情報地質 第27巻 第2号 056-057頁 2016年
Geoinformatics, vol.27, no.2, pp.056-057, 2016

Investigation of BS-Horizon Parameter Settings for Topographic
Surface Generation
Thi An TRAN *, Shinji MASUMOTO**, Venkatesh RAGHAVAN *, Susumu NONOGAKI ***Tatsuya NEMOTO** and Go YONEZAWA** Graduate School for Creative Cities, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku,Osaka 558-8585, Japan. E-mail: tranthian.gis@gmail.com.
** Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka558-8585, Japan. E-mail: masumoto@sci.osaka-cu.ac.jp.
*** Geological Survey of Japan, National Institute of Advanced Industrial Science and Technology,
Central 7, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8567, Japan.

Key words : BS-Horizon, DEM interpolation, Bi-cubic spline, elevation constraints

1. Introduction
BS-Horizon is a DEM generation program which wasdeveloped by Nonogaki et al., 2012. In this study, wetake up a detailed investigation of parameter settings for
BS-Horizon program and examine the effects inresultant topographic surface. Results reveal thereliance of generated surface on different parameters in
BS-Horizon program including Mx and My, α, m1 and m2.
2. BS-Horizon DEM generation
BS-Horizon program (Nonogaki et al., 2012) wasdeveloped based on bi-cubic spline interpolation
algorithm and exterior penalty function. Method used in
BS-Horizon program was already described in Nonogaki
et al., 2012. Several parameters were set for BS-Horizon
DEM calculation included Mx, My, α min, α max, NITR, m1and m2. In summary they can be explained as below;- Mx and My: the numbers of tiles that constitute thesurface domain (Ω) for the bi-cubic spline function- α min, α max: minimum and maximum penalties inpenalty function. α controls the balance between
smoothness of surface ( J ( f ) ) and the degree of violationof constraints ( R ( f ) ).
- Number of iterations (NITR): number of times
running program in a given α range.
- m1, m2: weight coefficients for the functions derived
from first and second order partial derivatives ofinterpolated surface.
3. Data Used
Test site is an lowland area located in the south ofDanang City, Vietnam. The topography is flat withelevation range from 0 to 7.2m. In this area, equality
constraints which are 9,730 elevation points have beencollected during field survey in 2009. In addition, theinequality constraints is characterized by elevation
between 0m and 10m contours in topographic map in2010. An inequality data included XY location, Z
coordinate and relation to neighboring elevation wasgenerated. Subsequently, the elevation points wascombined with inequality constraints to create anequality-inequality constrained data (in csv format) andused as input for BS-Horizon program.

4. Results and DiscussionBatch processing was carried out to perform surface
approximation in different parameter settings. Mx and
My were examined from 50 to 400. α was ranging from 1to 1012. m1, m2 were values ranging between 0 and 1.
Effects of these parameter settings on the resultant
surface estimation were examined.
4.1 Effects of M and α settings
Firstly m1 = 0.0, m2 = 1.0 was set as default in orderto analyze the effects of remaining parameters.
BS-Horizon DEM generation was applied using both
equality and equality-inequality constraints. As theresults, DEMs generated at first  value are same in J,
R and all other statistical parameters with respect to all
M settings. The iterative calculation by exterior penalty
function method enforces surfaces gradually satisfy
constrained condition.
In case of DEM derived from only equality data,when M = 50 to M = 100, R does not change much, but J
steeplyincreases.
Surfacesmoothness
reducessignificantly by the increase of . Surfaces tend to
expand areas of undershoot and overshoot elevation
when  increases. When M = 150 and above, R is rapidly
reduced by the change of . R is obtained as around 0.49
at first stage of  and gradually minimized to value
around 0.0025 in the later stage of . J and R tend tobecome constant in the upper  range. From M = 150, R
is obtained as minimum (0.0025) in upper  range and is
not improved even larger M settings.
In case of DEM generation using equality-inequality
data, when M = 50 to M = 200, there are three different
zones of J and R according to . Zone A shows the steadyincrease of J and steady decrease of R. In zone B, J
continuously increases and R tends to minimum values.
In zone C, both J and R show spikes especially the DEM
error (R) becomes maximum. When M = 250 to M =400,
there are no unstable zones (C zone). J and R become
constant in the upper range of alpha. The degree of
constraints violation (R) is also minimized with value
around 0.0025 in the B zone. R is obtained as minimum
value and the B zone does not change from M = 300.

