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Maximizing Visibility & Mobility Metrics in Large Terrain Cells: SDH Vienna 2006

Explore tradeoffs when siting multiple observers on large terrains. Learn about terrain properties, errors, and test data complexities at SDH Vienna 2006. Discover results, testing protocols, and steps for multiobserver siting to enhance visibility indices and viewsheds. Dive into challenging tasks like interpolating line-of-sight between posts and enforcing intervisibility. Gain insights on the impact and effectiveness of different methods in terms of visibility and mobility metrics in large terrain cells.

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Maximizing Visibility & Mobility Metrics in Large Terrain Cells: SDH Vienna 2006

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  1. Tradeoffs When Multiple Observer Siting on Large Terrain CellsSpatial Data Handling (SDH)Vienna, July 2006 W Randolph Franklin, Christian Vogt Rensselaer Polytechnic Institute mail@wrfranklin.org, 703-447-7808 http://wrfranklin.org 5/2/06 9pm

  2. Goals of this DARPA/DSO Geo* project • Alternate terrain representations • Compact; lossy - size / quality tradeoffs. • Bias representations towards legal terrain • Process datasets up to 10000x10000 • Uncompression speed is more important than compression speed. • Evaluate on visibility, mobility metrics. SDH Vienna 2006

  3. First: Study Terrain Properties • Many local max, few local min • Long range order - rivers • Elevation and slope discontinuities are common, and are very important for mobility and visibility SDH Vienna 2006

  4. Which is land, which water? You can answer this => there is unexploited structure. SDH Vienna 2006

  5. Where is This? SDH Vienna 2006

  6. Answer SDH Vienna 2006

  7. Examples of Other Errors SDH Vienna 2006

  8. Fourier Series • Widely used • Excellent for representing many physical phenomena, like vibrations. • Quite unsuitable for terrain. • They assume C∞ continuity • The truncated series is too smooth • …and has many local minima SDH Vienna 2006

  9. Sample Results • TIN: represented a 10800x10800 array to 3% max elevation error with 157,735 triangles. • Scooping: represented w111n31 with 7x7 linear scoops with average error 0.1% and max error 2%. • Using 7x7 scoops on one 3592x3592 dataset, multiobserver siting had only 6.5% error. • ODETLAPping 400x400 piece of Lake Champlain W with 1/9 the points: error was 0.9m (0.1%). • Combining TIN with ODETLAP: captures essence of surface with very few points. • ODETLAP: Can fill radius 40 circles of missing data. SDH Vienna 2006

  10. Test Data Complexities Varying Resolution Bunched Elevations SDH Vienna 2006

  11. Testing Protocols • Elevation error: max, RMS • Visibility index: set of hi-vis observers. • Joint viewshed from multiple observer siting – are observers sited on alternate rep just as good? • Smugglers’ path planning – is path planned on alternate rep really hidden? No toy datasets SDH Vienna 2006

  12. Interpolating LOS between posts • Challenging • Motivation: in one test, we tried various interpolation methods (min, max, linear) • ½ of all the targets changed visibility SDH Vienna 2006

  13. The Known Unknowns of Viewsheds • Small changes in LOS interpolation cause large changes in visibility. • One half of this cell has uncertain visibility. SDH Vienna 2006

  14. Protocol 3: Visibility Index Testing • Consider each post in term as an observer. • Compute its visibility index. • Monte Carlo sampling: pick T random targets, compute their visibility, and report the fraction visible. • Produce a map of all the visibility indexes. • Compare the visibility index map of the original terrain representation to the map of the alternative representation. SDH Vienna 2006

  15. Protocol 4: Multiple Observer Siting Testing • Site a set of observers, So, on the original terrain rep. • Site a set of observers, Sa, on the alternative terrain rep. • Transfer Sa to the original rep. • Compare quality of Sa to So. SDH Vienna 2006

  16. Multiobserver Siting Steps • Find approximate visibility index of every point in cell, using Monte Carlo sampling. • Partition the cell into blocks and pick the best potential observers in each block. • Using a greedy algorithm, select the best of the best observers. • We have considerably studied the tradeoffs here. SDH Vienna 2006

