International Journal of Geosciences, 2012, 3, 37-43
http://dx.doi.org/10.4236/ijg.2012.31005 Published Online February 2012 (http://www.SciRP.org/journal/ijg)
Optimal Scale Selection for DEM Based Slope
Segmentation in the Loess Plateau
Mingwei Zhao, Fayuan Li*, Guo’an Tang
Key Laboratory of Virtual Geographic Environment, Ministry of Education, Nanjing Normal University, Nanjing, China
Received May 9, 2011; revised August 9, 2011; accepted November 7, 2011
ABSTRACT
Optimal scale selection is the key step of the slope segmentation. Taking three geomorphological units in different parts
of the loess as test areas and 5 m-resolution DEMs as original test date, this paper employed the changed ROC-LV
(Lucian, 2010) in judging the optimal scales in the slope segmentation process. The experiment results showed that this
method is effective in determining the optimal scale in the slope segmentation. The results also showed that the slope
segmentation of the different geomorphological units require different optimal scales because the landform complexity
is varied. The three test areas require the same scale which could distinguish the small gully because all the test areas
have many gullies of the same size, however, when come to distinguish the basins, since the complexity of the three
areas is different, the test areas require different scales.
Keywords: Optimal Scale; Multiresolution; Slope Segmentation; Loess Plateau
1. Introduction
Quantificational analysis of loess terrain is a key subject
in the research of the loess plateau [1-7]. Slope is the
basic element of geomorphology. Based on slope point of
view, Tang et al. (2008) proposed slope spectrum to quan-
titatively describe loess landform [8], Zhou et al. (2010)
discussed the spatial pattern of loess landform based on
loess positive and negative terrain [9], and other re-
searches focus on the extracting of loess landform unit,
such as gully area, gully bottom area and inter gully area
[10]. However, their research cannot properly describe the
spatial structure of loess slope. Considering different
landform is composed by different slopes, so the study of
the spatial structure of loess slope could be a new way to
analyze the loess terrain [11].
In order to analyze the loess terrain based on slope,
different types of slope should be classified well and
truly. Slope classification has long been researched since
1950’s. Hammond (1964) gave a manual way based on
contoured map [12]. With the increasing availability of
commercial GIS software, Dikau et al. (1991) developed
GIS technology to automatic slope classification based
on Hammond’s method [13]. Philip (1998) put forward
an approach to the classification of the slope units using
digital data [14]. Dragut and Blaschke (2006) proposed
an object-oriented method to carry out the slope segmen-
tation process [15]. This method has been proven to be
reproducible, readily adaptable for diverse landscapes and
datasets. However, the limitation of this method is that it
request specify the scale level.
In fact, optimal scale selection is a key issue in the
image analysis [16,17]. As we known, image segmenta-
tion is the first step of image analysis, and it is also the
fundamental process of Object-oriented Remote Sensing
image classification. Most of the image segmentation
methods are based on image characteristic, take given
algorithm parameter, usually the parameter is a threshold
which can separate the adjacent area, to separate the im-
age into areas of different characteristic, so it is a scale
problem in nature [18]. Generally speaking, small scale
can generate smaller image area which could show more
details, while large scale generate larger image area which
could express the objects of unusual. In the process of
object-oriented remote sensing image classification, if
the scale selected is too large, some small object may be
submerged by the larger object; if the scale selected is
too small, the segmentation process may generate frag-
mentation result. So selecting the optimal segmentation
scale is the key issue in object-oriented remote sensing im-
age classification. There are many methods of optimal scale
selection for image segmentation based on pixel [19-22].
However, traditional pixel-based image segmentation
approaches are poorly suited to very high spatial resolu-
tion imagery [23,24]. Object-based image analysis became
prevalent through the realization that image-objects hold
more real-world value than pixels alone [25-27]. Though
*Corresponding author.
C
opyright © 2012 SciRes. IJG

M. W. ZHAO ET AL. 38
the object-based image analysis is becoming increasingly
prominent in remote sensing science [28], the optimal
scale selection is still dependent on subjective trial-and-
error method [29]. Aimed at these problems, Lucian et al.
(2010) put a new conception (ROC-LV) which could em-
ployed to select optimal scales in the object-based image
analysis. Tests on different types of imagery indicated
accurate results [30].
This paper applied the ROC-LV to select the optimal
scale for the DEM based slope segmentation. Because
the datasets tested in Lucian’s study is quite different with
the datasets used for the slope segmentation, the most
distinct difference is that there is no clear boundary among
different types of slope. So in this paper some change
was made in order to make the method suit to our study.
This paper took three geomorphological units in different
parts of the loess as test areas and 5 m-resolution DEMs
as original test date, used the changed ROC-LV to realize
slope segmentation. Experiment results show that though
the datasets are rather different with the ordinary imagi-
nary, the changed ROC-LV could still indicated the op-
timal scales for the slope segmentation based on DEMs.
2. Methods
2.1. Study Area and Data
Three areas, all located in Shaanxi province, are selected
as the test areas (Figure 1). The first area located in
Suide County, which is one of the key watersheds of soil
and water conservation. The highest elevation above sea
is 1115 m and the lowest elevation is 892 m. The main
landform of this area is Loess Hill. Average annual pre-
cipitation is 486 mm and average temperature is 9.7˚C.
The second area located in Ganquan County. The highest
elevation above sea is 1459 m and the lowest elevation is
1147 m. the main landform of this area is Loess Ridge.
Average annual precipitation is 670 mm and average
temperature is 10.4˚C - 13.6˚C. The third area located in
Yijun County. The highest elevation above sea is 1158 m
and the lowest elevation is 768 m. the main landform of
this area is Loess Tableland. Average annual precipita-
tion is 709 mm and average temperature is 8.9˚C. The
locations here belong to the continental monsoon climate.
The main vegetation covers are shrubs and grass, severe
soil and water loss is the main problems in these areas.
Test dates are the corresponding 5 m-grid resolution
Figure 1. Distribution of the test areas.

M. W. ZHAO ET AL. 39
DEMs produced according to the national standard of
China.
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
follows:
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 

,
f
ij

,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:
 
2
,ij
2
2
1
21
ja ia
ij kial ja
f
ij u
2
a

 
 


where ij

is the local variance. is the mean of the
pixel value in the window.
ij
u

Secondly, calculate the mean of all the local variance
of the image, so the mean local variance of the image can
be expressed as:

2
1
22La M
2
11
La Ma
ij
ia ja
a



 

2

where

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
objects.
1
1
ROC ll
l
LV LV
LV




LV
1l
LV
(3)
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

M. W. ZHAO ET AL. 40
eliminate the dimensional influence on the different lay-
ers.
min
max min
ij
pp
pp


p

p
pmax p
newij
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.

,ij
Then, carry out raster calculation according to formula
(5) to integrate three layers into a synthetical one.
123
3
ij ij
ppp


p
ij
ij syn
p (5)
where ij syn is the value of the pixel in the place


,ij
p
of the synthetical layer, 1ij

, 2ij , and 3ij
pp

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
scales.
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.

M. W. ZHAO ET AL. 41
(a)
(b)
(c)
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.
(A)

M. W. ZHAO ET AL. 42
(B)
(C)
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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