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Liu, X., Zhang, Z. and J. Peterson (2009). Evaluation of the performance of DEM interpolation algorithms for
LiDAR data. In: Ostendorf, B., Baldock, P., Bruce, D., Burdett, M. and P. Corcoran (eds.), Proceedings of the
Surveying & Spatial Sciences Institute Biennial International Conference, Adelaide 2009, Surveying & Spatial
Sciences Institute, pp. 771-780. ISBN: 978-0-9581366-8-6.
EVALUATION OF THE PERFORMANCE OF DEM
INTERPOLATION ALGORITHMS FOR LIDAR DATA
Xiaoye Liu
1, 2
, Zhenyu Zhang
1, 2
, Jim Peterson
2
1
Faculty of Engineering and Surveying
University of Southern Queensland, Toowoomba, Queensland 4350, Australia
2
Centre for GIS, School of Geography and Environmental Science
Monash University, Clayton, Victoria 3800, Australia
Email: Xiaoye.Liu@usq.edu.au
Zhenyu.Zhang@usq.edu.au
Jim.Peterson@arts.monash.edu.au
ABSTRACT
Airborne light detection and ranging (LiDAR) is one of the most effective means for
high quality terrain data acquisition. The high-accuracy and high-density LiDAR data
makes it possible to model terrain surface in more detail. Using LiDAR data for DEM
generation is becoming a standard practice in the spatial science community. Of the
three commonly used digital elevation models (e.g., triangular irregular network (TIN),
gridded DEM and contour line model), the gridded DEM is the simplest and the most
efficient approach in terms of storage and manipulation. However, this approach is
liable to introduce errors because of its discontinuous representation of the terrain
surface based on the interpolation process of sampled terrain points. Given the
characteristics of LiDAR data, much attention must be paid to the selection of an
appropriate interpolation algorithm, otherwise the accuracy of produced DEM from
LiDAR data will be compromised.
This study aims to evaluate the performance of commonly used interpolation algorithms
to the LiDAR data, including inverse distance weighted (IDW) method, Kriging
method, and local polynomial method. All these interpolation algorithms are applied to
DEMs generated from LiDAR at various data density levels. The performance of these
interpolation methods is evaluated by using both cross-validation and validation test
methods. The results showed the performance of each interpolation algorithm for two
study sites with different terrain types and analysed the relationship between
interpolation algorithms and LiDAR data density. Considering accuracy and computing
time for large volume of LiDAR data, IDW is recommended for LiDAR DEM
generation from this study.
INTRODUCTION
Digital elevation data and derived products such as digital elevation models (DEMs) are
critical components of spatial databases in a wide range of applications. They comprise
an essential layer within the national spatial data infrastructure (ICSM 2008). They are
so important that a National Digital Elevation Program (NDEP) in USA was established
to promote the exchange of accurate digital land elevation data among government,
private, and non-profit sectors and the academic community and to establish standards
This article was peer reviewed by two independent and anonymous reviewers
X. Liu, Z. Zhang and J. Peterson
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and guidance that will benefit all users (NDEP 2004; Jensen 2007). In Australia, the
National Elevation Data Framework (NEDF) initiative was established in 2008 as well.
The purpose of the NEDF initiative is to develop a collaborative framework that can be
used to increase the quality of elevation data and derived products such as DEMs
describing Australia’s landform and seabed (ICSM 2008). Drivers for the establishment
of the NDEP and NEDF are the need for high resolution elevation data to meet a range
of purposes and the rapid development of survey technologies such as airborne light
detection and ranging (LiDAR) for digital elevation data collection (ICSM 2008).
LiDAR offers the capability of obtaining high-density three-dimensional points, as
characterised by vertical accuracy of 10-50 cm and horizontal post spacing of 1-3 m
(ICSM 2008). The highest accuracy such as 10-15 cm RMSE (root mean square error)
can only be achieved under the most ideal circumstances (Hodgson and Bresnahan
2004). The actual accuracy of LiDAR elevation data in a project varies with factors
such as flying height, laser beam divergence, location of the reflected point within the
swathe, LiDAR system errors including errors from Global Positioning System (GPS)
and Inertial Measurement Unit (IMU), distance to ground base station, and LiDAR data
classification (filtering) reliability (Hodgson and Bresnahan 2004; Turton 2006).
Methods for quality assessment of LiDAR data vary with applications and delivered
products. For the purpose of DEM generation and delivered with classified LiDAR
point clouds, vertical accuracy with respect to a specified vertical datum is the principal
criterion in specifying the quality of LiDAR elevation data (Maune 2007). Quantitative
assessment of LiDAR elevation data is usually conducted by comparing high-accuracy
checkpoints with elevations estimated from the LiDAR ground data at the locations of
checkpoints. RMSE (root mean square error) can subsequently be calculated, and an
overall vertical accuracy of LiDAR data at 95 percent confidence level can be obtained.
