Optimizing Classification of Landform
Element Using Feature Space: A Case
Study in a Loess Area
Ge Yan
Postgraduate Student, Key Laboratory of Mechanics on Disaster and
Environment in Western China, Ministry of Education, School of Civil
Engineering and Mechanics, Lanzhou University, 730000 Lanzhou, Gansu, China
e-mail: [email protected]
Shouyun Liang*
Professor，Key Laboratory of Mechanics on Disaster and Environment in
Western China, Ministry of Education, School of Civil Engineering and
Mechanics, Lanzhou University, 730000 Lanzhou, Gansu, China
* Corresponding author e-mail: [email protected]
Yutian Ke
Postgraduate Student, Key Laboratory of Mechanics on Disaster and
Environment in Western China, Ministry of Education, School of Civil
Engineering and Mechanics, Lanzhou University, 730000 Lanzhou, Gansu, China
e-mail: [email protected]
Shijiang Liu
Postgraduate Student, Key Laboratory of Mechanics on Disaster and
Environment in Western China, Ministry of Education, School of Civil
Engineering and Mechanics, Lanzhou University, 730000 Lanzhou, Gansu, China
Hongliang Zhao
Instructor, Key Laboratory of Mechanics on Disaster and Environment in
Western China, Ministry of Education, School of Civil Engineering and
Mechanics, Lanzhou University, 730000 Lanzhou, Gansu, China
Zhikun Yang
Postgraduate Student, Key Laboratory of Mechanics on Disaster and
Environment in Western China, Ministry of Education, School of Civil
Engineering and Mechanics, Lanzhou University, 730000, Lanzhou, China
- 5813 -
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ABSTRACT
Landform element can be used to reveal the surface morphology, and it can also be classified by a
readily approach, Self Organizing Map (SOM), of which the assumed element amount determines the
consequence. However, the amount-selected process is not meticulously clarified in literature. To
conduct landform element classification of the Chinese Loess Plateau and also introduce this
classification approach, we studied the digital elevation model (DEM) of Qingcheng, trained SOM for
11 combinations when the amount was posited from 5 to 10. The suitable amount and subsequent
combination could be confirmed through distribution of mean morphometric parameters of landform
element in feature space. The optimum amount is suggested to be 8 and combined in two or three
dimension due to the best clustering of the parameters. Free from the limitation of element amount,
SOM is a flexible way for landform element classification in a distinct region such as the Loess
Plateau.
KEYWORDS:
The Loess Plateau; landform element; optimum amount; morphometric
parameter; Self Organizing Map (SOM)
INTRODUCTION
Information about terrain topography or land surface form is fundamental for conducting various
modeling studies in environmental science and applied geomorphology (Ehsani and Quiel 2008).
Terrain map could depict the principal capabilities and limitations of land to support many activities,
such as agricultural crop selection, forest harvesting and environmental sensitivity analysis
(MacMillan et al. 2004). Possible target units of mapping consist of landform elements, landform
types and land-systems in the order of increasing complexity (MacMillan et al. 2004; Minár and
Evans 2008). As the basic landform entity, landform element can be automatically extracted from the
DEM by many methods such as morphometric feature parameters (Wood 1996), fuzzy logic
(MacMillan et al. 2000; Schmidt and Hewitt 2004), object-based image analysis (Drăguţ and
Blaschke 2006), artificial neural networks (Ehsani and Quiel 2008) and pattern recognition (Jasiewicz
and Stepinski 2013). The automatic classification of landform element is to describe the surface
morphology based on morphometric parameters (Miliaresis 2001; Jamieson et al. 2004; Bue and
Stepinski 2006). Morphometric feature parameterization proposed by Wood (1996) determines 6
simple morphometric features as landform elements, involving saddles, channels, ridges, peaks, pits
and planes. This approach makes a distinction between horizontal and inclined surfaces and slopes by
slope tolerance (ST) and differentiates planar surfaces from ridges and channels by curvature
tolerance (CT) to, which means tolerance will affect the results directly. Schmidt and Hewitt (2004)
brought out fuzzy mathematics equation to define bending and tilting rate of units by fuzzy logic and
increased landform element amount to 8. Drăguţ and Blaschke (2006) divided the landform surface
into the upper, the middle and the lower part based on DEM data through multi-scale segmentation,
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then classified 9 types of landform elements according to morphometric parameters. The modified
approaches (Schmidt and Hewitt 2004; Drăguţ and Blaschke 2006) were a little bit cumbersome in
operation process, even though averted the influence from value of ST and CT. Ehsani and Quiel
(2008) presented an easier approach to realize the classification of the landform element by training
Self Organizing Map (SOM), and referred that optimum landform element amount for the best result
could be selected after some trials.
