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Computing a Family of Skeletons of Volumetric Models for Shape Description Tao Ju Washington University in St. Louis.

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Presentation on theme: "Computing a Family of Skeletons of Volumetric Models for Shape Description Tao Ju Washington University in St. Louis."— Presentation transcript:

1 Computing a Family of Skeletons of Volumetric Models for Shape Description Tao Ju Washington University in St. Louis

2 Skeleton A medial representation of an object – Thin (dimension reduction) – Preserving shape and topology

3 Where Skeletons Are Used Animating characters – Skeletal animation Shape analysis – Shape comparison – Character recognition Medical applications – Colon unwinding – Modeling blood vessels

4 New Application – Protein Modeling Identifying tubular and plate-like shapes is the key in locating α-helices and β-sheets in Cryo-EM protein maps Atomic Model Secondary Structures Cryo-EM map at intermediate resolution α β Tube Plate

5 Curvature Descriptors Depicting surface properties – Principle curvatures, shape index [Koenderink 92] – Cons: Easily disrupted by a bumpy surface Min Curvature Max Curvature Shape Index

6 Intuition Represent tubes and plates as skeleton curves and surfaces. = =   Skeleton

7 Thinning Classical method for computing skeleton of a discrete image V. Iterative process – At each iteration, remove boundary points from V – Retain non-simple boundary points Topology preservation [Bertrand 94] – Retain curve-end or surface-end boundary points Shape preservation [Tsao 81] [Gong 90] [Lee 94] [Bertrand 94] [Bertrand 95] Curve thinning or surface thinning Result in curve skeleton or surface skeleton

8 Problems Curve skeleton: containing mostly 1D edges Surface skeleton: contains mostly 2D faces Volume Image Curve Skeleton Surface Skeleton

9 Goal Compute simple and descriptive skeletons – Consists of curves and surfaces corresponding to tubes and plates Solution – Alternate thinning and pruning

10 Method Overview – Step 1 Surface Thinning Surface Pruning

11 Method Overview – Step 2 Curve Thinning Curve Pruning

12 End Points – A Geometric Definition Curves and surfaces – Consists of edges and faces Curve-end and surface-end points – Points not contained in any 1-manifold or 2-manifold 1-manifold2-manifold

13 Theorem Let V be the set of object points. x is a curve-end point if and only if: x is a surface-end point if and only if: = 0 N k (x,V)=N k (x)  V

14 Pruning Coupling erosion and dilation – Erosion: removes all curve-end (surface-end) points. – Dilation: extends discrete 1-manifold (2-manifold) from curve- end (surface-end) points. – d rounds of erosion followed by d rounds of dilation Erode Dilate

15 Surface Pruning Example d = 4 d = 7 d = 10

16 Curve Pruning Example d = 5 d = 10 d = 20 [Mekada and Toriwaki 02] [Svensson and Sanniti di Baja 03]

17 Results – 3D Models Original[Bertrand 95][Ju et al. 06]

18 Results – 3D Models OriginalSkeletons with different pruning parameters

19 Results – Protein Data Cryo-EM[Bertrand 95][Ju et al. 06]Actual Structure

20 Visualization: UCSF Chimera Cryo-EMSkeletonActual StructureOverlay

21 Collaboration and Outlook Future work – Descriptive skeleton of grayscale images – Descriptive skeleton on adaptive grids (octrees) – Protein model building Finding connectivity among α/β elements Using graph matching (Skeleton vs. protein sequence) Collaboration – National Center of Macromolecular Imaging (NCMI), Houston (M. Baker, S. Ludtke, W. Chiu)NCMI

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23 Thinning Example Original[Bertrand 95] Surface thinning Curve thinning


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