An Evaluation of Interpolation Methods for MOLA Data

1
Paper Number P42A-0567
An Evaluation of Interpolation Methods for MOLA
Data
Oleg Abramov and Alfred McEwen Department of
Planetary Sciences, University of Arizona
INTRODUCTION AND OBJECTIVES
RESULTS
RESULTS (cont)
The Mars Orbiter Laser Altimeter (MOLA)
instrument on the Mars Global Surveyor (MGS)
spacecraft has been collecting topography data
from the orbit of Mars during the last several
years. Over 600 million data points have been
acquired by the MOLA instrument. Currently,
global topography datasets are the main source of
the digital elevation models (DEMs) of localized
regions on Mars. These datasets are generated by
taking the median observed topography within a
specified degree area. At this time, the highest
resolution global dataset is at 32 pixels per
degree. However, the use of data interpolation
techniques can yield higher-resolution DEMs. On
the other hand, most common interpolation
algorithms were formulated to work with randomly
distributed data, and give visible artifacts when
applied to MOLA tracks. The challenge is to find
an algorithm that minimizes visible artifacts and
is quantitatively accurate at the same time.
The goal of this project was to test several
common interpolation techniques, namely
Delaunay-based Linear Interpolation, Splining,
Nearest Neighbor (also called Inverse Distance
Weighting), and Natural Neighbor. These
techniques were applied to MOLA data for
quantitative and qualitative testing.
Interpolation Algorithm Execution Time
Natural Neighbor 02 hours 08 minutes 47.53 seconds  
Linear 00 hours 00 minutes 05.70 seconds  
Nearest Neighbor 11 hours 09 minutes 11.58 seconds 
Splining 00 hours 00 minutes 30.55 seconds
Table 2. Execution times for the interpolation of
80732 data points to produce a DEM with a
resolution of 200 pixels/degree.
APPLICATIONS OF THE NATURAL NEIGHBOR ALGORITHM
Figure 2. Medium resolution (equivalent to 250
pixels/degree) interpolations. From left to
right Original DEM, Natural Neighbor
interpolation, Linear Interpolation, Nearest
Neighbor interpolation, Splining.
High resolution interpolation (1000 pixels/degree) Medium resolution interpolation (250 pixels/degree) Low resolution interpolation (82 pixels/degree)
Natural Neighbor 25.51 27.23 36.22
Linear 34.03 32.43 34.64
Nearest Neighbor 30.51 31.50 37.25
Splining 88.98 48.41 35.39
Figure 4. Color-coded, shaded relief perspective
view of Milankovic crater at 100 pixels/degree.
METHODS

• Pedr2tab program was used to extract MOLA data
  within
• specified latitude and longitude constraints
  from binary PEDR
• files.
• For quantitative analysis, a DEM of a part of
  Iceland was used.
• The general concept is to sample data from it
  simulating the way
• MOLA acquires data, interpolate that data, and
  then numerically
• compare the interpolated DEM to the original
  DEM.
• For qualitative analysis, the interpolation
  techniques were
• applied to the MOLA data of the Korolev crater
  region.
• The interpolation software was Natgrid for
  Natural Neighbor, IDL
• for Linear, GMT for Splining, and custom C
  code for Nearest
• Neighbor. Visualizations were created in OpenDX.

Table 1. Summary of the mean absolute error for
interpolation techniques. All values are in
meters. The Natural Neighbor algorithm yields the
lowest mean absolute error at high and medium
resolutions.
Figure 5. Color-coded, shaded relief map of the
Cerberus Fossae region at 200 pixels/degree. This
is a potential landing site for 2003 Mars
Exploration Rovers.
Figure 1. a) Random MOLA tracks are superimposed
over the known DEM. b) Elevation values
are obtained from the DEM at each simulated MOLA
point. An interpolated DEM is then created from
these points and compared to the original DEM.
CONCLUSIONS
It is clear that the Natural Neighbor algorithm
yields excellent results when applied to MOLA
data. Additional investigation in this area
should include testing of the Natural Neighbor
algorithm on other known DEMs and possibly
combining it with the median observed topography
technique. The current results indicate that
Natural Neighbor should be the algorithm of
choice when accuracy and appearance are required,
and Splining can be used as a quick first-order
interpolation technique.
Figure 3. Interpolation techniques applied to the
MOLA data of Korolev crater. Clockwise from top
left Natural Neighbor, Linear, Nearest
Neighbor, Splining. The resolution is 200
pixels/degree.
a.
b.