Laboratory of Mathematics in Imaging Harvard Medical School Brigham and Women’s Hospital Fast and Accurate Redistancing for Level Set Methods & Multiscale Segmentation of the Aorta in 3D Ultrasound Images Karl Krissian

McGill Montreal 2003 I. Level Sets  Introduction Narrow Band –initialization –distancing Experiments –MRA –SPGR white matter –RGB white matter Discussion

McGill Montreal 2003 Level Sets: principle –Implicit representation of the evolving surface. –Natural topology changes.

McGill Montreal 2003 Level Sets: forces 1.Smoothing: – mean curvature [Sethian 96, Caselles 97] – minimal curvature [Ambrioso and Soner 98, Lorigo et al. 00] 2.Advection or Contour attachment. 3.Balloon or expansion: – constant. – based on intensity statistics [Zeng et al. 98,Paragios and Deriche 00, Barillot et al. 00].

McGill Montreal 2003 CURVES Lorigo et al., Medical Image Analysis, Ambrioso, Soner, Journal Differential Geometry, CURve evolution for VESsel segmentation Codimension-2 Active Contours Provided by L. Lorigo MIT AI Lab. v is (positive) distance to curve  (  v,  2 v) is smaller principal curvature of tube d is some vector field in R 3 v t = |  v| (  v,  2 v) +  v · d

McGill Montreal 2003 CURVES Example co-dim 2 co-dim 1 Provided by L. Lorigo MIT AI Lab.

McGill Montreal 2003 Fast implementation Numerical stability and reinitialization: distance map –Fast Marching Method [Sethian, 99], computes geodesic distances with complexity n.log(n). Speed improvement: itkNarrowBandCurvesLevelSetImageFilter  Sub-voxel reinitialization: itkIsoContourDistanceImageFilter  Fast Distance Transform: itkFastChamferDistanceImageFilter

McGill Montreal 2003 I. Level Sets Introduction  Narrow Band  initialization –distancing Experiments –MRA –SPGR white matter –RGB white matter Discussion

McGill Montreal 2003 SubVoxel Reinitialization For the voxels neighbors to the isosurface, keep the same linearly interpolated surface: Remarks: Points with several neighbors crossing the surface. Regions of high curvature.

McGill Montreal 2003 Subvoxel versus Binary binary (+/- 0.5) subvoxel Evolution of a sphere of radius 3 voxels under constant propagation force.

McGill Montreal 2003 binarysub-voxel Sub-Voxel vs Binary

McGill Montreal 2003 I. Level Sets Introduction  Narrow Band initialization  distancing Experiments –MRA –SPGR white matter –RGB white matter Discussion

McGill Montreal 2003 Chamfer Distance Transform = Relative maximal error 7.356% [Borgefors, On Digital Distance Transforms in Three Dimensions, CVIU, 1996]

McGill Montreal 2003 Narrow Banded Fast DT

McGill Montreal 2003 Narrow-Banded Fast DT Main speed improvements: 1.Linear complexity. 2.Don’t compute voxels out of the narrow band. 3.Factorize the additions for each kind of neighbor. 4.Keep track of a bounding box. 5.Get positive and negative distances at the same time.

McGill Montreal 2003 Interpretation BinarySubvoxel

McGill Montreal 2003 I. Level Sets Introduction Narrow Band initialization distancing  Experiments –MRA –SPGR white matter –RGB white matter Discussion

McGill Montreal 2003 Experiments Image 200 3, Euclidian distance up to 5, Pentium III 1.1 GHz. time in seconds radius in voxels Spheres of increasing radii

McGill Montreal 2003 Accuracy experiments Constant evolution Curvature evolution 2D disk radius=30 3D sphere radius=30

McGill Montreal 2003 White matter from SPGR image

McGill Montreal 2003 Fast implementation Computation time (in sec.) for segmenting White Matter on a 256x256x124 Spoiled Gradient Recall MR.