The Loess Plateau is one of the most vulnerable areas of the geological environment. Landform
classification is always an effective approach to reveal the geological background. Meanwhile there is
a doubt whether landform elements could be classified by training SOM in this region. Therefore, we
studied a loess area in Qingcheng, trained SOM for 11 combinations after the amount assumed from 5
to 10, finally manage to find the suitable amount and the corresponding combination by clustering
characteristics of mean morphometric parameters of the landform element in the feature space.
Study area and data
The study area is located between 107°50′E and 108°00′E, and 35°56′N and 36°03′N (Figure 1)
which covers an area of 180 km2. It is located in Qingcheng County in Gansu Province, northwest of
China. Altitude ranges from 1015 m to 1425 m, and slopes from 0 to 40°. Moreover, this area is the
juncture of loess tableland (yuan) region and loess ridge-hill region of the Loess Plateau in the middle
reaches of Yellow River, where loess landform and gully are well developed. Additionally, a tributary
of Yellow River flows across the centre of this region and its river terraces are well formed.
Figure 1: The DEM of study area
The 1-arc-second ASTER GDEM data in TIF format were downloaded from USGS website and
adjusted to Beijing 1954 3 Degree GK Zone 35 in resolution of 30 m, then jointed and cut into 30-m
DEM (Figure 1) which ranges from 35755×103m to 35770×103 m in x and from 3983×103 m to
3995×103 m in y.
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METHODS
Morphometric parameterization
Based on Evans's (1972) hypothesis, Wood (1996) took slope, cross-sectional curvature, maximum curvature
and minimum curvature to identify morphometric features, containing point (peak, pit and pass), linear (ridge
and channel) and areal (planes) categories. By traversing DEM through the window of 15*15 (equal to 450
m*450 m), surface morphology can be derived by the following equation:
Z = ax 2 + by 2 + cxy + dx + ey + f
(1)
where x, y, and Z are local coordinates, and a to f are quadratic coefficients.
Then acquiring coefficient (a, b, c, d, e, f) by matrix operation on some local coordinates of grids
within the scope of window.
Afterwards, acquiring the following parameters of slope, cross-sectional curvature, maximum
curvature and Minimum curvature, respectively:
S = arctan(sqrt (d 2 + e 2 ))
(2)
C = n ∗ g (b ∗ d 2 + a ∗ e2 − c ∗ d ∗ e) (d 2 + e2 )
(3)
C max = n * g (−a − b + sqrt ((a − b) 2 + c 2 )
(4)
C min = n * g (−a − b − sqrt ((a − b) 2 + c 2 )
(5)
where g is the resolution of the DEM, n is the size of traversing window.
Morphometric parameters within specific window size can not be derived by ArcGIS.
Fortunately, so many operations can be fulfilled by assistant software along with the wide spread of
open-source GIS. This paper loaded DEM by GRASS GIS to calculate the first-order derivative
(slope) and the second-order derivatives (maximum, minimum and cross-sectional curvature). The
values of the curvature parameters were multiplied by 104 to simplify presentation.
Kohonen Self Organizing Map
SOM is a realistic model of biological brain function (Kohonen 2001), and consists of output map
units and input vectors, both of which are fully connected via weights. Output map units equal to
landform elements, which can be combined in one-dimension, two-dimension and multi-dimension.
Input vectors are the data to train SOM, such as the combination of four morphometric parameters
(Figure 2) in this research. SOM is a competitive network which continually uses topology to
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maintain characteristics (Kohonen 1989). Output map units of similar input vectors are also close
(Vesanto and Alhoniemi 2000; Bação et al. 2005).