  17. Step 1: VIX – Approximate Visibility Indices • For every potential observer in cell, pick T random targets within radius of interest. • Run a line of sight to each target and see if visible. • Estimated visibility index = fraction of targets that are visible. SDH Vienna 2006

  18. Step 2: FINDMAX – Find Subset of Top Observers • Goal: Reduce 3600x3600 posts to perhaps 1000 potential observer sites. • Partition cell into blocks (to force observers to spread out). • In each block, return observers with highest visibility indices. SDH Vienna 2006

  19. Step 3: VIEWSHED – Find Top Observers’ Viewsheds • Find (closest to) exact viewshed of every top observer from previous step. • If radius of interest=200, then 200x200 bitmap. • Run lines of sight from observer to perimeter, then back in and compute all visible points. • Time: area of bitmap. SDH Vienna 2006

  20. Step 4: SITE – Multiple Observer Siting • Greedy selection of observers. • At each step, pick observer whose viewshed adds most to cumulative viewshed. • This is fast with bitmap operations. • Selecting several hundred observers easy. SDH Vienna 2006

  21. Enforcing Intervisibility • After the first best-of-the-best, add only new observers that are inside the joint viewshed of the previous best-of-the-best. No intervis  Intervis  SDH Vienna 2006

  22. Effect of Intervisibility • This reduces the joint viewshed considerably. SDH Vienna 2006

  23. Reduced Resolution Effect on Siting • Lowering horizontal resolution lowers observer siting quality. • Lowering vertical resolution does not as much. • Visibility, computed on lower resolution, is too high. SDH Vienna 2006

  24. Experiments Reducing horizontal resolution Reducing vertical resolution SDH Vienna 2006

  25. Alternative Representations • TIN • Scooping • ODETLAP • Combinations of the above, e.g., ODETLAP uses TIN points. SDH Vienna 2006

  26. Note: Good compression techniques are multistep JPEG: • Rotate RGB -> YCrCb • Discrete cosine transform • Low-pass filter • Arithmetic encode Text compression: • Run length encoding • Burrows-Wheeler transformation • Move to front • Another run length encoding • Arithmetic encode SDH Vienna 2006

  27. TIN Status • We can process 10800x10800 arrays of posts in ½ hr on PC • No external storage is used. • Dataset formed by catenating nine 3601x3601 cells from data from the Savannah March kickoff meeting. • Elevation range: 3600. SDH Vienna 2006

  28. TIN Features • Progressive resolution since points are inserted greedily. • “Feature” points on peaks and ridgelines, and edges joining them, may be more important. • Our TIN program selects them automatically; no need for manual identification and constrained triangulation. • The points selected for the triangulation are assumed to be important, and can be fed into other methods, like ODETLAP. • TIN is a piecewise linear triangular spline. Preliminary experiments with a higher degree spline showed no consistent improvement, and so were suspended. SDH Vienna 2006

  29. Alternative Representations • TIN • Scooping • ODETLAP • Combinations of the above, e.g., ODETLAP uses TIN points. SDH Vienna 2006

  30. Scooping Representations • This is longterm research. • The goal is to smash through the information theoretic barrier to terrain compression by utilizing geologic information. • We are pursuing several representations in parallel. SDH Vienna 2006

  31. Scooping Status Several subprojects: • 3-axis milling machine experiments with set of simple drills. • Complete cover test with parameterized sloped drills. • Theoretical thinking about how scooping is different from, e.g, wavelets. SDH Vienna 2006

  32. More General (Sloped) Drills • Tradeoff powerful, large to encode, basis elements, vs small simple elements, of which we need more. • Sweet point: basis elements resemble object being approximated. • Purpose: to better understand scooping, while initiating experiments in slope-preservation during lossy compression. • Underlying assumption: little long range correlation of elevation or slope. SDH Vienna 2006

