Digital Terrain Model Interpolation for Mobile Devices Using DTED Level 0 Elevation Data

Murat Özyurt, Tuna Tuğcu, Fatih Alagöz

In proceedings of Mobilware 2009, The Second International ICST Conference on MOBILe Wireless MiddleWARE, Operating Systems, and Applications, April 27-29, 2009, Berlin, Germany.

Boğaziçi University, Computer Engineering Department Computer & Satellite Networks Research Laboratories

Digital Terrain Elevation Data

3D Digital Maps of Earth provide elevation values at specific longitudinal and latitudinal positions.

DTED maps consist of a square grid structure of cells covering the surface of Earth, with terrain elevation values sampled at the intersection points.

There are three distinct detail levels: Level 0, Level 1, and Level 2. DTED Level 0 contains the least amount of detail while requiring the minimum amount of storage space.

Higher levels require several gigabytes to represent the whole world, while at most a few hundred MBs will suffice for DTED Level 0 storage, depending on the data types used in the datafiles.

Sample DTED Level 0 grid layout
Top view of a sample DTED level 0 grid of 3D terrain cells.

3D Mobile Navigation

Application Terrain View
  • A 3D Mobile Navigation application has been developed for civil and defense uses.
  • Mobile devices inherently possess much less computation and storage capacity.
  • The Digital Terrain Map used in this application features a 240-meter resolution and spans a mountainous area of 14,400 km2.
  • Capacity limitations lead directly to the adoption of DTED Level 0 types of digital maps in mobile handheld applications.
Distance Calculation Utility

Level 1 to Level 0 Conversion

Level 0 maps are algorithmically downsampled and generated from Level 1 source profiles, where the spacing interval between two node points in Level 0 is roughly 1 km.

Cell conversion from DTED level 1 to DTED level 0
Figure: Cell conversion matrix from DTED Level 1 to DTED Level 0.

Each discrete cell in DTED Level 0 packages 7 targeted elevation metrics:

Although the locations of the 4 corner coordinates are mathematically fixed, the other 3 metric attributes (max, min, average) do not carry predefined position values inside the Level 0 cell grid.

In this architecture, the highest and lowest terrain features are localized inside the cell matrix, and the remaining coordinate nodes are smoothed via interpolation relative to the tracking average value across these 6 boundary reference points.

3D Rendering with Corner Points

Planar Surfaces (As-Is) Smoothed Surface Interpolation
Sample cell with corner points numbered
Sample cell with corner points numbered (1–4)
Sample smooth interpolation with 4 corner points
Sample smooth interpolation utilizing 4 corner landmarks

Terrain Cells in 3D View Based on Corner Points

Baseline Grid Map Layout
Grid Map Pipeline Source
3D Terrain Projection Output
Resulting 3D Render Projection

Using Maximum and Minimum Points

DTED Level 0 cells contain maximum and minimum elevation values extracted from the corresponding source DTED Level 1 cell. Programmatically locating these bounding points significantly improves the surface interpolation model in terms of maintaining consistency with the average overall elevation profile of the original terrain layout.

Initial 4-Point Interpolation
Enhanced Interpolation with Extremum Points

Figure: Comparison showing interpolation improvement after maximum and minimum points are located according to Singular Positioning.

Singular Positioning

DTED Level 0 cells store the absolute maximum and minimum elevation markers of their corresponding Level 1 parent cells. Explicitly defining coordinates for these extremums increases the precision of local terrain mesh generation, pinning down structural variances relative to the broader surface average.

Locating Segmentation Points Projected on x-y Plane
Locating Segmentation Points (Points Projected on x-y Plane)
Singular Segmentation Strategy Diagram

To calculate the spatial coordinates of a maximum or minimum feature point inside the grid cell boundaries, intermediate segmentation markers are generated based on the direct elevation deltas between corner points and the destination peak or valley target value.

As an example execution pathway, target boundaries p5-I and p5-II are localized inside the cell plane and are then bisected an additional time to pinpoint p5 (the designated maximum peak). Similarly, node p6 serves as the computed index representing the localized minimum valley point.

Mathematically, the smaller the structural elevation variance a specific corner boundary point maintains relative to the peak or valley threshold, the closer its coordinate position will sit next to that respective maximum or minimum node index.

Circular Positioning

Symmetric Corner Balance Condition

If diagonally opposing matrix corners hold identical altitude values (e.g., the NW point matches the SE point elevation, and the NE point mirrors the SW point elevation), a mathematical conflict occurs: both the singular maximum and minimum calculations resolve onto the exact same coordinate junction—the exact geometric center of the cell space.

To resolve this collision scenario, a circular tracking distribution algorithm deploying multiple secondary maximum and minimum node offsets is applied across the active region.

