1. IPMI 2013 Presentation, Asilomar, California
Gradient Competition Anisotropy for Centerline Extraction and Segmentation of Spinal Cords
Max W.K. Law, Gregory J. Garvin, Sudhakar Tummala, KengYeow Tay, Andrew E. Leung, Shuo Li
Presenter: Max W.K. Law
IPMI 2013 Presentation, Asilomar, California

2. IPMI 2013 Presentation, Asilomar, California
Overview
Introduction
Methodology
Gradient Competition
Orientation Coherence Anisotropy
Centerline Extraction and Segmentation
Experiment
Conclusion
IPMI 2013 Presentation, Asilomar, California

3. IPMI 2013 Presentation, Asilomar, California
Challenge
Neighboring disturbance and elliptical curvilinear objects in 3D
Object of interest, low contrast boundary
Neighboring objects, high contrast boundaries
IPMI 2013 Presentation, Asilomar, California

4. IPMI 2013 Presentation, Asilomar, California
Challenges
Neighboring disturbance and elliptical curvilinear objects in 3D
Neuron detection
(brightfield images)
Vascular
segmentation (MRA)
Airway segmentation (CT)
IPMI 2013 Presentation, Asilomar, California

5. Low-level Features Widely used State-of-the-art
Second order statistics and Hessian
State-of-the-art
Flux
F. Benmansour, L. Cohen, ``Tubular Structure Segmentation Based on Minimal Path Method and Anisotropic Enhancement’’, IJCV 2011, 92(2),
M. Law, A. Chung, ``Three Dimensional Curvilinear Structure Detection using Optimally Oriented Flux’’, ECCV 2008,
Medialness
M. Gulsun, H. Tek, ``Robust Vessel Tree Modeling’’, MICCAI 2008,
Superellipsoids
J. Tyrrell et al. ``Robust 3-D Modeling of Vasculature Imagery Using Superellipsoids’’, TMI 2007, 26(2),

6. Spinal Cord Spinal cord Cerebrospinal fluid Nerve root Bone marrow
Vertebral arch
Intervertebral discs
Ligament, vascular structure and more

7. IPMI 2013 Presentation, Asilomar, California
Spinal Cord
High contrast neighboring disturbance
Intensity varying
IPMI 2013 Presentation, Asilomar, California

8. Spherical Gradient Operator
Analyze image gradient on spheres
Voxel-wise detection
Multi-radius detection
IPMI 2013 Presentation, Asilomar, California 8

9. Gradient Competition - = Competition
Effective when the larger radius wins (reports a response larger than smaller radii do)
Advantage: Penalize oversized radius
Response obtained at a radius of interest
Residual response
Response obtained at a smaller radius - =
IPMI 2013 Presentation, Asilomar, California 9

10. IPMI 2013 Presentation, Asilomar, California
Gradient Competition
Spherical Gradient Operator
Optimal direction
Outward normal
Gradient
Sphere, radius=r Surface-area
Curvlinear object
Image gradient
Direction of interest
IPMI 2013 Presentation, Asilomar, California 10

11. Gradient Competition Gradient competition
Maximum residual-response across radii
Residual response
Response at the current radius
Response at smaller radii
Voxel-length
Min./max. semi-widths of the target

12. Gradient Competition Second optimal direction Gradient competition
Maximum residual-response across radii
Residual response
Response at the current radius
Response at smaller radii 12

13. Gradient Competition Structure orientation Curvilinearity ? Small
Image gradient ?
Small
Large
Negative
Large
Small
Small
Large
Random 13

14. Gradient Competition Anisotropy
Local Orientation Coherence
Advantage: Avoid path leakage
Orientation field
IPMI 2013 Presentation, Asilomar, California

15. IPMI 2013 Presentation, Asilomar, California
Gradient Competition Anisotropy
Maximize curvilinearity and orientation coherence
User provided spinal cord end points
Curvilinearity
Gaussian function, scale factor=
Structure orientation
Path orientation
IPMI 2013 Presentation, Asilomar, California 15

16. IPMI 2013 Presentation, Asilomar, California
Centerline Extraction
Maximize curvilinearity and orientation coherence
Time of arrival and minimal path
Small constant
Identity matrix
IPMI 2013 Presentation, Asilomar, California

17. IPMI 2013 Presentation, Asilomar, California
Centerline Extraction
Minimal path:
IPMI 2013 Presentation, Asilomar, California 17

18. Centerline Extraction
Comparison on synthetic orientation field
Without orientation coherence
With orientation coherence , ,
Result of
(left)
where
(right)

19. IPMI 2013 Presentation, Asilomar, California
Segmentation
Voxel-to-centerline intensity discrepancy
Extract low discrepancy region
Extracted centerline
Discrepancy mean, weighted by
Smoothness strength
Region within distance from centerline
Segmentation result,
IPMI 2013 Presentation, Asilomar, California

20. Experiment Measured at the centerline of highlighted objects
Structure orientation discrepancies on 3 sets of synthetic tubes
Set 1
Set 2
Set 3
Measured at the centerline of highlighted objects
Isosurface of one of the synthetic tube sets
Cross sections of noise corrupted synthetic tubes, when major diameters of the detection targets are 8, 6 and 4.
IPMI 2013 Presentation, Asilomar, California

