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Building of statistical models

Building of statistical models. Guido Gerig Department of Computer Science, UNC, Chapel Hill. Statistical Shape Models. Drive deformable model segmentation statistical geometric model statistical image boundary model

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Building of statistical models

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  1. Building of statistical models Guido Gerig Department of Computer Science, UNC, Chapel Hill

  2. Statistical Shape Models • Drive deformable model segmentation • statistical geometric model • statistical image boundary model • Analysis of shape deformation (evolution, development, degeneration, disease)

  3. Manual Image Segmentation • Manual segmentation in all three orthogonal slice orientations. • Instant 3D display of segmented structures. • Cursor interaction between 2D/ 3D. • Painting and cutting in 3D display. • Open standard s (C++, openGL, Fltk, VTK). IRIS segmentation tool: Segmentation of hippocampus/amygdala from 3D MRI data.

  4. SNAP (prototype): 3D level-set evolution Preprocessing pipeline and manual editing Boundary-driven and region-competition snakes SNAP: Segmentation by level set evolution

  5. Segmentation by level set evolution (midag.cs.unc.edu)

  6. Extraction of anatomical models: SNAP Tool: 3D Geodesic Snake • Segmentation by 3D level set evolution: • region-competition & boundary driven snake • manual interaction for initialization and postprocessing (IRIS) free dowload: midag.cs.unc.edu

  7. M-rep PDM Modeling of Caudate Shape Surface Parametrization

  8. Parametrized 3D surface models Smoothed object Raw 3D voxel model Parametrized surface • Ch. Brechbuehler, G. Gerig and O. Kuebler, • Parametrization of closed surfaces for 3-D shape description, • CVIU, Vol. 61, No. 2, pp. 154-170, March 1995 • A. Kelemen, G. Székely, and G. Gerig, • Three-dimensional Model-based Segmentation, • IEEE TMI, 18(10):828-839, Oct. 1999

  9. Surface Parametrization Mapping single faces to spherical quadrilaterals Latitude and longitude from diffusion

  10. Initial Parametrization a) Spherical parameter space with surface net, b) cylindrical projection, c) object with coordinate grid. Problem: Distortion / Inhomogeneous distribution

  11. Parametrization after Optimization a) Spherical parameter space with surface net, b) cylindrical projection, c) object with coordinate grid. After optimization: Equal parameter area of elementary surface facets, reduced distortion.

  12. Optimization: Nonlinear / Constraints

  13. Shape Representation by Spherical Harmonics (SPHARM)

  14. Reconstruction from coefficients Global shape description by expansion into spherical harmonics: Reconstruction of the partial spherical harmonic series, using coefficients up to degree 1 (a), to degree 3 (b) and 7 (c).

  15. Importance of uniform parametrization

  16. 3 7 1 12 Parametrization with spherical harmonics

  17. Correspondence through Normalization • Normalization using first order ellipsoid: • Spatial alignment to major axes • Rotation of parameter space.

  18. 3D Natural Shape Variability: Left Hippocampus of 90 Subjects

  19. Computing the statistical model: PCA

  20. Major Eigenmodes of Deformation by PCA • PCA of parametric shapes  Average Shape, Major Eigenmodes • Major Eigenmodes of Deformation define shape space  expected variability.

  21. 3D Eigenmodes of Deformation

  22. Set of Statistical Anatomical Models

  23. Correspondence through parameter space rotation Parameters rotated to first order ellipsoids • Normalization using first order ellipsoid: • Rotation of parameter space to align major axis • Spatial alignment to major axes

  24. Rhodri Davies and Chris Taylor MDL criterion applied to shape population Refinement of correspondence to yield minimal description 83 left and right hippocampal surfaces Initial correspondence via SPHARM normalization IEEE TMI August 2002 Correspondence ctd.

  25. Correspondence ctd. Homologous points before (blue) and after MDL refinement (red). MSE of reconstructed vs. original shapes using n Eigenmodes (leave one out). SPHARM vs. MDL correspondence.

  26. Model Building VSkelTool Medial representation for shape population Styner, Gerig et al. , MMBIA’00 / IPMI 2001 / MICCAI 2001 / CVPR 2001/ MEDIA 2002 / IJCV 2003 /

  27. VSkelToolPhD Martin Styner Surface M-rep PDM M-rep Caudate Voronoi M-rep+Radii • Population models: • PDM • M-rep Voronoi+M-rep Implied Bdr

  28. II: Medial Models for Shape Analysis Medial representation for shape population Styner and Gerig, MMBIA’00 / IPMI 2001 / MICCAI 2001 / CVPR 2001/ ICPR 2002

  29. Common model generation Study population Common model ... Model building Training population Boundary: SPHARM Medial: m-rep Two Shape Analyses - New insights, findings

  30. 1. Shape space from training population • Variability from training population • Major PCA deformations define shape space covering 95% • Variability is smoothed • Sample objects from shape space 1. 2. 3.

  31. 2. Common medial branching topology • a. Compute individual medial branching topologies in shape space • b. Combine medial branching topologies into one common branching topology

  32. 2a. Single branching topology • Fine sampling of boundary • Compute inner Voronoi diagram • Group vertices into medial sheets (Naef) • Remove unimportant medial sheets (Pruning) • 98% vol. overlap

  33. 2b. Common branching topology For all objects in shape space • Define common frame for spatial comparison • TPS-warp objects into common frame using boundary correspondence • Spatial match of sheets, paired Mahalanobis distance • No structural (graph) topology match Warp topology using SPHARM correspondence on boundary Match whole shape space Final topology Initial topology (average case) Match Match

  34. 3. Optimal grid sampling of medial sheets • Appropriate sampling for model • How to sample a sheet ? • Compute minimal grid parameters for sampling given predefined approximation error in shape space

  35. 1 2 3a. Sampling of medial sheet • Smoothing of sheet edge • Determine medial axis of sheet • Sample axis • Find grid edge • Interpolate rest • m-rep fit to object (Joshi)

  36. 3b. Minimal sampling of medial sheet • Find minimal sampling given a predefined approximation error 3x6 3x12 3x7 4x12 2x6

  37. Medial models of subcortical structures Shapes with common m-rep model and implied boundaries of putamen, hippocampus, and lateral ventricles. Each structure has a single-sheet branching topology. Medial representations calculated automatically.

  38. Medial models of subcortical structures Shapes with common topology: M-rep and implied boundaries of putamen, hippocampus, and lateral ventricles. Medial representations calculated automatically (goodness of fit criterion).

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