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

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

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

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

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), 192-210 M. Law, A. Chung, ``Three Dimensional Curvilinear Structure Detection using Optimally Oriented Flux’’, ECCV 2008, 368-382 Medialness M. Gulsun, H. Tek, ``Robust Vessel Tree Modeling’’, MICCAI 2008, 602-611 Superellipsoids J. Tyrrell et al. ``Robust 3-D Modeling of Vasculature Imagery Using Superellipsoids’’, TMI 2007, 26(2), 223-237

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

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

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

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

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

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

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

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

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

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

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

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

Centerline Extraction Comparison on synthetic orientation field Without orientation coherence With orientation coherence , 1 , 1.5 Result of (left) where (right)

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

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

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

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

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

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

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

IPMI 2013 Presentation, Asilomar, California Discussion IPMI 2013 Presentation, Asilomar, California

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

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

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

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

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

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

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

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

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

Centerline Extraction IPMI 2013 Presentation, Asilomar, California 36

Time of arrival function

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

Centerline Extraction Comparison on synthetic orientation field Without orientation coherence With orientation coherence , 1 , 1.5 Path extracted according to

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

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

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), 1632-1548

IPMI 2013 Presentation, Asilomar, California Reference Vesselness, Vesselness-FM A. Frangi, W. Niessen, K. Vincken, M. Viergever, ``Multiscale Vessel Enhancement Filtering’’, MICCAI 1998, 130-137 M. Hassouna, A. Farag, ``Multistencils fast marching methods: A highly accurate solution to the Eikonal equation on cartesian domains’’, PAMI 2007 29(9) 1563-1574 OOF, 4D-Anisotropy M. Law, A. Chung, ``Three Dimensional Curvilinear Structure Detection using Optimally Oriented Flux’’, ECCV 2008, 368-382 F. Benmansour, L. Cohen, ``Tubular Structure Segmentation Based on Minimal Path Method and Anisotropic Enhancement’’, IJCV 2011, 92(2), 192-210 Multiphase CV-Functional T. Chan, L. Vese, ``Active Contours without Edges’’, TIP 2001, 10(2), 266-277 E. Bae, J. Yuan, X.-C. Tai, ``Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach’’, IJCV 2011, 92(1), 112-129 IPMI 2013 Presentation, Asilomar, California