21. Experiment Centerline extraction Object of interest
Gradient competition with orientation coherence
Isosurface of the synthetic tubes
Cross section of noise corrupted synthetic tubes
Object of interest
Ground truth
Vesselness-FM
4D-Anisotropy
Gradient competition,
no orientation coherence 21

22. IPMI 2013 Presentation, Asilomar, California
Experiment
Clinical Data
10 T1- and 15 T2-MRI
Centerline extraction accuracy
IPMI 2013 Presentation, Asilomar, California

23. IPMI 2013 Presentation, Asilomar, California
Experiment
Clinical Data
10 T1- and 15 T2-MRI
Segmentation accuracy
IPMI 2013 Presentation, Asilomar, California

24. IPMI 2013 Presentation, Asilomar, California
Experiment
Clinical Data
Resultant centerline
Ground truth centerline
Resultant segmentation
Ground truth segmentation
IPMI 2013 Presentation, Asilomar, California

25. IPMI 2013 Presentation, Asilomar, California
Summary
Eliminate neighboring disturbance
Gradient Competition
Orientation Coherence Anisotropy
General elliptical curvilinear structure detection - =
IPMI 2013 Presentation, Asilomar, California

26. IPMI 2013 Presentation, Asilomar, California
Discussion
IPMI 2013 Presentation, Asilomar, California

27. IPMI 2013 Presentation, Asilomar, California
Discussion
IPMI 2013 Presentation, Asilomar, California 27

28. IPMI 2013 Presentation, Asilomar, California
Discussion
IPMI 2013 Presentation, Asilomar, California 28

29. IPMI 2013 Presentation, Asilomar, California
Discussion
IPMI 2013 Presentation, Asilomar, California 29

30. IPMI 2013 Presentation, Asilomar, California
Problem statement
Object of interest
Curvilinear object, can be elliptical
Handle neighboring disturbance
Input
End points of the object
Model parameter
Rough estimation of maximum/minimum possible widths of the object of interest
IPMI 2013 Presentation, Asilomar, California 30

31. Gradient Competition Anisotropy
Elliptical curvilinear object
Neighboring disturbance
Curvlinear object
Gradient of the object
Gradient of neighboring objects
IPMI 2013 Presentation, Asilomar, California 31

32. IPMI 2013 Presentation, Asilomar, California
Method background
Multi-radius, voxel-wise detection
Curvlinear object
Outward normal
Gradient
Sphere, radius=r Surface-area
Neighboring
structure
IPMI 2013 Presentation, Asilomar, California 32

33. IPMI 2013 Presentation, Asilomar, California
Method background
Multi-radius, voxel-wise detection
Outward normal
Gradient
Sphere, radius=r Surface-area
Curvlinear object
IPMI 2013 Presentation, Asilomar, California 33

34. IPMI 2013 Presentation, Asilomar, California
Imaging
T1-MR
3.3x0.5729x0.5729mm3
TR: 450ms, TE, 13ms
1.5T, Sagittal
T2-MR
0.4375x0.4375x1mm3
TR: 1500ms, TE, 150ms
1.5T, Axial
IPMI 2013 Presentation, Asilomar, California

35. Gradient Competition Anisotropy
Gradient competition metric
Isotropy
Anisotropy, no orientation coherence
Anisotropy, with orientation coherence
IPMI 2013 Presentation, Asilomar, California 35

36. Centerline Extraction
IPMI 2013 Presentation, Asilomar, California 36

37. Time of arrival function

38. Centerline Extraction
Local Orientation Coherence
Stick tensor
Stick, plate, ellipsoid or ball tensor
IPMI 2013 Presentation, Asilomar, California

39. Centerline Extraction
Comparison on synthetic orientation field
Without orientation coherence
With orientation coherence , ,
Path extracted according to

40. Analytical form of optimal direction
Six linear image filtering at each radius
Tensor field, find using eigen-decomposition
Max W.K. Law, Albert C.S. Chung, ``Three dimensional curvilinear structure detection using optimally oriented flux``, ECCV 2008

41. Optimally Oriented Flux
Curvilinear/planar object detection
MatLab code available
Support GPU computation

42. Numerical solvers
J.M. Mirebeau, ``Anisotropic fast-marching on cartesian grids using lattice basis reduction``, In Press
T. Chan, S. Esedoglu, M. Nikolova, ``Algorithms for finding global minimizers of image segmentation and denoising models``, SIAM J. App. Math. 2006, 66(5),

43. IPMI 2013 Presentation, Asilomar, California
Reference
Vesselness, Vesselness-FM
A. Frangi, W. Niessen, K. Vincken, M. Viergever, ``Multiscale Vessel Enhancement Filtering’’, MICCAI 1998,
M. Hassouna, A. Farag, ``Multistencils fast marching methods: A highly accurate solution to the Eikonal equation on cartesian domains’’, PAMI (9)
OOF, 4D-Anisotropy
M. Law, A. Chung, ``Three Dimensional Curvilinear Structure Detection using Optimally Oriented Flux’’, ECCV 2008,
F. Benmansour, L. Cohen, ``Tubular Structure Segmentation Based on Minimal Path Method and Anisotropic Enhancement’’, IJCV 2011, 92(2),
Multiphase CV-Functional
T. Chan, L. Vese, ``Active Contours without Edges’’, TIP 2001, 10(2),
E. Bae, J. Yuan, X.-C. Tai, ``Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach’’, IJCV 2011, 92(1),
IPMI 2013 Presentation, Asilomar, California