Prior to learning, the amount of landform element and subsequent combination are set by defining
the properties of SOM, as well as distribution scaling, topological relations and iterations. The
combination of output map units can be set as different dimension after the amount posited, for
example, the combinations could be [8, 1], [4, 2] and [2, 2, 2] if the amount is 8(Figure 3).
Distribution scaling is the spatial scope that could contain all the map units, it can be achieved
depending on the range of input variables. The Euclidian distance between vectors is mainly affected
by input variables, and the organization of the map will be dominated by the maximum scaling
variable if the standardization process were not conducted. So it is necessary to standardize all input
morphometric parameters within the range from -1 to 1, and distribution scaling expresses as the twodimensional matrix which is formed by maximum value 1 and minimum value -1. Topological
relation shows the connecting format of input map units, which can be orthogonal, hexagonal and
trigonal topology, and the frequently used one is trigonal and so in this paper. Iterations are essential
to the calculation amount, so it is very necessary to control iterations for shortening the mapping time
and the iteration values of rough tuning and fine tuning are set as 100 and 200 respectively.
During the learning process, each input vector (xsi) is put into the neuron network to calculate the
Euclidian distance between xsi and all output map units or nodes. The node (q) with the shortest
Euclidian distance is commonly regarded as the Best Matching Unit and selected as the winner. The
input vector of this study is a four-dimensional vector combined by slope, cross-sectional curvature,
minimum curvature and maximum curvature.
q = arg min x si − mi
(6)
i
where q is the map unit of winner, and xsi and mi are the i-th element of the input vector xs and i-th
element of the map vector unit, respectively.
The winning map unit will be the centre of an update neighborhood within which nodes and the
related weights will be renovated, so the nodes of SOM will compete with each other to gain the
victorious node to best present the particular input sample, then become the corresponding output
map unit. The above process will be repeated for every input vector.
After the learning phase, the SOM consists of a bulk of vectors, which are similar vectors nearby and dissimilar
vectors further apart (Richardson et al. 2003; Mingoti and Lima 2006). Meanwhile, we took the fourdimensional vector that combined by four morphometric parameters as the input data of the trained SOM to
acquire the corresponding output map unit.
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A
B
C
D
Figure 2: The distribution of morphology parameters derived from the DEM: A, Slope; B,
Cross-sectional curvature; C, Minimum curvature; D, Maximum curvature.
RESULTS
We trained SOM in different map unit amount and the corresponding combinations to find the
suitable amount of landform elements in the study loess area. The map units counting from 5 to 10
can be combined as [10, 1], [9, 1], [8, 1], [6, 1], [7, 1], [5, 1], [5, 2], [3, 3], [4, 2], [3, 2] and [2, 2, 2]
(Figure 3). Ehsani and Quiel (2008) managed to classify the landform elements by SOM, and
presented the distribution of mean morphometric parameters in the form of the feature space (Figure
3L). Definition of landform element relies on its distribution patterns in feature space.
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Figure 3: The distribution of mean morphometric parameters of the landform elements in the
feature space: A represents the result in combination of [10,1]; the following figures from B
to H share the same pattern as A and the combination formations are presented on the upper
right corner respectively; L represents the distribution of those in Poland (Ehsani and Quiel
2008). [i,1] represents the linear combination of i map units; [i,2] and [i,3] represent the
planar combination of 2*i and 3*i map units; [2,2,2] represents the stereo combination of 8
map units.
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A
B
Figure 4: Morphometric feature map based on SOM method. A and B represents the results
in the combinations of [4, 2] and [2, 2, 2], respectively.
As demonstrated in Figure 3L, landform elements can be divided into three groups according to
mean cross-section curvature, including channel, planar and ridge; then further classified by mean
slope. Absolute value of cross-section curvature of planar is the minimum, while that of channel and
ridge are rather large, negative value for channel and positive for ridge. Differences between crosssection curvatures of landform elements in ridge, are relatively larger, while that in channel and
planar are smaller. So the cross-section curvatures of landform elements in first and second group
should be as same as possible when selecting the optimum scheme. We also display mean
morphometric parameters of landform elements in feature space respectively for all amounts and
corresponding combinations (Figure 3A~K). The selection processes for the optimum are as follows.
