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Plasmasphere Feature Tracking via Tomographic Backprojection

Plasmasphere Feature Tracking via Tomographic Backprojection. T. S. Newman R. Kandimalla N. Santhanam C. Wang H. Zhang D. Gallagher‡ Dept. of Computer Science University of Alabama in Huntsville ‡ Nat’l Space Science and Technology Center / MSFC. Organization. The Problem

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Plasmasphere Feature Tracking via Tomographic Backprojection

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  1. Plasmasphere Feature Tracking via Tomographic Backprojection T. S. Newman R. Kandimalla N. Santhanam C. Wang H. Zhang D. Gallagher‡ Dept. of Computer Science University of Alabama in Huntsville ‡ Nat’l Space Science and Technology Center / MSFC

  2. Organization • The Problem • Related Work • New Approach • Results and Analysis • Conclusion

  3. The Problem I • Specific Problem: • Plasmasphere Density Reconstruction • N 2D --> True 3D • Wider Application: • Limited-Angle Volume Reconstruction • e.g., large-object scanning

  4. The Problem II: Data • The 2D Views • IMAGE EUV • External, Global Views • 84o x 90o FOV • 150x140 pixels • Every 10 min. • He+: 30.4 nm

  5. The Problem III: Sample View May 24,2000 from http://euv.lpl.arizona.edu/euv/

  6. The Problem IV: Constraints • Moving Target --> Few Images • Shadow • Airglow

  7. Related Work: Methods • Popular Tomographic Reconstruction • Filtered Backprojection • Many views! • Algebraic Reconstruction • Alternative

  8. camera slice 1 slice 2 slice 3 slice 4 2D cut-away view Related Work: ART I • Typical ART Scenario camera pixel slice k slice k+1

  9. camera slice 1 slice 2 slice 3 slice 4 2D cut-away view Related Work: ART I • Typical ART Scenario camera pixel slice k Point-sampling slice k+1

  10. Related Work: ART I • Typical ART Scenario camera camera pixel slice 1 slice 2 slice 3 slice k slice 4 2D cut-away view Point-sampling slice k+1

  11. Related Work: ART II • Intensity Distribution: • Unknowns (X): intensity values of samples • Coefficients (A): beam-cell intersection weights • Pixel values (P) AXP

  12. Related Work: ART III • Simul. Alg. Recon. Tech. (SART) • Initialize unknowns vector (X) (Zeroes?) • Update X iteratively • Average the corrections of all beams in a view: * Already-computed unknowns aid

  13. The New Approach’s Framework • Volume-sampling traversal mechanism • 3D rectilinear grid • Each region: cell • From each image’s pixel: • Generate beam • Find intersected cells • Pixel intensity: accumulate particles along beam • Multiple views Beam-Cell Intersection

  14. SVD and New Approach where: A is MxN U is MxN column-orthogonal W is NxN diagonal V is NxN orthogonal • Column-ortho.: • Row-ortho.: • Key point: obtain U, W, V • A is Sparse, Nearly Singular • Singular Value Decomposition? • Used by Few • -RAM!

  15. SVD and New Approach where: A is MxN U is MxN column-orthogonal W is NxN diagonal V is NxN orthogonal • Column-ortho.: • Row-ortho.: • Key point: obtain U, W, V • A is Sparse, Nearly Singular • Singular Value Decomposition? • Used by Few • -RAM! • -Slow!

  16. The New Approach: Hybrid Lanczos • Lanczos: • Effective, indirect SVD method • Tri-diagonalizes • Fewer operations than standard SVD • Hybrid (Lanczos+SART): • Lanczos as initial estimate • SART to refine * Improves accuracy (Zhang + Newman, 2003)

  17. Incorporating Physical Constraints • Reducing Unknowns: • North-to-South Symmetry • Plasma Density Empirical Model • Plasmapause Exploitation

  18. slice equator Symmetry Constraint • Symmetric cells: same intensity • About equator • Solve one set • Advantages: • Less unknowns • Over-determined => More accurate Equator Unknowns

  19. Physical Constraints: Density Model • Symmetry and Empirical Data • Solid lines: measurements • Dashed lines: empirical model Figure adapted from Song et al.’s “Development of empirical model for the plasmasphere”

  20. Reconstruction Exploiting the Model I • Quantized L shells; • Solve these at equator • Per Cell: L values at corners • Distance-weighting of closest L’s. • 1 unknown / shell • Mean L (e.g., Lm = 1.875) • => Between L1 = 1.5 and L2 = 2

  21. Exploiting the Model II: Alternate Approach Solve nonlinear least-squares problem in order to fit parameters in in Nonlinear Model : Levenberg-Marquardt method Nonlinear Model of plasma density model A, B, R, D, γ : parameters which decide plasma density in one MLT plane

  22. Vi + 1 Vi Vi - 1 Original contour New contour New position (minimum energy location) Original position Plasmapause Exploitation • Detecting Plasmapause: • Find Earth Center • Template-matching (find airglow) • Find Plasmapause (using snakes) • Snake initialization • Use Earth center • Snake Energy Minimization • Voronoi Diagram to avoid loops • Two-phase Approach

