The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
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As Table 2 and Table 3 (see chapter 2) already show, most of 
the changes indicated by the per-pixel indicators are changes in 
vegetation, i.e. either an increase or decrease of the vegetations 
vitality. Therefore, a change in vegetation is given, if a segment, 
which has been segmented on the basis of the Diffnorm- 
channels, shows discrepancies in the NDVIs calculated for tO 
and tl. By calculating the ratio between the mean NDVI tl and 
mean NDVI t0 of an object no change is given if the ratio is ex 
actly at 1.0. In terms of indicating a gradual change the more 
the ratio between the mean NDVI tl and mean NDVI t0 of an 
object is unequal to 1.0 the more a change in vegetation is given. 
This expression can be depicted by a fuzzy membership func 
tion as displayed in Figure 5, whereas here each NDVI has been 
normalized to a range of 0.0 to 1.0 before and as upper and 
lower bound for absolute membership (i.e. a definite change) 
0.9 and 1.1 respectively were set. 
Figure 5: Fuzzy membership function to express changes in the 
vitality of vegetation by the ratio of the NDVIs of tO an tl. 
In terms of expressing gradual changes, the membership func 
tion in Figure 5 can be interpreted as follows: if the ratio be 
tween NDVI t i and NDVI t0 of an object is exactly 1.0 no change 
in vegetation is given. If it is below 0.9 or above 1.1 there is 
definitely a change in vegetation given. If the ratio is between 
1.0 and 1.1 or 0.9 and 1.0 a gradual change of vegetation ac 
cording to the degree of membership (p) is given. This way, an 
increase or decrease in vegetation vitality can be described 
analogous so that a definite decrease is given with a ratio below 
0.9 and vice versa for an increase. However, as demonstrated in 
Figure 6, increases or decreases of the NDVI are given in agri 
cultural areas the same way as for example changes from vege 
tated to non-vegetated areas and vice versa. As shown in Figure 
6 due to the relatively high dynamic of agricultural areas in the 
NDVI (or any other measurers sensitive for vegetation vitality), 
increases or decreases of the NDVI mostly occur in such areas. 
However, in the most cases these increases or decrease cannot 
be interpreted as changes of land use. On the other side, changes 
of vegetation in agricultural areas typically occur steadily and 
more or less equally distributed within a field (as field in this 
context areas with equal cultivation and not of equal land tenure 
are meant). Thus, in many cases such changes can be discrimi 
nated from other changes by regarding the homogeneity of 
change within a change area. To describe the homogeneity of a 
change related to its area, e.g. the differences of the standard 
deviations (Aa) for each channel at tO and tl within the change 
area can be ana lyzed. However, a disadvantage of this approach 
is to find suitable thresholds to determine whether a change is 
homogeneous or not, since the standard deviation depends on 
the size of a segment. Thus, in order to evaluate the usability of 
Aa we determined the thresholds of -20 respectively +20 em 
pirically in conjunction with the membership-functions as dis 
played in Tab. 4. Besides, these values approximately coincide 
with the overall a/2 of the per object Aa. When working with 
object hierarchies, as like with Definiens™ Developer, another 
approach to define the homogeneity or heterogeneity of change 
within an area is to analyze the relationship of the size of a 
change area to the number of sub-segments generated by an 
over-segmentation as described in chapter 3.2. For this ap 
proach an indication can be given by the ratio of sub-segments 
to the number of pixels within the segment itself: assuming a 
segment containing k pixels and n sub-segments whereas the 
segmentation to generate the sub-segments aggregates pixels, so 
that for the segment itself k > n > I is true. Then by dividing n 
by k a maximum of homogeneity is given if n = 1 and k > 1. 
Since n / k converges to 0 if n f k f 1, a minimum of homoge 
neity is given if n = k and n > I and k > 1. Therefore, a linear 
membership function can be defined which expresses the degree 
of homogeneity in change respectively, (see Tab. 4). An ap 
proach, that it capable to combine an arbitrary number of prop 
erties to determine a degree of change is given by a modifica 
tion of a procedure which has been used by Earth Satellite Cor 
poration, named Cross-Correlation-Analysis (Koeln et al., 2000). 
In this method, class boundaries from the older thematic map 
separate image pixels into distinct class zones. Within these 
boundaries the pixels as of a new unsupervised classification are 
validated using a multivariate z-statistic. This idea has been 
adopted and slightly adjusted within this project using the De- 
COVERtO mapping as reference (super-objects within the 
object-hierarchy) and computing the Z-Value for each sub 
object within the boundaries of a tO mapping object: 
with: 
v i(i = mean of property i of the sub-object at point of time tl. 
/u i o = mean of property i of the super-object at point of time tO. 
<j i/o = standard deviation of property i of the super-object at 
point of time tO. 
Figure 6: Classified change segments by decrease or increase of 
the NDVI and DeCOVER tO mapping superimposed to 
Diffnorm-channels (R=Diff_norm nir, G=Diff_norm red, 
B=Diff_norm green.)