Scope

1. Evolutionary Feature Extraction for SAR Air to Ground Moving Target Recognition – a Statistical ApproachTheory of Statistical MeasuresDr. Janusz StarzykOhio University

2. Scope • Signal Characterization • Clustering • Baseline Approach • Principal Component Analysis • Hybrid Distance • Piecewise Linear Approach • Test Results • Conclusion

3. Data Description • MSTAR program data collections 1 & 2, scene 1 • 1-D High Range Resolution (HRR) data • 10 target classes • Two target classes (BMP2 and T72) have variants • The HRR data extracted from X-band 1x1 foot resolution SAR images • data collected at 15o were used for testing and 17o for training

4. 2S1 BRDM2 SAR Images

5. HRR Profile Extraction from SAR chip

6. Example Range/Pose Chip Data Plot

7. Example HRR Profile

8. 2S1 BRDM2 Images of the Experiment Targets BMP2-c21 BTR60 BTR70-c71

9. Clustering for Classification of HRR Signals • Why to use clustering in classification • What are the shortcomings of the traditional clustering • Our program • Test results

10. Problems in Clustering

11. Popular Clustering Methods • Parametric approach • k-means approach • Normal Decomposition • Nonparametric approach • valley-seeking

12. Shortcomings of the Clustering Methods • Parametric approaches • pre-assuming number of clusters • Non-Parametric approaches • sensitive to the control parameters used in the algorithm • dependent on the distribution of data • not able to accurately approximate the overlapped distributions

13. Data Clustering Algorithm • Extraction of the seed clusters • Coverage of the training data signals by the seed clusters • Size of the seed cluster • Merging of the clusters with a similar distribution

14. Sample of Clustering Results

15. Cluster Growth Program

16. Statistical Concepts in Clustering • MD - Minimum Distance • AMD - Average Minimum Distance • X - the mean value of AMD • Z - the lower bound of AMD • Y - the upper bound of MD

17. A Distribution of MD and AMD

18. Threshold Selection for the Cluster Growth Program • Design of the statistical experiment 1. Generate uniformly distributed data 2. Calculate the minimum distance for every point 3. Draw the distribution of the MD and AMD

19. A Distribution of MD

20. A Distribution of AMD

21. Definition of Threshold Where MminD is the mean of the minimum distances in the current cluster. and Ratio =Y/Z=spread of the minimum distance/minimum AMD

22. Results of the Experiment

23. The Cluster Merging Algorithm • Focus - how to identify the clusters whose distributions are consistent? • Generate two groups of uniformly distributed points with different sizes and mean values • Calculate the NOA between two groups • Change R_size and Distance and repeat the above experiment. • The NOA rule

24. Definition of NOA

25. The Touch Point of Two Clusters The parameters affecting the NOA • Distance - the distance between the means of two clusters • R_size - the ratio of two clusters’ sizes

26. NOA with different Distance and R_size

27. Merging Program • Using the threshold to decide whether to merge the clusters in the same class • Using the NOA value to the nearest cluster from a different class to terminate the selection for the current cluster

28. Cluster Merging Examples

29. Baseline Approach • 1 foot range resolution with 1.5x oversample • Full aspect training and testing • Training on MSTAR targets at 17o depression angle (1365 profiles total) • Testing on MSTAR targets at 15o depression angle (1134 profiles total) • Baseline algorithm (+/- 5 degrees template aspect gate) with 1-look • Leaving-One-Out Method (LOOM) applied to supplement unknown targets

30. Alignment in theBaseline Program

31. Alignment in theBaseline Program To minimize ErrorB solve which gives

32. Alignment Result 1.4 Template Observation 1.2 Absolute difference Aligned difference 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 0 10 20 30 40 50 60 70

33. 6 5 4 3 2 1 0 0 50 100 150 200 250 300 350 400 MSE for different targetsw.r.t template of target 2s1_b01 MSE-> Azimuth->

34. Decision Threshold • Rejection threshold computed for each target and pose from MSE for testing targets against templates • tjp = meanjp + factor * stdj • j is the target and p is the pose index • meanis computed using 5 point moving average • std is computed over all pose angles

35. Threshold Selection

36. Prej = 1.2% Pdec = 98.8% Pid = 78% Pmis-id = 20.8% Pfa = 82% Baseline Classification Result(Factor =2)

37. Principal Component Analysis Template is defined using and has singular values n is the number of template signals m is the number of features The covariance

38. Distance Measures Consider an observation point and define • Euclidean Distance • Mahalanobis distance

39. Comparison between MD and ED In the original space In the projected space

40. MD confusion table(3.5 degrees data) Pdec = 96.4% Pid = 37.2% Pmis-id = 59.2% Pfa = 93%

41. Definitions of Hybrid Distance HD • Euclidean Distance • Mahalanobis distance • Hybrid distance Cmtrx should combine the characters of the ED and MD

42. Definitions of HD • HD1 • HD2

43. Definitions of HD • HD3 • HD4

44. 15 15 10 10 5 5 0 0 -5 -5 -10 -10 -15 -15 -15 -10 -5 0 5 10 15 20 25 -20 -15 -10 -5 0 5 10 15 20 15 10 5 0 -5 -10 -15 -15 -10 -5 0 5 10 15 20 25 Synthetic Examples

45. Classification Results for Synthetic Experiments

46. Example HRR Trajectory Plot

47. Hybrid Distance Clusters Signal values Azimuth

48. Classification Results for HRR Trumpet Data (HD & Baseline) Template: several chips within 10 degree Observation: 5-points averaged chip data

49. Classification Results for HRR Trumpet Data (HD & Baseline) Template: a chip data; Observation: 5-points averaged chip data

50. ROC Curves for HRR Trumpet Data (HD & Baseline T10-5a) 1 0.9 0.8 0.7 Baseline Result Hd1 Result Probability of False Alarm Probability of Correct Classification given Declaration Hd2 Result 0.6 Hd4 Result 0.5 0.4 0.3 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Probability of Declaration