Home Articles Comparison of Decimation and Averaging Methods of DEM’s Resampling

Comparison of Decimation and Averaging Methods of DEM’s Resampling

 

Kazimierz Becek
Geography Department, Faculty of Arts and Social Sciences
Universiti Brunei Darussalam
Jalan Tungku Link, BE1410 Gadong, Brunei Darussala
Ph: +673 8760 540
[email protected]

There are two independent sources of the SRTM.C digital elevation model: the Jet Propulsion Laboratory (JPL), and National Geospatial-Intelligence Agency (NGA). The major difference between both datasets is that the former was downsampled from the original one to three-arc-second elevation posting by averaging and the latter by decimation. JPL decided to use averaging because according to "most analysts the averaging method produces a superior product by decreasing the high frequency 'noise' that is characteristic of radar-derived elevation data". On the other hand, NGA used so called "subsampling" method, known also as decimation method. The paper presents the results of a simulation study aimed at quantitative assessment of errors caused by downsampling of a DEM using decimation and averaging methods. It was found that: (1) Resampling by averaging causes valleys and ridges to be too high or too low, respectively. (2) The variance of discrepancies between resampled and referenced DEM does depend on roughness of terrain. (3) The resampling of a DEM by averaging could be used to construct a method for drainage pattern extraction.

Introduction
The eleven-day space shuttle mission in February 2000 was almost completely dedicated to acquisition of data using the C (? = 5.3cm) and X ((? = 3.1cm) band of electromagnetic waves of small aperture radar (SAR) working in so-called interferometric mode (InSAR). The space mission was officially known as the shuttle radar topography mission or SRTM for short. The final product of the mission is a digital elevation model (DEM) covering almost 80% of the land masses of earth. This remarkable dataset is a product of collaboration between the American, German and Italian space agencies. The X band of the SRTM DEM (SRTM.X) was prepared by the German and Italian space agencies, and is available for fee of about €500 per 15 by 15 arc-minute tiles. One arc-second (about 30m at equator) is the spatial resolution of the X band DEM. Because the X band instrument worked at the constant incidence angle this version of the DEM does cover about 30% land masses of earth. Much larger area was covered by the C band instrument which operated in the so-called scanning mode. The SRTM.C is available over land masses between 56o south and 60o north of equator at deliberately degradated resolution of the three arc-second (about 90m at equator). The degradation process was performed for the national security reasons (?) over the non-USA territories. The accuracy of both datasets is in the range of about ?4-6m (one standard deviation) (SLATER et al, 2006).

There are two Internet sources of the SRTM.C, e.g. the Jet Propulsion Laboratory (JPL) and the National Geospatial-Intelligence Agency (NGA) (SLATER et al, 2006). Unfortunately, the datasets are not identical. The difference is in the resampling procedure used. The motivation for this project is a qualitative statement produced by JPL saying that according to “most analysts the averaging method produces a superior product by decreasing the high frequency ‘noise’ that is characteristic of radar-derived elevation data” (NASA 2005). This is a comment regarding the SRTM.C distributed by the National Geospatial-Intelligence Agency (NGA – former National Imagery and Mapping Agency, or NIMA) which was resampled to the three arc-second resolution by ‘subsampling’ or sometimes known as decimation method. Despite the above justification of the superiority of the averaging method, NGA used so-called “subsampling” method. Most likely the decision was taken based on the fact that the “subsampling” is the same method the NGA used to generate the Digital Terrain Elevation Data (DTED) level 1 (NASA 2005).

The objective of this project is to identify which of the two resampling methods lead to superior results in qualitative terms, and to determine whether the roughness of the terrain is a factor influencing the magnitude of disparities between both resampling methods. The investigation was conducted by comparing resampled with the original dataset.

Resampling
Resampling is a process of changing the resolution of a digital dataset. There are two types of resampling: a) upsampling, and b) downsampling. The first one increases the resolution; whereas the second one reduces the resolution of the dataset. Resampling is an irrevocable procedure because it is a many-to-one (or one-to-many in case of upsampling) type of operation. Upsampling in geosciences is rarely performed. This fact justifies that resampling will mean downsampling, whenever possible. Resampling is usually performed to lower the resolution of the DEM to the scale of a cartographic output or to achieve a regular grid from randomly collected elevation points.

Resampling of a DEM is a source of discrepancies between resulting and reference DEMs. The discrepancies are usually expressed in terms of standard deviation of height differences between resampled and reference models. There are three factors influencing the magnitude of the discrepancies: a) terrain roughness, b) resolution of the resulting DTM, and c) the type of the resampling method.

