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Localized Statistical Models in Computer Vision Shawn Lankton Ph.D. Thesis Defense September 8, 2009 Professor Allen Tannenbaum - Academic Advisor Professor Anthony Yezzi - Committee Chair Professor Jeff Shamma - Committee Member

  1. Localized Statistical Models in Computer Vision Shawn Lankton Ph.D. Thesis Defense September 8, 2009 Professor Allen Tannenbaum - Academic Advisor Professor Anthony Yezzi - Committee Chair Professor Jeff Shamma - Committee Member Professor Ghassan Al Regib - Committee Member Professor Arthur Stillman - Committee Member Professor Marc Niethammer - Committee Member Tuesday, September 8, 2009

  2. Outline • Introduction and Background • Localized Segmentation Framework • Vessel Analysis and Plaque Detection • Conclusions 2 Tuesday, September 8, 2009

  3. Computer Vision Chapter 1 3 Tuesday, September 8, 2009

  4. Computer Vision Image Acquisition Image Processing Image Understanding 4 Tuesday, September 8, 2009

  5. Image Processing Segmentation Image Acquisition Image Acquisition Detection Tracking Image Processing Image Processing Registration Image Understanding Image Understanding Shape Analysis 5 Tuesday, September 8, 2009

  6. Hypothesis By localizing the analysis of visual information, assumptions about image-makeup and object-appearances can be relaxed... thereby improving the accuracy of segmentation, detection, and tracking results. 6 Tuesday, September 8, 2009

  7. Hypothesis localization improves results. 7 Tuesday, September 8, 2009

  8. Active Contours and Level Set Methods Chapter 2 8 Tuesday, September 8, 2009

  9. Segmentation 9 Tuesday, September 8, 2009

  10. Segmentation • Thresholding • Region Growing • Graph Cuts • Snakes/Active Contours 10 Tuesday, September 8, 2009

  11. Active Contours 11 Tuesday, September 8, 2009

  12. Implementation • Represent the contour • Parametrized • Implicit 12 Tuesday, September 8, 2009

  13. Level Sets 13 Tuesday, September 8, 2009

  14. Definitions • An Image I : R N → R on the domain Ω A Contour Γ embedded in φ : R N → R • • Such that Γ = { x ∈ Ω | φ ( x ) = 0 } Sethian. Level Set Methods and Fast Marching Methods. 1999 14 Tuesday, September 8, 2009

  15. Definitions  1 φ < − ǫ inside  0 φ > ǫ H φ = outside smooth otherwise   1 φ = 0 the contour  | φ | < ǫ δφ = 0 the rest smooth otherwise  15 Tuesday, September 8, 2009

  16. Define an Energy • Observe the image • Make an assumption • Craft an energy accordingly Mumford and Shah “Boundary Detection by Minimizing Functionals,” JIU, 1988 16 Tuesday, September 8, 2009

  17. Uniform Mean Modeling Energy Assumption: The foreground and background will be approximately constant. � H φ ( I − µ in ) 2 dx E ( φ ) = 0 if I = µ in inside Γ Ω � (1 − H φ )( I − µ out ) 2 dx + + 0 if I = µ out outside Γ Ω � δφ ( x ) �∇ φ ( x ) � dx + λ small if Γ is smooth Ω Chan and Vese. “Active contours without edges,” TIP, 2001 17 Tuesday, September 8, 2009

  18. Energy Minimization ∇ φ E ( φ ) = − d φ dt � ∇ φ � � � d φ ( I − µ in ) 2 − ( I − µ out ) 2 + λ div dt = δφ �∇ φ � | ∇ φ | φ t +1 = φ t + dt · d φ dt 18 Tuesday, September 8, 2009

  19. Complex Images 19 Tuesday, September 8, 2009

  20. A Localized Active Contour Model Chapter 3 20 Tuesday, September 8, 2009

  21. Localizing ≤ r . x B ( x, y ) B ( x, y ) · H φ ( y ) B ( x, y ) · (1 − H φ ( y )) Lankton and Tannenbaum “Localized Region-Based Active Contours,” TIP, 2008 21 Tuesday, September 8, 2009

  22. Localized Contours � � E ( φ ) = B ( x, y ) · F ( I, φ , x, y ) δφ ( x ) dy dy dx Ω x Ω y � + λ δφ ( x ) �∇ φ ( x ) � dx Ω x � ∇ φ ( x ) � ∂φ � ( x ) = δφ ( x ) B ( x, y ) · ∇ φ ( y ) F ( I, φ , x, y ) dy + λδφ ( x ) div �∇ φ ( x ) � | ∇ φ ( x ) | ∂ t Ω y 22 Tuesday, September 8, 2009

  23. Computing the Energy E ( φ ) = + + dF dF dF + dF + + + dF dF ... etc. 23 Tuesday, September 8, 2009

  24. Internal Energies • Local Uniform Modeling • Local Mean Separation • Local Histogram Separation 24 Tuesday, September 8, 2009

  25. Localized Means � Ω y B ( x, y ) · H φ ( y ) · I ( y ) dy µ in ( x ) = � Ω y B ( x, y ) · H φ ( y ) dy � Ω y B ( x, y ) · (1 − H φ ( y ) ) · I ( y ) dy µ out ( x ) = � Ω y B ( x, y ) · (1 − H φ ( y ) ) dy 25 Tuesday, September 8, 2009

  26. Local Uniform Mean Modeling Energy Assumption: The foreground and background are approximately constant locally . F um = H φ ( y ) ( I ( y ) − µ in( x ) ) 2 + (1 − H φ ( y ) )( I ( y ) − µ out( x ) ) 2 26 Tuesday, September 8, 2009

