1. Relationships between Land Cover and Spatial Statistical Compression in High-Resolution Imagery James A. Shine 1 and Daniel B. Carr 2 34 th Symposium on the Interface 19 April 2002 1 George Mason University & US Army Topographic Engineering Center 2 George Mason University

2. Outline of Talk The Variogram Motivation and Procedure Past Results Present Results Analysis and Conclusions Future Work

3. Spatial Statistics: The Variogram - A plot of average variance between points vs. distance between those points (L2) -If data are spatially uncorrelated, get a straight line -If data are spatially correlated, variance generally increases with distance -Directional component also a consideration (N-S, E-W, omnidirectional)

4. Typical image variogram (left), Important quantities (right)

5. Some graphs of variogram models

6. A double or nested variogram

7. Variogram Applications - Determination of range for sampling applications: ground truth supervised classification -Model for estimation/prediction applications (forms of kriging)

8. Outline of Talk The Variogram Motivation and Procedure Past Results Present Results Analysis and Conclusions Future Work

9. MOTIVATION Large data sets, computational challenges (10^6-10^7 data points per km^2 at 1 m resolution for pixels) Large computation times not conducive to real-world applications such as rapid mapping Compression will reduce computation time, But how much can we reduce without losing information?

10. PROCEDURE Transfer data from imagery to text file Compute variograms (FORTRAN code) Format and plot the variograms Compare variograms with full data sets vs variograms with reduced data sets

11. Imagery Ft. A.P. Hill, Ft. Story (both in Virginia) : 1-meter resolution, 4-band CAMIS imagery, collected by US Army Topographic Engineering Center (TEC) Others: 4-meter resolution, 4-band IKONOS imagery, obtained from TEC’s imagery library and also commercially available. Bands: 1. Blue (~450 nm) 2. Green (~550 nm) 3. Red (~650 nm) 4. Near Infrared (~850 nm)

12. Outline of Talk The Variogram Motivation and Procedure Past Results Present Results Analysis and Conclusions Future Work

13. Previous Results: Ft. A.P. Hill, VA (Shine, Interface 2001) Mostly forest, some manmade 2196 x 2016=4.4x10^6 pixels

14. Compression works well for AP Hill imagery; Band 1 (blue) variograms shown below

15. Other A.P. Hill bands also compressed well: Band 2 (Green), N-S at right, E-W bottom left, Average bottom right

16. Band 3 (Red), N-S at right, E-W bottom left, Average bottom right

17. Band 4 (IR), N-S at right, E-W bottom left, Average bottom right

18. Outline of Talk The Variogram Motivation and Procedure Past Results Present Results Analysis and Conclusions Future Work

19. Fort Story, VA results completed, Plus some new imagery: New York City Ft. Stewart, GA Ft. Moody, GA Wright-Patterson AFB, OH Ft. Huachuca, AZ

20. Fort Story, VA New York City Ft. Stewart, GA Ft. Moody, GA Wright-Patterson AFB, OH Ft. Huachuca, AZ

21. Original Ft. Story image: Water, forest, urban 3999x4999= 2.0x10^7 pixels

22. Ft. Story,original Band One (Blue) N-S at right, E-W bottom left, Average bottom right

23. Ft. Story,original Band Two(Green) N-S at right, E-W bottom left

24. Ft. Story Results -Full variogram is very smooth (exponential/spherical), but compression is not good; compressed variogram significantly different from full variogram -Why does AP Hill compress well and Story does not? Could be losing a level on a nested model (right), but perhaps different landcover or terrain reacts differently to compression. -Need to compare different types of imagery and hopefully make some inferences

25. Subarea from Ft. Story: just forest 524x408=2.1x10^5 pixels

26. Ft. Story forest subimage Band One (Blue) N-S at right, E-W bottom left Average bottom right

27. Ft. Story forest subimage results -Variograms seem to be unbounded (linear) -Compression matches original pretty well, much better than for the full image -Do some more tests with other images and landcovers

28. New Results: Fort Story, VA New York City Ft. Stewart, GA Ft. Moody, GA Wright-Patterson AFB, OH Ft. Huachuca, AZ

29. New York City 2000 x 2000 Urban, water, smoke (9/12/01)

30. New York City Blue E-W, N-S, average

31. New York City Green E-W, N-S, average

32. New York City Results -Variogram seems unbounded (linear) -Almost no difference between the full and compressed variograms