  23. (1) EUV data viewed as grayscale image (2) Histogram-equalized EUV data (3) Processed to remove noise (4) Snake initialization (5) Intermediate result (1st phase) (6) End of 1st phase (7) Intermediate result (2nd phase) (8)End of 2nd phase (Final snake) Current iteration Previous iteration Tracking 20th frame 25th frame 30th frame 35th frame Snakes overlaid on several frames from an image sequence * Ten iterations for each frame Automated Boundary Localization

  24. Improved Edge Algorithm for Extracting Plasmapause in Eq. Plane Minimum L Algorithm: For each LOS, among all dipole field lines touching it, find field line w/ min. L. Compute field line’s L and MLT coordinates. (The (L, MLT) pairs define plasmapause in eq. plane.) Roelof Edge Algorithm: For a position (r, θ, φ) along any LOS, L : defined by f (r, θ, φ; L) = 0  : MLT, defined by g(r, θ, φ; ) = 0 For each LOS, there is a (L, ) curve. c(θ, φ)= 0 : ‘cone’ of all LOS tangent to the plasmapause. All (L, ) curves drawn for LOS lying on the edge cone c(θ, φ)= 0 form an outer bound to the plasmapause in Equatorial plane

  25. One Enlarged Result

  26. Synthetic Image Comparison EUV image: 2001/161/11:29 synthetic image, Edge Alg. plasmapause Roelof Edge Alg. plasmapause Min L Alg. plasmapause boundary synthetic image Min L Alg. real image Conclusion：Min L Algorithm is better for non-convex plasmapause boundary.

  27. Results I • Test w/ Synthetic Datasets • Synthetic plasmaspheric volume datasets • Follow Carpenter-Anderson model • Dipole Dataset 1: 16*18*8 • Dipole Dataset 2: 224*252*112, with noise

  28. Results: Experiment I • SART vs. SVD-based vs. Hybrid Tech. • Dipole Dataset 1 • 10 30 x 28 Images, 0-90o Qualitative Results: Isosurfaces (a) Dipole Dataset (b) Pure SART (V1) (c) SVD-Based (V2) (d) Hybrid (V3)

  29. Experiment I (cont’d) Quantitative Results

  30. Experiment II • Validate volume-sampling w/o noise • Compared with point-sampling • Same Dataset, Views • Hybrid technique (c) Point-Sampling (V4) (a) Dipole Dataset (b) Volume-Sampling (V3)

  31. Experiment II: Quantitative Results

  32. Experiment III • Validate volume-sampling w/ noise • Vs. point-sampling • Dipole Dataset 2, 10 views • Hybrid technique (d) Point-Sampling(V6) (b) Lo-res Sampling (a) Noisy Dataset (c) Volume-Sampling (V5)

  33. Experiment III: Quantitative Results

  34. Experiment IV: Empirical Model I • Dipole Dataset 2 • Recovered at 36x32x16 • 10 150x140 images, 0-90o Isosurface, Synthetic Dipole Volume Lanczos Alone, No Empirical Model New method alpha = 4

  35. Fitting parameters in plasma density model using real images EUV image: 2001/159/18:07 Longitude parts: 18 Parameters number: 72 Volume size 128*144*64 The number of Pixels in selected region: 6848 Initial guess:  a[1]=5000.0;a[2]=0.200;a[3]=0.0300;a[4]=5.000; a[5]=5000.0;a[6]=0.200;a[7]=0.0300;a[8]=5.000; a[9]=5000.0;a[10]=0.200;a[11]=0.0300;a[12]=5.000; ……a[61]=5000.0;a[62]=0.200;a[63]=0.0300;a[64]=5.000; a[65]=5000.0;a[66]=0.200;a[67]=0.0300;a[68]=5.000; a[69]=5000.0;a[70]=0.200;a[71]=0.0300;a[72]=5.000; Green: Selected region to fit in image

  36. The number of Pixels in selected region: 6848 Average error per pixel = 6.79 (The range of intensity of pixels is from 0 to 835.044.) a[1]=8513.4;a[2]=-3.213;a[3]=1.3961;a[4]=4.005; a[5]=4908.3;a[6]=0.340;a[7]=0.3157;a[8]=4.151; a[9]=3808.1;a[10]=5.908;a[11]=-2.0125;a[12]=4.859; …… a[61]=9318.5;a[62]=-8.299;a[63]=2.4683;a[64]=3.998; a[65]=6694.3;a[66]=-5.691;a[67]=1.7878;a[68]=4.616; a[69]=10043.7;a[70]=-3.447;a[71]=1.4214;a[72]=4.050; (135 Iterations) Fitted image after 135 iterations Real image

  37. Web-based Tool

  38. Step 1: Input parameters in reconstructing volume. Step 2: Upload EUV images; Select method to get plasmapause in image.

  39. Step 3: Draw plasmapause boundary in EUV image. Step 4: Display plasmapause at equatorial plane; download plasmapause file.

  40. Ongoing Work • Improve Reconstruction • More physical constraints • Rotational Effects • Handle Noise • Volume Visualization of Plasmasphere • Feature Tracking • Time-Variant Phenomena • Community Accessibility to Tools

  41. Conclusion • New Plasmapause Localization Techniques and Tools • New hybrid reconstruction technique • Recovery from limited views • Volume-sampling • Lanczos SVD-based processing • Initialize SART with vector from Lanczos • Physical Constraints

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