The roughness of terrain is usually expressed in terms of variance or (standard deviation) of the terrain’s height undulations. The major problem raised by some authors in relation to this indicator of terrain roughness is that this is a global or an average measure, and as such it is spatially independent. Nevertheless, this is the most frequently used quantitative descriptor of topography.

Resampling of a DEM involves finding elevations and locations of new grid posts based on the posts and elevations of the input DEM. The resolution of the destination DTM should be determined by both roughness of terrain and scale of the final cartographic presentation. Nearest neighbour, bilinear and cubic convolution are commonly used in geosciences resampling algorithms. Somewhat less known is the decimation method which is known in signal processing as one of many types of low-pass filters. Figure 1 shows how the averaging and decimation algorithms work.

The operational difference between the averaging and decimation method is that the latter method expands horizontally elevation of the central pixel preserving its original value; whereas in the former method the value for the new pixel is artificial e.g. it is created by averaging of elevations of all pixels within the 3 by 3 pixel window.


Figure 1. Decimation (a) and averaging (b). In both resampling methods 3 by 3 pixel window is replaced by the one pixel window. The value of the new pixel is the value of the central pixel, z0 (decimation), or the average value of all nine pixels z0 to z8 (averaging).

Simulation study
The simulation was performed using 5 by 5 km, regularly spaced 30 by 30 m DTM, developed from the one-meter contours over a test site located in Queensland, Australia (27056’28.5”S, 153015’52.5”E, and 27059’28.5”S, 153019’22.5”E – WGS84). Mean elevation of the test site was 84.3 m varying between 7.2m and 276.9m. The standard deviation of terrain undulation was ±44.9m (variance = 2016m2). The 30m grid size corresponds to the one arc-second SRTM.C. The reference DTM was resampled by averaging and decimation methods to get a 90m grid size resembling the three arc-second SRTM.C datasets. Resulting DTMs have been compared with the reference (e.g. 30 by 30m) DTM. The mean height and its standard deviation (one s) were chosen as the quantitative measures of the disparities between both methods. A binary image showing the spatial distribution of the height differences has also been derived. The following are the results of the above described simulation.

Results
The first test was conducted to assess the statistics of height differences between the referenced DTM which was resampled to 90 by 90 m resolution using the averaged method, and the 30 by 30m reference DTM. The results of the comparison: Averaged minus Accurate are shown in Figure 2.


Figure 2. Results of Test 1. Binary image and histogram of errors in height as a result of downsampling by averaging. Negative errors in black. Gaussian fitting curve was drawn for mean and STD as shown on the Figure.

The binary image of errors in Figure 2 reveals an interesting pattern, which resembles the extremes of the topographic features (valleys – white and ridges – black) of the test site (see Figure 5). This observation indicates that indeed the resampling by averaging smooths out a DTM. However, this applies not only to “the high frequency ‘noise’ that is characteristic of radar-derived elevation data” (NASA 2005), but also to the topography itself. As it is clearly visible from the image on Figure 2, the averaged SRTM.C is too high in valley regions and too low over ridges. This characteristic of the averaged SRTM.C dataset (distributed by JPL) has already been reported in GUTH 2006.
The second test was performed to compare the resampled by decimation with the reference DTMs.


Figure 3. Result of Test 2. Binary image and histogram of errors in height as a result of downsampling by decimation. Negative errors are in black. Gaussian fitting curve was drawn for mean and STD as shown on the Figure.

The image in Figure 3 also reveals topographic features of the test site, but they are not that clear as in Figure 2. The mean value of the discrepancies for both methods is almost equal to zero which indicates that resampling of a DTM by either method does not introduce any systematic error. The standard deviation of the height differences caused by decimation is smaller than by the averaging method by about 11% (±3.57m versus ±3.95m).

It would be natural to suspect that the above results are somehow depended on roughness of terrain. The following is a summary of a simulation study of this factor. In order to investigate this relationship a number of different types of terrain would be needed. One way to get statistically sufficient set of test datasets would be deployment of a some kind of topographic surfaces generator; fractal based, for example AHMADZADEH et al., 2001. Instead of generating a number of artificial terrains, or acquiring real ones, a different strategy was adopted. The test dataset was classified using a local measure of roughness of terrain. It could be defined as variance of elevation within the 3 by 3 pixel window. Figure 4 shows a graph of the averaged variance of height difference between the averaged and decimated DTMs versus roughness of terrain. Clearly, there is a relationship between the terrain roughness and the variance of the discrepancy between the reference and resampled DTMs. It could also be concluded that, the averaged method produces superior output than the decimation method.