The vertical accuracy of LiDAR data can be affected by various ground cover types
because vegetation may limit ground detection. Furthermore, in LiDAR data filtering
process, some non-ground LiDAR points may not be filtered out and be labelled as
ground points. Therefore, ASPRS (2004) required that the vertical accuracies of LiDAR
data should be assessed separately for each of land cover categories and combined land
cover.
Aforementioned accuracy assessment addressed the absolute vertical accuracy of
LiDAR data with regard to a national defined vertical datum. Absolute vertical accuracy
accounts for all effects of systematic and random errors. For some applications of
digital elevation data, however, the relative vertical accuracy is more important than the
absolute vertical accuracy (NDEP 2004). Relative vertical accuracy, also referred to as
point-to-point accuracy (Weydahl et al. 2007), is affected by the random errors in a
dataset. In the case of derivative products that make use of the local differences among
adjacent elevation values such as slope and aspect calculations, the relative vertical
accuracy is especially important. Relative vertical accuracy may be difficult to assess
unless a very dense set of reference points is available (NDEP 2004; ICSM 2008).
LiDAR data have high-sampling density, and LiDAR-derived DEMs have high
resolution. Therefore, it is possible to assess the relative vertical accuracy of LiDAR
data.
X. Liu, Z. Zhang and J. Peterson
773
DEMs are digital representations of the Earth’s terrain surface. A natural terrain surface
is a continuous surface and comprises an infinite number of points (El-Sheimy et al.
2005). With a point sampling method, the terrain surface can be approximated to the
required degree of accuracy by DEM with a finite number of sampled points. Different
DEMs have been developed to represent the terrain surface. The grid DEM, the
triangular irregular network (TIN), and the contour line model are the most commonly
used DEMs. The grid DEM use a matrix structure that implicitly records topological
relations between data points (El-Sheimy et al. 2005). Each grid cell has a constant
elevation value for the whole cell (Ramirez 2006). This constant elevation value is
usually obtained by interpolation among adjacent sampling points. Interpolation is an
approximation procedure in mathematics and an estimation issue in statistics (Li et al.
2005). It is the process of predicting the values of a certain variable in unsampled
locations based on measured values at points within the area of interest (Burrough and
McDonnell 1998). Interpolation in grid digital elevation modelling is used to estimate
the terrain height value of a point (the centre of cell) by using the known elevations of
neighbouring points (Li et al. 2005). There are many factors that affect the DEM
accuracy, but the interpolation is the most important factor affecting the relative vertical
accuracy of the DEM.
There are many interpolation methods for DEM generation, including deterministic
methods such as inverse distance weighted (IDW), geostatistical methods such as
Kriging, and polynomial-based methods such as local polynomial (LP). The variety of
available interpolation methods has led to questions about which is most appropriate in
different contexts and has stimulated several comparative studies of relative accuracy
(Zimmerman et al. 1999). To evaluate the performance of some commonly used
interpolation methods, a variety of empirical studies have been conducted to assess the
effects of different methods of interpolation on DEM accuracy. There seems to be no
single interpolation method that is the most accurate for the interpolation of terrain data
(Fisher and Tate 2006). None of the interpolation methods is universal for all kinds of
data sources, terrain patterns, or purposes. Few studies have addressed the interpolation
issues for DEM generation from LiDAR data (Lohr 1998; Lloyd and Atkinson 2002,
2006; Liu 2008). Given the specific characteristics (high density and large volume) of
LiDAR data, study is needed for the evaluation of the performance of DEM
interpolation algorithms for LiDAR data.
The ideal method for the assessment of the accuracy of a DEM generated by
interpolation is to compare the produced DEM with a “true” terrain surface. These kinds
of “true” terrain surfaces are not available in practice. Using a DEM of relatively higher
accuracy as reference is an option, but access to such a DEM can not be assumed when
a new DEM-generation project is being implemented. Validation and cross-validation
methods can be used to assess the accuracies of DEMs generated from different
interpolation algorithms. For validation method, whole dataset is separated to training
and test datasets. Test data are used as checkpoints while the training data are then used
to produce DEMs with different interpolators. Differences between elevations of test
data and correspondent elevations from DEMs are calculated to assess the accuracies of
DEMs. Cross-validation removes one data point at a time, and uses the reminder data
points to predict the data value at the location of removed data point. The predicted and
X. Liu, Z. Zhang and J. Peterson
774
actual values at the location of removed data point are compared to assess the
performance of interpolation methods.