It can be noticed that the landform elements acquired in planar or stereo combinations present
more obvious clustering than linear does, so landform element classification in planar or stereo
combination is more suitable than linear. By the way, landform elements in Figure 3G and Figure 3G
are best matching with the 8 elements in Figure 3L. So it is considered that the amount of landform
elements is considered to be 8 and combination could be [4, 2] in two dimension, as well as [2,2,2] in
three dimension.
When combination is [4, 2], the mean cross-sectional curvature values of class 1 and class 2 are
negative, and defined as channel; whilst those of class 2, class 3 and class 8 are approximately 0, and
defined as planar; those of class 5, class 6 and class 7 are positive, and defined as ridge. Further
naming can be decided based on mean slope, and it is the same with the naming of [2, 2, 2] (Table 1).
Vol.21 [2016], Bund. 17
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Table 1: Statistics and naming of the landform elements
[4, 2]
[2, 2, 2]
Item
number
count
item name
count
item name
1
35373
Very steep slope, channel
30330
Very steep slope, planar
2
10730
Steep slopes, planar
32479
Crestline, ridge
3
13394
Moderate-steep slope,
transition zone, planar
6200
Steep slopes, planar
4
29543
Moderate slope, channel
24889
Moderate slope, ridge
5
22487
Very steep slope, ridge
27479
Very steep slope, channel
6
32425
Crestline, ridge
7197
Moderate-steep slope,
transition zone, planar
7
20127
Moderate slope, ridge
27546
Moderate slope, channel
8
35921
Gentle slopes to flat,
valley bottoms, planar
43880
Gentle slopes to flat,
valley bottoms, planar
DISCUSSION
The positive part of class 8 in Figure 4 reflects the distribution of loess tablelands (yuan), and the
negative is in accord with the developing of river terraces. Moreover, class 6 in Figure 4A or class 2
in Figure 4B reveals the distribution of loess ridges. Therefore, the classification results could reveal
the development of loess landform to some extent in the study area. Loess tablelands, loess ridges and
river terraces are well developed according to the amount of landform elements (Table 1).
From the above analysis, SOM method on classifying the landform elements in the Loess Plateau
area is feasible and applicable. The optimum amount is suggested to be 8 in study area, while it is 10
in Poland (Ehsani and Quiel 2008), which means the same geomorphology may have difference in
varying areas. So SOM should be trained again in a new area.
Various approaches applied for classifying the landform elements are always limited by the
amount of landform elements (Wood 1996a; MacMillan et al. 2000; Schmidt and Hewitt 2004;
Drăguţ and Blaschke 2006; Jasiewicz and Stepinski 2013), while SOM method is not. The results
gained by SOM method are directly determined by classification amounts and matching
combinations. The best clustering characteristics of mean morphometric parameters of landform
element in feature space reveal the optimum scheme. So the optimal classification result (Figure 3)
can be selected by different assumed amounts and the corresponding combinations (Figure 4).
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Meanwhile, we find out that planar and the stereo combinations are superior to the linear
combination.
CONCLUSIONS
To demonstrate whether landform elements could be classified by training SOM in the Loess
Plateau. This paper presents an experiment, the selection process of the optimum scheme for
landform element classification in a loess area in Qingcheng County.
The results show: 1) Landform element amount is suggested to be 8, and the combinations should
be linear or stereo. The element amounts in groups of channel, planar and ridge are 2, 3 and 3
separately when the combination is linear; the element amounts in groups of channel, planar and ridge
are 2, 4 and 2 respectively when combination is stereo; 2) the classification of landform elements has
indication on the development characteristics of the loess landform; 3) compared with other
approaches, SOM is not limited by the amount of elements because it can find the optimum scheme
by the assumed different map unit amounts and the corresponding combinations. This study could
provide guidance information for the application of SOM on landform element segmentation in
distinct areas.
However, there still remains some shortages. The input values, morphometric parameters, are
derived from calculation window size of 15*15, but conditions of other size scales were not studied.
Moreover, SOM calculation is rather heavy and yet the study area is small, the fulfillment of
landform element classification in a large area needs to be further researched.
ACKNOWLEDGEMENTS
This study was supported by the National Natural Science Foundation of China (No. 41272326).