It has to be mentioned that the graph in Figure 4 was restricted to the local roughness of terrain of ?10m or 100m2. It was done so due to the fact of rapidly decreasing number of the 3 by 3 pixel tiles with higher degree of roughness. A consequence of this is the increasing level of noise clearly visible in Figure 4. This has to be compared with the roughness of terrain of the test site of about 2016m2 (?44.9m) for which the resampling by decimation produces better results than averaging method by about 11% (±3.57m versus ±3.95m). In light of the above, the simulation study does not conclusively answer the question of supremacy of either resampling method.


Figure 4. Variance of difference in height as a function of terrain roughness. The local terrain roughness is expressed as variance of elevation within the 3 by 3 pixel window.

A ‘By-Product’
Figure 5 shows the sunshodowed representation of the DTM over the test site with overlaid few vectors extracted from Figure 2. A match between the vectors representing ridges and valleys and the DTM is clearly visible. This would suggest that the resampling by averaging could be used to construct a method for drainage pattern extraction. Some recent attempts to develop a procedure using different strategies are reported, for example, by CANDEIAS 1996 and LIN et al., 2006.


Figure 5. Test DTM overlaid with few vectors extracted from Figure 2. Ridges and valleys are in yellow and white, respectively. The thin white line represents the cadastral boundaries of the Nerang State Forest which is irrelevant for the purpose of the study.

The issue will be further investigated and reported on in the forthcoming papers.

Conclusions
The comparison study of the resampling methods, namely decimation or subsampling and averaging were carried out in order to quantify the magnitude of discrepancies between two available versions of the SRTM.C dataset, DTED Level 1 distributed by NGA (National Geospatial-Intelligence Agency), and ‘finished’ distributed by NASA (NASA 2005). The following is a list of observations justified by the study:

 

  1. Resampling by averaging causes valleys and ridges to be too high or too low, respectively. This effect could be used to construct an extractor of extremes of terrain surfaces.
  2. In quantitative terms resampling by averaging produces superior results to the decimation method at least in the low range of roughness of terrain. For the higher range of the roughness the results of this study are inconclusive.

The first observation confirms that what was concluded after comparing the SRTM.C with the National Elevation Dataset (NED) over a much larger area, e.g. the USA territory (GUTH 2006).

The second observation simply means that for quantitative applications of the SRTM.C it is advisable to use the SRTM.C decimated dataset because it provides the ‘true’ values of elevation. The averaged version of SRTM.C introduces systematic errors by lowering peaks and ridges and raising valleys. This version is more suitable for displaying purposes because it also smooths out radar speckle. Missing pixels, so called ‘data voids’ were also filled out.

References

  • AHMADZADEH, M.R. & PETROU, M., 2001: Error Statistics for Slope and Aspect When Derived from Interpolated Data. IEEE Trans. Geosciences and Remote Sensing, Vol. 39, no. 9, pp.1823 – 1833.
  • CANDEIAS, A.L.B., 1996: Drainage Network Extraction from a SAREX’92 RADAR image. In proc. of SIBGRAPI, pp. 243 – 250. Available online:https://mirror.impa.br/sibgrapi96/trabs/pdf/a07.pdf.
  • GUTH, P. L. 2006: Geomorphometry from SRTM: Comparison to NED. Photogrammetric Engineering & Remote Sensing (PE&RS), Vol. 72, No. 3, March 2006, pp 269-277.
  • LIN, W., CHOU, W., LIN, C., HUANG, P. & TSAI, J., 2006: Automated suitable drainage network extraction from digital elevation models in Taiwan's upstream watersheds. Hydrological Processes, Vol. 20, 2, pp 289-306.
  • NASA, 2005: SRTM Topography. Available online (March 2007): https://ftp//e0srp01u.ecs.%20nasa.gov/srtm/-version2/Documentation/SRTM_Topo.pdf.
  • SLATER, J. A., GARVEY, G., JOHNSTON, C., HAASEN, J., HEADY, B., KROENUNG, G. & LITTLE, J., 2006: The SRTM data “finishing” process and products. Photogrammetric Engineering and Remote Sensing, Vol. 72, No. 3, pp. 237-247.