This study aims to evaluate the performance of commonly used interpolation algorithms
for LiDAR data, including IDW method, Kriging method, and local polynomial method.
The performance of these interpolation methods is evaluated by using both cross-
validation and validation test methods. The effects of LiDAR data density on the
performance of different interpolation algorithms were also tested.
MATERIALS AND METHODS
Study Area
The study area is in the region of Corangamite Catchment Management Authority
(CCMA) in south western Victoria, Australia. The landscape in the region can be
depicted to north and south highlands and a large Victoria Volcanic Plain (VVP) in the
middle. The VVP is dominated by Cainozoic volcanic deposits. It is characterized by
vast open areas of grasslands, small patches of open woodland, stony rises denoting old
lava flows, numerous volcanic cones and old eruption, and is dotted with shallow lakes
both salt and freshwater. Terrain types vary between the comparatively treeless basins
of internal drainage on Victoria Volcanic Plains (VVP) to dissected terrains north and
south. The plains have high priority for a range of research projects pertaining to
environment management issues addressed in the catchment management strategy plan.
LiDAR data from the first stage of CCMA LiDAR project covered an area of 6900 km².
In this study, two LiDAR tiles (covered an area of 5 km by 5 km each) were selected as
the test sites, shown in Figures 1 and 2. Site one is relative flat, with several shallow
gullies. Site two is dominated by volcanic derived stony rises, with rough terrain.
LiDAR Data
LiDAR data were collected over the period of 19 July 2003 to 10 August 2003. The
primary purpose of this LiDAR data collection was to facilitate more accurate terrain
pattern representation for the implementation of a series of environment related projects.
The LiDAR data have been classified into ground and non-ground points by using data
filter algorithms across the project area. Manual checking and editing of the data led to
further improvement in the quality of the classification. The resulting data products used
for DEM generation are irregularly distributed LiDAR ground points, with an average
spacing of 2.2 m (AAMHatch 2003). The accuracy of LiDAR data was estimated as 0.5
m vertically and 1.5 m horizontally (AAMHatch 2003). The LiDAR data were delivered
as tiles in ASCII files containing x, y, z coordinates and intensity values.
Methods
Using the Geostatistical Analyst extension of ArcGIS 9.3, LiDAR data points for the
two test sites were first randomly selected and separated to two datasets: 90% for
training dataset and 10% for test dataset. Training datasets were used for subsequent
reduction to produce a series of dataset with different data density, representing the
100%, 75%, 50% and 25% of the original training dataset. Using reduced datasets, a
DEM was created using IDW, Kriging and local polynomial algorithms at each data
density level, e.g., a total of twelve DEMs at 100%, 75%, 50% and 25% of training
X. Liu, Z. Zhang and J. Peterson
775
datasets for each test site. The elevation value of each check point from test dataset was
compared to the correspondent elevation value from DEMs produced at each of data
density levels. Root mean square error (RMSE) and mean absolute error were calculated
to assess the performance of different interpolation algorithms at different LiDAR data
density levels.
Fig. 1: Study site one
Fig. 2: Study site two
The performance of IDW, Kriging and local polynomial interpolation methods was also
tested using the cross-validation in ArcGIS Geostatistical Analyst extension. The cross-
validation removes one LiDAR data point at a time, and interpolates elevation at the
location of the removed point using the reminder LiDAR points. The difference
between the actual elevation value of the removed data point and the interpolated
elevation corresponding to this point was calculated. This process was repeated until
every LiDAR point has been removed once in each dataset. The overall performance of
the interpolator is then evaluated by statistical means such as the RMSE and mean
absolute error.
X. Liu, Z. Zhang and J. Peterson
776
RESULTS AND DISCUSSION
RMSEs obtained from validation and cross-validation with different interpolators at
various LiDAR density levels for site one and site two are presented in Table 1, and
depicted in Figures 3 and 4 as well. At all LiDAR density levels, both validation and
cross-validation showed that local polynomial method has the lowest RMSE values at
site one and site two. Compared to IDW and Kriging, the local polynomial performed
extremely well on flat terrain (site one). Kriging usually gave the biggest RMSEs with
exception at 25% data density for site one.
RMSEs from all three interpolation algorithms increased with the decrease of LiDAR
data density at both test sites. However, there is only slight increase of RMSEs with
Kriging from both validation and cross-validation, indicating that Kriging is insensitive
to data density on a flat terrain like the test site one. On a complex terrain (site two), all
three interpolation algorithms are sensitive to data density, showing significant
increases when LiDAR data density decreased from 100% to 25%. Even on flat terrain
(site one), both IDW and local polynomial algorithms are sensitive to data density,
being significant when density decreasing from 75% to 25% of the original data.
