pixel. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996