Circular Anchor Pattern Topology

Under this approach, the absolute center of the cell layout is assigned the minimum (or maximum) value, while being uniformly ringed by four matching maximum (or minimum) node structures. Additional specialized control point markers are layered along the exterior perimeter circles.

These secondary control points function strictly as tuning elements to lock the aggregate arithmetic mean of the resulting interpolated grid cell surface to match the true baseline parameters supplied by the uncompressed parent DTED Level 1 dataset.

Geometric Bias Area Balancing

If the delta between the average and the minimum value (AVG – MIN) tracks smaller than the delta between the maximum and the average value (MAX – AVG), it indicates that the vast majority of the spatial landmass area sits lower than the mean elevation, clustering nearer to the valley floor.

Positioning the singular maximum anchor point directly in the center of the cell grid while radiating four matching minimum anchors outward onto an external perimeter circle balances the resulting mesh surface geometry to fit this specific skew profile.

Dominant Peak Profile Map
Condition: MAX – AVG > AVG – MIN
Dominant Basin Profile Map
Condition: MAX – AVG < AVG – MIN
Cross Section Profile Comparison Diagram
Figure: Central profile cross sections charting the boundary adjustments for both interpolation scenarios.

Even though only a marginal fraction of the grid elements within our target study region mathematically encounter the geometric criteria forcing a circular distribution, the technique is systematically applied as a stabilization override whenever maximum and minimum anchors map too closely together.

The total volume of explicit control nodes required to resolve circular geometry maps out to exactly three times the density profile of the standard singular approach. Consequently, this method outputs superior fidelity and smoother contour surface maps.

However, because the associated programmatic overhead involving matrix inversion and linear transformation steps scales heavily on low-power mobile architectures, the application threshold determining when to tag cells for circular processing must be carefully managed to remain within sensible hardware bounds.

Visualization of Sample Region Map Matrix
Digital map visualization of the evaluation area composed of 14,400 active cells.

Results of Interpolation

Based on the Inverse Distance Weighting (IDW) interpolation analysis, the proposed technique yields significantly better interpolation accuracy compared to baseline models that utilize only the available corner points of grid cells.

Closeness to Real Average
Cell Size (points) % Of Cells Where Method Finds Better Average Mean and Std. Deviation of Average Value Difference
IDW IDW Extra Equal Distance Mean (IDW) Std. Dev. (IDW) Mean (IDW Extra) Std. Dev. (IDW Extra)
6x6 3.55% 93.69% 2.76% -57.74m 45.38m -40.7m 39.05m
11x11 2.28% 96.67% 1.06% -68.72m 52.13m -44.1m 43.38m
26x26 1.82% 97.63% 0.56% -77.39m 56.58m -42.4m 43.76m
51x51 1.57% 97.83% 0.60% -81.47m 58.35m -39.6m 42.34m
Closeness to Real Elevation Values of Interpolated Points
Cell Size (points) % Of Cells Closer To Real Elevation Values Mean and Standard Deviation of Elevation Value Difference
IDW IDW Extra Equal Distance Mean (IDW) Std. Dev. (IDW) Mean (IDW Extra) Std. Dev. (IDW Extra)
6x6 17.30% 46.38% 36.32% -57.40m 68.50m -40.52m 63.05m
11x11 16.20% 57.30% 26.49% -68.35m 71.25m -43.84m 63.78m
26x26 14.10% 67.84% 18.06% -76.99m 72.91m -42.18m 62.03m
51x51 13.16% 73.09% 13.75% -81.07m 73.72m -39.46m 60.24m
Percentage of points with interpolated elevation differences less than 50 and 20 meters from real values.
Cell Size Total Points IDW 50m IDW 20m IDW Extra 50m IDW Extra 20m
6x6 518,400 58.39% 33.30% 66.72% 42.67%
11x11 1,742,400 50.46% 23.68% 64.03% 37.39%
26x26 9,734,400 43.35% 17.68% 64.91% 37.06%
51x51 37,454,400 39.67% 15.76% 66.43% 37.97%

Distribution of point elevation difference values. (Number of points vs. meters).

Conclusions

Adding more points to the four corner points of each DTED Level 0 cell data, it is possible to obtain better interpolation values for elevations of unknown points. Using inverse distance weighting algorithm with additional reference points, we obtain a closer average value for an entire cell, to the real cell average, in more than 90% of 14400 sample cells, compared to IDW algorithm applied only to four corner points of DTED Level 0 data. This algorithm will be utilized in the mobile implementation of a 3D Navigation system. For the time being, the application uses static points at a resolution of 240m and this algorithm will bring in the flexibility of resolution variability to be used in civil applications.

Acknowledgments

This research has been partially supported by The State Planning Organization of Turkey (DPT), under grant number DPT 07K120610. Ms. Aslı Bassa from Université Joseph Fourier has also documented her contributions to this work in her training report.