McGill Montreal 2003 Magnetic Resonance Angiography initial iso-surface Fast Marching resultFast Chamfer result Resampling Minimal curvature Speed up: Narrow Band Dist x 7 Total Processing x 2 Multi-Threading x 6

McGill Montreal 2003 Applications MR Angiography Segmentation result Maximum Intensity Projection

McGill Montreal 2003 Applications MR Angiography Segmentation result Iso-surfaces 112, 60 and 40

McGill Montreal 2003 High res. RGB White Matter Color Image: -cropped: 1056x seed points -2D level set data provided by Peter Ratiu

McGill Montreal 2003 High res 3D RGB White Matter 800x1056x1211 sub-volume –Pyramidal multiscale –2 seed points 200x264x302100x132x15150x76x75

McGill Montreal 2003 Interface Integration VTK-tclITK-tclVTK-tcl Generic slicer module (tcl/tk) ConnectVTKToITK ConnectITKToVTK vtkSlicerITK module Input image volume Output image volume

McGill Montreal 2003 Graphical Interface Open Source: Insight Toolkit:

McGill Montreal 2003 Conclusion Exact linear Euclidian Distance [Danielsson, 80] –Propagation, Parallel (multi-threaded) Multi-Channel images (RGB, blood flow, multi- modalities, diffusion tensor) Skeleton Shape constraints Bayesian approach with several level sets.

McGill Montreal 2003 Outline II. Multiscale Segmentation  Introduction  Methodology  Results  Conclusion and future work

McGill Montreal 2003 Introduction Medical Interest 3D Ultrasound for vascular and gastrointestinal surgery. low cost and no radiation exposure. with or without preoperative CT. need of automatic segmentation of the aorta.

McGill Montreal 2003 Introduction non homogeneous intensity close vessels

McGill Montreal 2003 Multiscale methods Linear multiscale analysis –Robustness –Accuracy –Optimization

McGill Montreal 2003 Hessian matrix eigenvalues eigenvectors Hessian matrix and local structure  Linear structures [Lorenz et al.]  VOLUMINAL MODELS Taylor expansion:

McGill Montreal 2003 Cylindrical model Analytic analysis –Radius estimation –Optimization of the response –Behavior of the Hessian matrix

McGill Montreal 2003 cylindrical Cylindrical model toroidal Toroidal model elliptical Elliptical model Hessian matrix

McGill Montreal 2003 Methodology –Hessian Matrix –Structure Tensor –New Second Order Orientation Descriptor –3 parameters Extraction of local orientations

McGill Montreal 2003 Methodology –Properties: zoom invariance. Symmetric positive. Continuity of the eigenvectors. Orientation extraction for both contours (1 st order derivatives) and lines (2 nd order derivatives). Extraction of local orientations

McGill Montreal 2003 Single scale response computation Pre-selection of candidates Plan of the cross-section Response

McGill Montreal 2003 Methodology Homogeneity constraint Eccentricity constraint Tubular constraints

McGill Montreal 2003 Normalization of the response function  = 1.0  = 1.28  =1.65  = 2.12  = 2.72  = 3.5  -normalization [Lindeberg, 96] Estimation of the vessel radius éZoom invariance éMaximization of the maximal response

McGill Montreal 2003 « height ridge » [Furst et al, 97] « marching lines » [Thirion et Gourdon, 97; Fidrich, 97; Lindeberg, 96, Furst et al, 96] is a local maximum Extraction of local maxima

McGill Montreal 2003 Tangent vessels Junctions Curvature Images of variable width Tests on synthetic images

McGill Montreal 2003 Methodology Scales –10 scales, logarithmic discretization Extraction of local maxima Multiscale analysis

McGill Montreal 2003 Methodology Results

McGill Montreal 2003 Outline Results

McGill Montreal 2003 Outline Conclusion and Future Work Conclusion Semi-automatic segmentation of aorta in 3D Ultrasound. Model Based multiscale linear approach. Second Order Orientation Descriptor. Homogeneity and eccentricity constraints. Future work Active contours. Validation.