The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
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large if the boundary corresponds to an image edge and thus to 
a real grey level discontinuity, whereas it will be small for 
edges that separate two segments of a similar distribution of 
grey values. 
2.3 Merging of Regions Having Similar Attributes 
The RAG and the attributes of both its nodes and its edges are 
the basis for merging neighbouring regions to improve the 
initial segmentation. It is the goal of this process to merge 
regions that have similar radiometric properties and noise levels, 
but that are not separated by a significant edge. First, a distance 
metric Dy is computed for each edge e^. 
D., = 
(g' -g' Y • (Q‘ + Q' Y ■(g' -g' ) 
\® avg Oavg ) Y<- gg gg ) \&avg Oavg ) 
%N,\-a 
(2) 
In Equation 2, the vector g‘ avg - g‘ avg is the difference vector 
between the average grey level vectors of the two regions, and 
^n.i- is the 1- quantile of a chi-square distribution with N 
degrees of freedom, where N is the number of image. Two 
regions Sj and Sj are said to have similar attributes if the value 
of Dy is smaller than 1. This corresponds to a statistical test 
whether the difference between two grey level vectors having 
the covariance matrices Q' gg and ff gg is significant, though it is 
not a test whether the difference between the average grey level 
vectors is significant. In any case, the selection of a threshold 
for the difference between grey level vectors is replaced by 
selecting a significance level 
However, the distance metric D tj is not the only indicator used 
for identifying similar homogeneous regions. Dy is small if the 
difference between the average grey level vectors is small or if 
the variances of the grey levels inside a region are large. This 
means that if one image segment is highly textured (e.g. 
because it contains trees), it might be merged with neighbouring 
segments that are quite homogeneous, because the grey level 
difference can be statistically explained by the variances of the 
grey levels in the highly textured segment. Thus, we restrict the 
set of regions that can be merged to those having a similar level 
of noise. We introduce a second metric, the variance factor Efy 
that compares the two noise levels var‘ and var * 1 of 5, and Sf. 
f: = ■ 
NPi,,NPj,l-a 
(3) 
In Equation 3, it is assumed that var 1 > varF NPt N . Pj ¡_ is the 
1- quantile of a Fisher distribution with NPi and N-Pj 
degrees of freedom, where N is the number of image bands and 
Pi and Pj are the numbers of pixels assigned to S, and S r The 
segments may only be merged if F v i j is smaller than a threshold. 
Using a value of 1 for that threshold corresponds to a statistical 
test for the identity of the two noise levels. 
Finally, even if two segments have similar grey level 
distributions and a similar noise level, they still might be 
separated by a significant edge, e.g. by a small path between 
two fields, as it is the case in the upper comer in Figure 2a. As 
stated above, an edge in the RAG contains the vector of average 
grey levels and the covariance matrix of the grey levels of the 
boundary between the two neighbouring segments and a 
measure Ty for the strength of the boundary. Two segments may 
only be merged if the distance metric according to Equation 1 
between the merged segment and the boundary region is smaller 
than 1 and if Ty is smaller than 0.5, i.e. if less than 50% of the 
pixels separating 5, and Sj are edge pixels. 
Thus, by applying the rules described in this section, a set of 
tuples of regions 5, and Sj that may be merged can be 
constructed. This set is ordered by the distance metrics Dy; the 
first element thus corresponds to the two segments having the 
most similar grey level distributions while still having a similar 
noise level and not being separated by a significant edge. These 
segments are merged, including the boundary pixels that 
formerly separated them, and the RAG is updated. In this 
context, the segment label image has to be changed, the 
attributes of the new merged segment have to be determined, 
and the edges of the RAG have to be updated. This analysis is 
repeated iteratively until no more segments can be merged. 
Figure 4 shows the segment label image generated by grouping 
the original labels in Figure 3a. 
Figure 4. Segment label image generated by grouping the 
original labels in Figure 3a. 
3. USING THE SEGMENTATION ALGORITHM FOR 
THE VERIFICATION OF CROPLAND 
The segmentation algorithm presented in the previous section 
was implemented in the software system BARISTA (Barista, 
2008). In this section we will describe its integration into the 
WiPKA-QS verification process for cropland objects. We will 
show the individual stages of the process using the image 
shown in Figure 1 as an example. Figure 5a shows the initial 
segmentation of that image after Watershed segmentation using 
a smoothing scale of . = 1. Figure 5b shows the results of the 
merging process described in Section 2. 
The results shown in Figure 5b are not perfect. The main 
management units have been separated correctly, but there 
remains some noise in the form of small insular segments and 
especially at the region boundaries. As mentioned in section 1, 
several objects of the same land cover type are permitted inside 
an ATKIS cropland object, and the existence of small areas 
having a different land cover class is tolerated if a size 
threshold is not exceeded and if the actual land cover is similar 
to cropland (e.g. grassland). These definitions can be used to 
further improve the segmentation in Figure 5b. Regions that are 
surrounded by just one other region and are smaller than a 
given area threshold are merged with the surrounding segment. 
Figure 6 shows the results of merging small insular regions 
smaller than 1000 m 2 with their surrounding larger segments.