  27. Local Uniform Mean Modeling Energy Assumption: The foreground and background are approximately constant locally . (a) Initialization (b) Global UM (c) Local UM 27 Tuesday, September 8, 2009

  28. Local Mean Separation Energy Assumption: The foreground and background are different locally . F ms = − ( µ in( x ) − µ out( x ) ) 2 Yezzi et al. “A Fully Global Approach to Image Segmentation... ,” JVCIR 2002 28 Tuesday, September 8, 2009

  29. Local Mean Separation Energy Assumption: The foreground and background are different locally . (a) Initialization (b) Global MS (c) Local MS 29 Tuesday, September 8, 2009

  30. Local Histogram Separation Energy Assumption: The foreground and background have different histograms locally . � � F hs = P u,x ( z ) P v,x ( z ) dz z Bhattacharyya Measure Michailovich et. al. “ Image segmentation using … Bhattacharyya ... ” TIP 2007 30 Tuesday, September 8, 2009

  31. Local Histogram Separation Energy Assumption: The foreground and background have different histograms locally . (a) Initialization (b) Global HS (c) Local HS 31 Tuesday, September 8, 2009

  32. Back to These Guys Local Mean Separation 32 Tuesday, September 8, 2009

  33. Studying Local Energies • Choosing the radius • Initializing the contour 33 Tuesday, September 8, 2009

  34. Choosing the Radius (a) Initialization (b) r = 3 (c) r = 5 (d) r = 7 (e) r = 9 (f) r = 15 r = 9 r = 15 r = 7 34 Tuesday, September 8, 2009

  35. Choosing the Radius 35 Tuesday, September 8, 2009

  36. How to Initialize (a) (b) (c) (d) (e) (f) (g) (h) 36 Tuesday, September 8, 2009

  37. How to Initialize (a) Brain 1 (b) Brain 2 37 Tuesday, September 8, 2009

  38. Benefits of Localized Segmentation • Complex problems become simple • Natural solution to many problems • Scale is controllable 38 Tuesday, September 8, 2009

  39. Volumetric Quantification of Neural Pathways Chapter 4 39 Tuesday, September 8, 2009

  40. Tractography • Diffusion Imaging • Brain Connectivity • Localize Orientation Analysis Lankton et. al. “Localized … Fiber Bundle Segmentation.” MMBIA, 2008 40 Tuesday, September 8, 2009

  41. Cingulum Bundle Segmentation 41 Tuesday, September 8, 2009

  42. Soft Plaque Detection in Coronary Arteries Chapter 5 42 Tuesday, September 8, 2009

  43. Vessel Analysis • Important • Challenging • Segmentation • Plaque Detection Lankton et al. “Soft Plaque Detection...,” MICCAI Workshop 2009 43 Tuesday, September 8, 2009

  44. Coronary Anatomy • Coronaries • RCA • LAD • LCX 44 Tuesday, September 8, 2009

  45. CTA Imagery • In-vivo, 3-D scan • X-ray Attenuation • Contrast Agent 45 Tuesday, September 8, 2009

  46. Vessel Segmentation • Simple initialization • No leaks • Branch handling • No shape information 46 Tuesday, September 8, 2009

  47. Local Means 47 Tuesday, September 8, 2009

  48. Vessel Segmentation Localized Uniform Mean Modeling Energy F um = H φ ( y ) ( I ( y ) − µ in( x ) ) 2 + (1 − H φ ( y ) )( I ( y ) − µ out( x ) ) 2 Domain restriction: ˜ Ω = Ω ∩ ( I < − 600 HU) 48 Tuesday, September 8, 2009

  49. Vessel Segmentation LAD RCA 49 Tuesday, September 8, 2009

  50. Soft Plaque Detection • Dangerous • Hard to see • No good tools 50 Tuesday, September 8, 2009

  51. Soft Plaque Detection • Two-front approach • Inside moves out • Outside moves in 51 Tuesday, September 8, 2009

  52. Detection Energy Localized Means Separation Energy = ( µ in ( x ) − µ out ( x )) 2 F ms = ( x ) − Clever initializations are required 52 Tuesday, September 8, 2009

  53. Creating Initializations � � � E shrink ( φ ) = ( B ( x, y ) · H φ ( y ) ) y ) ) dy dx + λ δφ ( x ) �∇ φ ( x ) � dx δφ ( x ) Ω x Ω y Ω x � dx + λ δφ ( x ) �∇ φ ( x ) � dx E grow ( φ ) = − H φ ( x ) Ω x 53 Tuesday, September 8, 2009

  54. Steps for Detection • Segment the Vessel • Create Initialization • Run Local Mean Separation • Check for Differences 54 Tuesday, September 8, 2009

  55. 3-D Example 55 Tuesday, September 8, 2009

  56. 2-D Results (a) Initial Surfaces (b) Result of Evolution (c) Expert Marking (d) Detected Plaque 56 Tuesday, September 8, 2009

  57. 2-D Results (a) Initial Surfaces (b) Result of Evolution (c) Expert Marking (d) Detected Plaque 57 Tuesday, September 8, 2009

  58. 3-D Results (LCX) 58 Tuesday, September 8, 2009

  59. 3-D Results (LAD) 59 Tuesday, September 8, 2009

  60. 3-D Results (RCA) 60 Tuesday, September 8, 2009

  61. 3-D Results (RCA) 61 Tuesday, September 8, 2009

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