On flat terrain, RMSEs from all three interpolation algorithms are smaller than those
corresponding to complex terrain. For example, with cross-validation at 100% LiDAR
data density, the local polynomial yielded a RMSE of 0.149 m at site one, and 0.250 m
at site two. It gave an indication that terrain type has a significant impact on
interpolation results. On flat terrain, interpolators performed well, while on complex
terrain, interpolation process may introduce more errors, even in the case of high-
density sampling data.
Tab.1: RMSEs obtained from validation and cross-validation with different
interpolators at various LiDAR density levels for site one and site two
Site one Site two
Density Interpolator Validation
Cross-
validation Validation
Cross-
validation
100%
Kriging 0.174 0.174 0.358 0.411
IDW 0.165 0.165 0.294 0.296
LP 0.150 0.149 0.250 0.250
75%
Kriging 0.174 0.174 0.411 0.282
IDW 0.166 0.166 0.327 0.328
LP 0.150 0.150 0.282 0.282
50%
Kriging 0.175 0.175 0.500 0.500
IDW 0.170 0.170 0.382 0.383
LP 0.155 0.155 0.315 0.317
25%
Kriging 0.176 0.175 0.694 0.696
IDW 0.181 0.180 0.508 0.505
LP 0.163 0.162 0.406 0.405
X. Liu, Z. Zhang and J. Peterson
777
Kriging was originally developed to estimate the spatial concentrations of minerals for
the mining industry. Kriging takes into account both the distance and the degree of
variation between sampling data. From a statistical perspective, Kriging is a sound
method (Lu and Wong 2008). In practice, however, it may not satisfy users. This study
demonstrated that Kriging did not work well for LiDAR data on both flat and complex
terrains. Furthermore, it is not a quick interpolator, consuming more computer
resources, especially for large volume of LiDAR data. The local polynomial
interpolation fits the specified order (zero, first, second, third, and so on) polynomial
using points within the defined neighbourhood. It is a moderately quick interpolator
(ESRI 2008). In our study, it provided better results than other two algorithms on flat
terrain.
The IDW interpolation assumes the closer a sample point is to the prediction location,
the more influence it has on the predicted value. It estimates a point value using a
linear-weighted combination set of sample points. The weights assigned depend only on
the distances between the point locations and the particular location to be estimated, but
the relative locations between sampling data are not considered (Myers 1994).
Therefore, the use of IDW is straightforward and non-computationally intensive (Lu and
Wong 2008). The IDW works well for dense and evenly distributed sample data (Childs
2004). This study showed that even on complex terrain, IDW can produce good results,
without significant difference with those from the local polynomial. Considering its
simplicity, quick computation and availability in almost all the GIS software, IDW is
the most suitable interpolation method for LiDAR data.
0.14
0.15
0.16
0.17
0.18
0.19
0.20
100% 75% 50% 25%
Kriging IDW LP
(a)
0.14
0.15
0.16
0.17
0.18
0.19
0.20
100% 75% 50% 25%
Kriging IDW LP
(b)
Fig. 3: RMSEs from different interpolators at various LiDAR density levels for site one,
(a) using validation, (b) using cross-validation
X. Liu, Z. Zhang and J. Peterson
778
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
100% 75% 50% 25%
Kriging IDW LP
(a)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
100% 75 % 50% 25%
Kriging IDW LP
(b)
Fig. 4: RMSEs from different interpolators at various LiDAR density levels for site two,
(a) using validation, (b) using cross-validation
CONCLUSION
Relative vertical accuracy of DEMs may be more important than absolute vertical
accuracy in some applications. Selection of an appropriate interpolator could be critical
for DEM generation as it is an important factor affecting the relative vertical accuracy
of the DEM. This study used validation and cross-validation to evaluate the
performance of IDW, Kriging and local polynomial algorithms for LiDAR data on two
different terrains. Results showed that Kriging did not work well. The local polynomial
performed much better than IDW on flat terrain, but there was no significant difference
with IDW on complex terrain. Accuracies from interpolators became worse with the
decrease of LiDAR data density, with Kriging being insensitive to data density on flat
terrain. As a trade-off between accuracy and computing time for large volume of
LiDAR data, IDW is the recommended interpolation method for DEM generation from
LiDAR data.
REFERENCES
AAMHatch. 2003. Corangamite CMA airborne laser survey data documentation.
AAMHatch Pty Ltd, Melbourne, Australia, 10 p.
