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
Outline • Introduction and Background • Localized Segmentation Framework • Vessel Analysis and Plaque Detection • Conclusions 2 Tuesday, September 8, 2009
Computer Vision Chapter 1 3 Tuesday, September 8, 2009
Computer Vision Image Acquisition Image Processing Image Understanding 4 Tuesday, September 8, 2009
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
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
Hypothesis localization improves results. 7 Tuesday, September 8, 2009
Active Contours and Level Set Methods Chapter 2 8 Tuesday, September 8, 2009
Segmentation 9 Tuesday, September 8, 2009
Segmentation • Thresholding • Region Growing • Graph Cuts • Snakes/Active Contours 10 Tuesday, September 8, 2009
Active Contours 11 Tuesday, September 8, 2009
Implementation • Represent the contour • Parametrized • Implicit 12 Tuesday, September 8, 2009
Level Sets 13 Tuesday, September 8, 2009
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
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
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
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
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
Complex Images 19 Tuesday, September 8, 2009
A Localized Active Contour Model Chapter 3 20 Tuesday, September 8, 2009
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
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
Computing the Energy E ( φ ) = + + dF dF dF + dF + + + dF dF ... etc. 23 Tuesday, September 8, 2009
Internal Energies • Local Uniform Modeling • Local Mean Separation • Local Histogram Separation 24 Tuesday, September 8, 2009
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
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
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
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
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
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
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
Back to These Guys Local Mean Separation 32 Tuesday, September 8, 2009
Studying Local Energies • Choosing the radius • Initializing the contour 33 Tuesday, September 8, 2009
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
Choosing the Radius 35 Tuesday, September 8, 2009
How to Initialize (a) (b) (c) (d) (e) (f) (g) (h) 36 Tuesday, September 8, 2009
How to Initialize (a) Brain 1 (b) Brain 2 37 Tuesday, September 8, 2009
Benefits of Localized Segmentation • Complex problems become simple • Natural solution to many problems • Scale is controllable 38 Tuesday, September 8, 2009
Volumetric Quantification of Neural Pathways Chapter 4 39 Tuesday, September 8, 2009
Tractography • Diffusion Imaging • Brain Connectivity • Localize Orientation Analysis Lankton et. al. “Localized … Fiber Bundle Segmentation.” MMBIA, 2008 40 Tuesday, September 8, 2009
Cingulum Bundle Segmentation 41 Tuesday, September 8, 2009
Soft Plaque Detection in Coronary Arteries Chapter 5 42 Tuesday, September 8, 2009
Vessel Analysis • Important • Challenging • Segmentation • Plaque Detection Lankton et al. “Soft Plaque Detection...,” MICCAI Workshop 2009 43 Tuesday, September 8, 2009
Coronary Anatomy • Coronaries • RCA • LAD • LCX 44 Tuesday, September 8, 2009
CTA Imagery • In-vivo, 3-D scan • X-ray Attenuation • Contrast Agent 45 Tuesday, September 8, 2009
Vessel Segmentation • Simple initialization • No leaks • Branch handling • No shape information 46 Tuesday, September 8, 2009
Local Means 47 Tuesday, September 8, 2009
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
Vessel Segmentation LAD RCA 49 Tuesday, September 8, 2009
Soft Plaque Detection • Dangerous • Hard to see • No good tools 50 Tuesday, September 8, 2009
Soft Plaque Detection • Two-front approach • Inside moves out • Outside moves in 51 Tuesday, September 8, 2009
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
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
Steps for Detection • Segment the Vessel • Create Initialization • Run Local Mean Separation • Check for Differences 54 Tuesday, September 8, 2009
3-D Example 55 Tuesday, September 8, 2009
2-D Results (a) Initial Surfaces (b) Result of Evolution (c) Expert Marking (d) Detected Plaque 56 Tuesday, September 8, 2009
2-D Results (a) Initial Surfaces (b) Result of Evolution (c) Expert Marking (d) Detected Plaque 57 Tuesday, September 8, 2009
3-D Results (LCX) 58 Tuesday, September 8, 2009
3-D Results (LAD) 59 Tuesday, September 8, 2009
3-D Results (RCA) 60 Tuesday, September 8, 2009
3-D Results (RCA) 61 Tuesday, September 8, 2009
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