ls0 ws0">
DEMs produced according to the national standard of
2.2. LV and ROC-LV
The original idea of using local variance to select optimal
scale was raised by Woodcock, Strahler and Jupp (1998)
[31]. Given the same region’s image with different scales,
we can find the optimal scale through calculating each
image’s local variance. The calculation steps are list as
Firstly, set an analysis window on each image, move
the window through the entire image and calculate the
variance of all the pixel value in the window on each
position. Suppose the window is ,
21 21aa 
,ij is the pixel value of the position, then
the local variance of the window which take this pixel as
the center can calculate by the following formula:
 
ij kial ja
ij u
 
where ij
is the local variance. is the mean of the
pixel value in the window.
Secondly, calculate the mean of all the local variance
of the image, so the mean local variance of the image can
be expressed as:
22La M
La Ma
ia ja
 
the image’s local variance, L is the rows of
the image and M is the columns of the image.
Finally, take the images’ spatial resolution as abscissa,
the mean local variance as the vertical coordinates, and
plot the local variance graph. Observe the variance trend
of the local variance as the scale become coarser, the
scale can select as the optimal scale at which the local
variance achieve the peak in the local variance graph.
Kim (2008) made advances toward addressing this is-
sue in the context of OBIA by exploring the relationship
between segmentation variance and spatial autocorrela-
tion at different scale parameters to define the optimal
object size [32]. The above methods focused on one op-
timal scale, which is appropriate for simple scene models;
however, many environmental problems cannot be han-
dled at a single scale of observation, researchers often
have to deal with nested models of a scene. As such,
multiscale analysis and representation require more than
one suitable scale parameter to account for different lev-
els of organization in landscape structure.
Lucian (2010) calculate the local variance of objects
generating through segmentation under different scales,
in order to assess the dynamics of the local variance from
an object level to another, the author use a measure called
rate of change (ROC). Through several experiment ana-
lysis, the author found that the peaks in the LV-ROC
graph could indicate the object level at which the image
can be segmented in the most appropriate manner.
However, the method put forward by Lucian requested
too much calculation. On the other hand, it is difficult to
select the optimal scales using the local variance based
on pixel graph. SO we utilize Lucian’s method as re-
ference, define the rate of change in the same way. The
difference is our calculation is based on pixel, rather than
ROC ll
where l is the local variance at the target level and
is the local variance at next lower level.
2.3. Segmentation on eCongnition
An object-oriented method proposed by Dragut and Blas-
chke (2006) is adapted to loess slope segmentation [14].
Firstly, several data layers are extracted from Digital Ele-
vation Models (DEM): profile curvature, plan curvature
and slope gradient. Secondly, every data layer is taken as
a single-band image, and then the three single-band im-
ages are combined into a multiband image. Then append
a new process in the process tree. Six parameters should
be defined: (a) segmentation algorithm, multiresolution seg-
mentation is selected in this paper; (b) Image Object Do-
main, since the segmentation would be carried out based
on the original image, so pixel level is selected; (c) Im-
age Layer weights, we defined the same weight for the
three single-band image; (d) Scale parameter, the defini-
tion of this parameter is discussed in the next part of the
paper; (e) Composition of homogeneity criterion, the pa-
rameter shape define the weight that the shape criterion
should have when segmenting the image. The higher its
value is, the lower the influence of color on the segmen-
tation process. The parameter compactness defines the
weight of the compactness criterion. The higher the value,
the more compact image objects may be. By lots of ex-
periments, we set the shape as 0.3 and the compactness
0.5. The entire tests are run on the eCongnition software
which is developed by Definiens Company.
3. Result and Discussions
The segmentation process requests three layers: slope,
plan curvature and profile curvature. In order to make the
analysis easy to interpret and make sure the result con-
sistent, the three images were integrated into a synthetic-
cal layer according to the weights 1, 1, and 1. The con-
crete fusion process could be carried out as following:
Firstly, calculate each layer according formula (4) to
make the pixel value range from 0 to 1. This process can
Copyright © 2012 SciRes. IJG
eliminate the dimensional influence on the different lay-
max min
p (4)
where ij is the original value of the pixel in the place
, and newij is the calculated value of the same
pixel; min is the minimum value and is the
maximum of the layer.
Then, carry out raster calculation according to formula
(5) to integrate three layers into a synthetical one.
ij ij
ij syn
p (5)
where ij syn is the value of the pixel in the place
of the synthetical layer, 1ij
, 2ij , and 3ij
is the
value of the pixel in the same place of the three layers.
Haven obtained the single synthetical layer. This paper
employed ArcGIS 10.0 to calculate the local variance at
different scales. Firstly, use the Block Statistics tool to
calculate the local variance under the 3 × 3 window, and