ASPRS. 2004. ASPRS Guidelines, Vertical Accuracy Reporting for LiDAR Data.
Arerican Society for Photogrammetry and Remote Sensing (ASPRS) Bethesda,
Maryland, USA, 20 p.
Burrough, P. A. and McDonnell, R. A. 1998. Principles of Geographical Information
Systems, Oxford: Oxford University Press.
Childs, C. 2004. Interpolation surfaces in ArcGIS spatial analyst. ArcUser, July-
September:32-35.
El-Sheimy, N., Valeo, C. and Habib, A. 2005. Digital terrain modeling: acquisition,
manipulation, and application, Boston and London: Artech House.
ESRI. 2008. Using ArcGIS Geostatistical Analyst. Environmental Systems Research
Institute, Redlands, CA, USA, 300 p.
Fisher, P. F. and Tate, N. J. 2006. Causes and consequences of error in digital elevation
models. Progress in Physical Geography, 30(4):467-489.
Hodgson, M. E. and Bresnahan, P. 2004. Accuracy of airborne lidar-derived elevation:
empirical assessment and error budget. Photogrammetric Engineering and Remote
Sensing, 70(3):331-339.
X. Liu, Z. Zhang and J. Peterson
779
ICSM. 2008. ICSM Guidelines for Digital Elevation Data. Inter-Governmental
Committee on Surveying and Mapping (ICSM), Canberra, Australia, 49 p.
Jensen, J. R. 2007. Remote Sensing of the Environment: an Earth Resource Perspective,
Upper Saddle River, NJ: Pearson Prentice Hall.
Li, Z., Zhu, Q. and Gold, C. 2005. Digital Terrain Modeling: Principles and
Methodology, Boca Raton, London, New York, and Washington, D.C.: CRC Press.
Liu, X. 2008. Airborne LiDAR for DEM generation: some critical issues. Progress in
Physical Geography, 31(1):31-49.
Lloyd, C. D. and Atkinson, P. M. 2002. Deriving DSMs from LiDAR data with kriging.
International Journal of Remote Sensing, 23(12):2519-2524.
Lloyd, C. D. and Atkinson, P. M. 2006. Deriving ground surface digital elevation
models from LiDAR data with geostatistics. International Journal of Geographical
Information Science, 20(5):535-563.
Lohr, U. 1998. Digital elevation models by laser scanning. Photogrammetric Record,
16:105-109.
Lu, G. Y. and Wong, D. W. 2008. An adaptive inverse-distance weighting spatial
interpolation technique. Computer and Geosciences, 34:1044-1055.
Maune, D. F. 2007. DEM User Requirements. In Maune, D. F. (Eds.), Digital Elevation
Model Technologies and Applications: The DEM Users Manual, 2nd Edition,
Bethesda, Maryland: American Society for Photogrammetry and Remote Sensing.
449-473.
Myers, D. E. 1994. Spatial interpolation: an overview. Geoderma, 62:17-28.
NDEP. 2004. Guidelines for digital elevation data, Version 1.0,
http://www.ndep.gov/NDEP_Elevation_Guidelines_Ver1_10May2004.pdf, National
Digital Elevation Program (NDEP). (accessed 18 January 2009).
Ramirez, J. R. 2006. A new approach to relief representation. Surveying and Land
Information Science, 66(1):19-25.
Turton, D. A. 2006. Factors Influencing ALS Accuracy. AAMHatch Pty Ltd, Brisbane,
Australia, 5 p.
Weydahl, D. J., Sagstuen, J., Dick, Ø. B. and Rønning, H. 2007. SRTM DEM accuracy
assessment over vegetated areas in Norway. International Journal of Remote
Sensing, 28(16):3513-3527.
Zimmerman, D., Pavlik, C., Ruggles, A. and Armstrong, M. P. 1999. An experimental
comparison of ordinary and universal Kriging and inverse distance weighting.
Mathematical Geology, 31(4):375-389.
BRIEF BIOGRAPHY OF PRESENTER
Xiaoye Liu is a lecturer in the Faculty of Engineering and Surveying at the University
of Southern Queensland. Xiaoye has both bachelor and master degrees in surveying
from the Wuhan Technical University of Surveying and Mapping (now merged to
Wuhan University) in China. She also obtained a master degree in applied information
technology from School of Computer Science and Software Engineering, Monash
University. Xiaoye has many years experience of teaching and research in spatial
science. She specializes in GIS and remote sensing applications in natural resources and
environmental management, digital terrain modelling and feature extraction from
LiDAR and other spatial data. Her research interests also include digital image
processing, spatial database, GPS and software development.