  33. Regular Scoop Details • 7x7 Scoop size will represents 49 elevations using only 3 coefficients • 7 is not a magic number but good enough for Level 2 DTED cells • Large Errors are rare and mean error is very low, less than 2m • Each scoop is a tilted plane which minimizes the error • Regularity brings simplicity to the representation SDH Vienna 2006

  34. Regular 7x7 Tile Scoop Representation W111°N31° Reconstructed (Left), Error (Right) Factor of 49 reduction in number of points SDH Vienna 2006

  35. Percent of Elevation Errors onW 111° N 31° SDH Vienna 2006

  36. 7x7 Regular Sloped Scoop VIX Evaluation • Comparing Postings with Visibility Index Larger Than 80% • Original (Above), Reconstructed (Below) • Yellow: High VIX • Green: Low VIX • Difference is not easy to discern SDH Vienna 2006

  37. Viewshed Evalution of Regular Scooping • Dataset: 3595×3595 • Number of observers: 81 • Elevation range: 809 to 2882. • Observer/target height is 10. • Radius of interest: 300. SDH Vienna 2006

  38. Multiobserver Viewshed Comparison Original Terrain Rep Tile 7 Alternate Terrain Rep SDH Vienna 2006

  39. Alternative Representations • TIN • Scooping • ODETLAP • Combinations of the above, e.g., ODETLAP uses TIN points. SDH Vienna 2006

  40. ODETLAP Review • Solve an overdetermined variant of a Laplacian PDE. • Known pts: zij = hij • All pts: 4zij = zi-1j + zi+1j + zij-1 + zij+1 • Easily processes 400x400 arrays of elevation posts in Matlab. SDH Vienna 2006

  41. ODETLAP Advantages • Infers local maxima. • Surface doesn’t droop. • Utilizes isolated data, if available. • Interpolates broken contours. • Conformal (handles nested kidney-bean contours) • Conflates inconsistent data, with user-defined weights. SDH Vienna 2006

  42. ODETLAP on Nested Squares • Various smoothness settings are possible. • R=3 gives • Completely smooth silhouettes, • Average error = 2.7% • Max error = 12%. SDH Vienna 2006

  43. ODETLAP on Regular Points • Initially sample that with a subarray of regularly spaced points, every K points in each direction. • When computing a complete surface from the sample points, parameter R trades off accuracy vs smoothness. • Observe tradeoff of data size versus K, R on a mountainous region of the USGS Lake Champlain W level 1 DEM. SDH Vienna 2006

  44. Lk Champlain ODEPLAP Experiments K: spacing of fitted points R: smoothness vs accuracy (Data range: 1378) SDH Vienna 2006

  45. Factor of 9 Reduction • ODETLAP used 1/9 as many points to represent this surface with an elevation error of 0.9m in a range of 1378. SDH Vienna 2006

  46. Alternative Representations • TIN • Scooping • ODETLAP • Combinations of the above, e.g., ODETLAP uses TIN points. SDH Vienna 2006

  47. ODETLAPping Important Points • The preceding fits a surface to a regular grid of points. • Fitting “important” points should be better. • Use our TIN program, which, at each step, inserts the point farthest from the existing surface. • Use the first N points selected by TIN. SDH Vienna 2006

  48. ODETLAPping TIN Points • Test: 400x400 sections: w111n3110, 3111, 3112. R=0.3 • Compare ODETLAPping first 1000 points selected by TIN with regular grid of 1000 points. • Measure average, max, abs error over all original points. • TIN: average is worse but max is better, but up to factor of 5. • TIN points produce a better conditioned surface. • Refined: Insert worst points into TIN ODETLAP. Result: even better conditioned surface. SDH Vienna 2006

  49. Fitting Regular vs TIN Points Fitting 100 Regular Points • Original W111n3110 data (160,000 points) • Fitting TIN points matches the character of the surface better Fitting 100 TIN Points SDH Vienna 2006

  50. Fitting Regular vs TIN Points Fitting 36 Regular Points • Original W111n3111 data • Fitting TIN points matches the character of the surface better Fitting 30 TIN Points SDH Vienna 2006

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