then change the analysis scale by change the size of the
moving window to calculate the new local variance; Re-
peat the above work until the scale up to some decided
value. At last, we obtain the local variance at different
3.1. LV and ROC-LV Graph
Utilized the local variance at different scales, one could
plot the LV-Scale graph (Figure 2). Figure 2 shows that
the local variance increased as the resolution becomes
coarser, but the velocity of the increase declines. The
local variance tends to become a fixed value when the
scale became large enough. These results could be ex-
plained as following: when the image’s resolution is much
smaller than the objects’ size, in another word, the reso-
lution is very high, each pixel in the image has high cor-
relation with its neighbor, so the local variance is small;
as the objects’ size is equivalent to the spatial resolution,
the value of each pixel is different with others, so the
correlation decrease, leading the local variance increase.
In the experiment of this paper, because there are no ob-
vious boundaries among different slopes, so the local
variance doesn’t mount up to a peak, the local variance
increase more slowly as the spatial resolution becomes
coarser, finally tends to become a fixed value.
Haven obtained the local variance at different spatial
resolution; the local variance-rate of change (LV-ROC)
could be calculated according to the formula (3). Fur-
thermore, one could plot the LV-ROC-Scale graph (Fig-
ure 2). Be aware that in this paper we removed five
points in the front, because comparing with the other
values, the five values in the front is too high, so it is
difficult to find the jump points when plot them together.
From the Figure 2, it could be found that as the spatial
become coarser, the local variance decrease with many
jumping points. Because these jumping points could in-
dicate the large change of the local variance under certain
spatial resolution, these jumping points likely indicated
the optimal segmentation scales.
3.2. Segmentation Results
This paper selected three obvious jumping points for
each experiment areas, marked with broken line in the
LV-ROC graph. For Suide, scales relevant to the jump-
ing points are 40, 90, and 110; for Ganquan, scales rele-
vant to the jumping points are 45,105 and 115; for Yijun,
scales relevant to the jumping points are 45,105 and 155.
Carry out the segmentation process under the three scales.
The segmentation results are listed in Figure 3. In order
to observe the equality of the segmentation, the segmen-
tation results were overlaid on the hillshade of the origin-
nal DEMs.
The segmentation results showed that at the small
scale, boundaries of different slopes’ could be segmented
from the synthetical layer. As the scale became large, the
segmentation results became fuzzier, because many simi-
lar slopes can’t be differentiated; as the scale kept on in-
creasing, the small basins were seemed as a type of slope.
So we could conclude that the three segmentation results
reflect the objects’ boundaries of different levels. Com-
pare the experiment results of the three areas, it could
also be found that the first and second optimal scale for
the three areas are similar, the reason is that all the test
areas have lots of gullies of the same size on the whole.
However, since the Yijun area is more flat than Suide area
and Ganquan area, so the third optimal scale for the Yi-
jun area is much larger.
4. Discussion and Conclusions
Although the production of multiscale representation of
spatial entities has been technically enhanced in OBIA
through image segmentation, choosing the suitable levels
of representation has remained a challenge. Kim et al.
(2008) proved that LV graphs indicate the optimal scale
parameter for delineating forest stands, but their work
focused on a single scale. Although our segmentation
process is pixel based, the LV graph doesn’t peak or de-
clined, the graphs we obtained followed a relatively
smooth variogram shape. While appropriate for detecting
a single scale, the LV graph is not suitable for a multis-
cale approach. So this paper applied Lucian’s conception in
choosing the optimal scale in the multiresolution seg-
mentation process.
Lucian’s work calculated the local variance based on
segmentation results, this idea may appropriate for im-
ages which contain objects that have obvious boundary.
Copyright © 2012 SciRes. IJG
Copyright © 2012 SciRes. IJG
Figure 2. LV and LV-ROC Graphs of the three experiment areas. (a) LV and LV-ROC graphs of Suide; (b) LV and LV-ROC
graphs of Ganquan; (c) LV and LV-ROC graphs of Yijun.
Figure 3. Segmentation results of the three experiment areas under different scales. (A) Segmentation results of Jiuyuangou
under scale 4,090,110; (B) Segmentation results of Ganquan under scale 45,105,115; (C) Segmentation results of Yijun under
scale 45,105,155.
However, in this paper, slopes of different types don’t
have obvious boundary. So it is not appropriate to calcu-
late the local variance based on segmentation results. The
study firstly infused the three images into a synthetical
one as the original layer to calculate the LV and ROC-
LV instead. The segmentation results of the three test
areas with different landform characters showed that this
changed method is efficient for multiscale slope seg-
mentation. Furthermore, the method may also afford a
new idea for traditional digital image process, especially
for the multi-band image analysis.
5. Acknowledgement
Thanks for financially support from the National Natural
Science Foundation of China (No. 40930531, No. 4080
1148, No. 41171299).
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