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W Randolph Franklin, Christian Vogt Rensselaer Polytechnic Institute

Tradeoffs When Multiple Observer Siting on Large Terrain Cells Spatial 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. Goals of this DARPA/DSO Geo* project.

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W Randolph Franklin, Christian Vogt Rensselaer Polytechnic Institute

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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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