33. New Results: Fort Story, VA New York City Ft. Stewart, GA Ft. Moody, GA Wright-Patterson AFB, OH Ft. Huachuca, AZ

34. Fort Stewart Mostly fields 2559x2559= 6.5x10^6 pixels

35. Ft. Stewart Blue E-W, N-S, average

36. Ft. Stewart Green E-W, N-S, average

37. Ft. Stewart Red E-W, N-S, average

38. Ft. Stewart IR E-W, N-S, average

39. Ft. Stewart Results -Full variogram is very smooth (exponential/spherical) -Almost no difference between full and compressed variograms, except very slightly in Blue band

40. New Results: Fort Story, VA New York City Ft. Stewart, GA Ft. Moody, GA Wright-Patterson AFB, OH Ft. Huachuca, AZ

41. Ft. Moody fields 1202x1742= 2.1x10^6 pixels

42. Ft. Moody fields Blue E-W, N-S, average

43. Ft. Moody fields Green E-W, N-S, average

44. Ft. Moody fields Red E-W, N-S, average

45. Ft. Moody fields IR E-W, N-S, average

46. Ft. Moody forest 1325x1767= 2.3x10^6 pixels

47. Ft. Moody forest, Blue, E-W (no spatial dependence after 3 pixels, so compression is useless; all bands and directions give same non-dependence)

48. Ft. Moody Results -Field subset variogram is mixed: mostly linear in visible bands, mostly spherical/exponential in IR band. Compresses well although compressed variogram is greater in magnitude than full variogram for the Blue and Green bands -Forest subset shows no spatial dependence, compression is irrelevant

49. New Results: Fort Story, VA New York City Ft. Stewart, GA Ft. Moody, GA Wright-Patterson AFB, OH Ft. Huachuca, AZ

50. Wright-Patterson AFB, Ohio mostly fields, some urban 1385x1692=2.3x10^6 pixels

51. Wright-Patterson Blue E-W, N-S, average

52. Wright-Patterson Green E-W, N-S, average

53. Wright-Patterson Red E-W, N-S, average

54. Wright-Patterson IR E-W, N-S, average

55. Wright-Patterson Results -A slight loss of variogram with compression, especially in blue and green -Spherical/exponential variogram

56. New Results: Fort Story, VA New York City Ft. Stewart, GA Ft. Moody, GA Wright-Patterson AFB, OH Ft. Huachuca, AZ

57. arid desert and mountains with dry drainage patterns 2551x1806= 4.6x10^6 pixels

58. Ft. Huachuca Blue E-W, N-S, average

59. Ft. Huachuca Green E-W, N-S, average

60. Ft. Huachuca Red E-W, N-S, average

61. Ft. Huachuca IR E-W, N-S, average

62. Huachuca Results -Almost no loss of variogram with compression. -Variogram is smooth (spherical/exponential)

63. Computing Benchmarks -Plots of overall execution time versus total number of pixels to be processed: without Ft. Story fullwith Ft. Story full

64. Ratio of computation time (full/reduced) increases as pixel size increases

65. Outline of Talk The Variogram Motivation and Procedure Past Results Present Results Analysis and Conclusions Future Work

66. Most losses occurred in the Blue and Green bands; Red and IR seem to compress better. Checkered fields in particular showed a slight loss in compression for Blue and Green (Wright-Patterson and Ft. Stewart) Most land cover types show a spherical/exponential type of variogram. The exceptions seem to be pure forest (linear or no spatial variation) and pure urban (linear) Mixtures in particular seem to show a spherical/exponential type of variogram.

67. Still no definitive answer to the major loss of spatial information for full Ft. Story image. Best theory: have lost a level of variation in a nested spherical or exponential model (low-level scale <= 20 meters). Overall, spatial statistical compression works well for a wide variety of land cover types; may lose some information, but the range is pretty constant, and the gain in computation is immense. (Be careful with forests, though – further tests definitely needed there).

68. Outline of Talk The Variogram Motivation and Procedure Past Results Present Results Analysis and Conclusions Future Work

69. Compare random,average compression with systematic compression Test for further compression (64X) with 1 m imagery Improve software code and streamline implementation Parallelize variogram computations Improve graphs