57

Distribution of field survey elevation points on study
area in different M settings show that, M from 150 andabove have more than 50% of tiles having no elevation
points that may cause different representations to theearth surface. On the contrary, M from M = 50 to M = 90
provide large number of tiles having more than four
control points which also increase RMS error of splineinterpolation results. In this case study, M from 100 to
120 are suitable for BS-Horizon DEM generation, sincenumber of tiles without elevation points is about 30 40% and most elevation points in a tile distribute withinfour. This study is using M = 100 as parameter settingfor BS-Horizon surface estimation (Figure 1)
Comparing  at first stage ( = 1.0×101 to  =1.0×103) and later stage ( = 1.0×106 to  = 1.0×1012), it
is observed that contours extracted from DEM at laterstage of  are rounded up in some areas especially alongroads and in the boundary between two topographic
areas. In most cases of M, DEM at first stage of  aremore clearly in representing topography of some mainfeatures such as roads or rivers, and the contours arealso enough detail. This study is applying  = 1.0×101(Figure 1a) in case of DEM generation using equality
constraints and  = 1.0×103 (Figure 1b) in case of using
equality-inequality constraints.
4.2. Evaluating effect of m1 and m2 setting
m1, m2 were set as different values starting from m1 =0.0, m2 = 1.0 to m1 = 1.0, m2 = 0.0 with increment step of0.1. DEM representations gradually change according to
the increase of m1 at any value of M or alpha. However,the degrees of change are not same at every condition. In
case of small alpha ( = 1.0×101 to  = 1.0×103) the
topographic change from m1 = 0.0 to m1 = 1.0 are obvious.
DEM surfaces tend to be steeper according to theincrease of m1. The generated contours usually round up
where elevation points are available. This is because of
the slope gradient is increased around these elevation
points. On the contrary, when m1 is small and m2 isemphasized, surface curvature around elevation points isincreased and generated contour becomes undulated
which considering relation to neighboring elevation
points. In the upper  range, surfaces are not muchdifference from m1 = 0.0 to m1 = 0.9 since the RMS error
are same. The only difference is DEM in case of m1 = 1.0.
m1, m2 have different effect on surface representation.
The weights for these parameters depend on theapplication and characteristics of study area. This study
aims to generate DEM for a lowland area which has
small slope gradient, therefore, m1 = 0.0, m2 = 1.0 is used
as condition for BS-Horizon DEM generation.
4.3. Discussion
Considering surface behaviors in case of using onlyequality and case of using equality-inequality data, it
can be seen that;
In case of DEM generated from only equality data, Jand R become stable in upper  range when M = 150. In
case of DEM from equality-inequality constraints, J andR become stable in latter stage of alpha from M = 250.
This study is using alpha in early stage therefore M =100 can be applied for both DEMs from equality andequality-inequality constraints. In case of applying
upper alpha range for DEM generation, it should
consider different M settings for each case.

The suitable surface in case of DEM using equality
data is obtained at  = 1.0×101. In case of DEM derived
from equality-inequality constraints, the suitable one isobtained at  = 1.0×103 which is slightly shifted fromcase using equality data.
DEM generated from only equality data usuallyprovide significant undershoot elevation. Theseundershoots mainly locate along rivers where there areno field data or in the transition between two different
land-use. The integration of inequality constraint into
BS-Horizon reduces the number of undershoot elevationon the approximation results. However DEMs generated
from equality-inequality constraints still remain someplaces having undershoots, especially when alphasetting is significant increased.
The parameters in BS-Horizon may be different inother study areas depending on the size and topographic
characteristics of study area. It is therefore suggested
that suitable parameters need to carefully examined,
considering the characteristics of particular study area.
5. Conclusion
Bi-cubic spline algorithm and exterior penalty
function method implemented in the BS-Horizon
program offers advantage of defining equality-inequality
elevation constraints to interpolate topographic surface.
Evaluation of parameter settings for BS-Horizon
topographic surface estimation has provided a better
understanding of effects of parameters such as M, , andm1, m2 that are involved in the estimation. The results ofthis experiment are very important in effectively using
available data to generate more reliable estimate of the
topographic surface.

a. DEM generated fromb. DEM generated fromequality data.

equality-inequality data.

( = 1.0×101)( = 1.0×103)

Figure 1. Results of DEM generation using BS-Horizon program.
(M = 100, m1 = 0.0, m2 = 1.0)

References
Nonogaki, S., Masumoto, S. and Shiono, K. (2012) Griddingof geological surfaces based on equality-inequality
constraints from elevation data and trend data.
International Journal of Geoinformatics, vol.8, no. 4,
pp.49-60.