REFERENCES
1. Bação, F., Lobo, V. and Painho, M. (2005) “The self-organizing map, the Geo-SOM, and
relevant variants for geosciences”, Computers & Geosciences, 31(2), 155-163.
2. Bue, B. D. and Stepinski, T. F. (2006) “Automated classification of landforms on Mars”,
Computers & Geosciences, 32( 5), 604-614.
3. Drăguţ, L. and Blaschke, T. (2006) “Automated classification of landform elements using
object-based image analysis”, Geomorphology, 81( 3), 330-344.
Vol.21 [2016], Bund. 17
5823
4. Ehsani, A. H. and Quiel, F. (2008) “Geomorphometric feature analysis using
morphometric parameterization and artificial neural networks”, Geomorphology, 99( 1),
1-12.
5. Evans, I. S. (1972) “General geomorphometry, derivatives of altitude, and descriptive
statistics”, Spatial analysis in geomorphology, pp17-90.
6. Jamieson, S. S. R., Sinclair, H. D. and Kirstein, L. A. et al. (2004) “Tectonic forcing of
longitudinal valleys in the Himalaya: morphological analysis of the Ladakh Batholith,
North India”, Geomorphology, 58( 1), 49-65.
7. Jasiewicz, J. and Stepinski, T. F. (2013) “Geomorphons—a pattern recognition approach
to classification and mapping of landforms”, Geomorphology. 182, 147-156.
8. Kohonen, T. (1989) “Self-organization and associative memory”, Springer Press, pp312.
9. Kohonen, T. (2001) “Self-organizing maps”, Springer, pp266-270.
10. MacMillan, R. A., Pettapiece, W. W. and Nolan, S. C. et al. (2000) “A generic procedure
for automatically segmenting landforms into landform elements using DEMs, heuristic
rules and fuzzy logic”, Fuzzy sets and Systems, 113( 1), 81-109.
11. MacMillan, R. A., Jones, R. K. and McNabb, D. H. (2004) “Defining a hierarchy of
spatial entities for environmental analysis and modeling using digital elevation models
(DEMs)”, Computers, Environment and Urban Systems, 28( 3), 175-200.
12. Miliaresis, G. C. (2001) “Geomorphometric mapping of Zagros Ranges at regional
scale”, Computers & Geosciences, 27(7), 775-786.
13. Minár, J. and Evans, I. S. (2008) “Elementary forms for land surface segmentation: The
theoretical basis of terrain analysis and geomorphological mapping”, Geomorphology,
95(3), 236-259.
14. Mingoti, S. A. and Lima, J. O. (2006) “Comparing SOM neural network with Fuzzy cmeans, K-means and traditional hierarchical clustering algorithms”, European Journal of
Operational Research, 174( 3), 1742-1759.
15. Richardson, A. J., Risien, C. and Shillington, F. A. (2003) “Using self-organizing maps to
identify patterns in satellite imagery”, Progress in Oceanography, 59(2), 223-239.
16. Schmidt, J. and Hewitt, A. (2004) “Fuzzy land element classification from DTMs based
on geometry and terrain position”, Geoderma, 121(3), 243-256.
17. Vesanto, J. and Alhoniemi, E. (2000) “Clustering of the self-organizing map”, Neural
Networks, IEEE Transactions on, 11(3), 586-600.
18. Wood, J. (1996) “The Geomorphological Characterization of Digital Elevation
Models”,Ph.D. Thesis, Department of Geography, University of Leicester, Leicester, UK.
Vol.21 [2016], Bund. 17
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19. Zhang, Z. H. (1986) “Explanatory notes to geomorphologic map of the loess plateau in
China”, Geological Publishing House, Beijing, China.
© 2016 ejge
Editor’s note.
This paper may be referred to, in other articles, as:
Ge Yan, Shouyun Liang, Gansu, China, Yutian Ke, Shijiang Liu, Hongliang
Zhao, Zhikun Yang: “Optimizing Classification of Landform Element Using
Feature Space: A Case Study in a Loess Area” Electronic Journal of
Geotechnical Engineering, 2016 (21.17), pp 5814-5824. Available at
ejge.com.