Volumetric Segmentation of Complex Bone Structures from Medical Imaging Data Using Reeb Graphs
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1 Volumetric Segmentation of Complex Bone Structures from Medical Imaging Data Using Reeb Graphs Vitalis Wiens May 6, 2013 Computer Graphik Institut für Informatik II Universität Bonn Wiens: Reeb Graph Segmentation 1 May 6, 2013
2 Decomposition of bone structures Segmentation of 3D-Images Wiens: Reeb Graph Segmentation 2 May 6, 2013
3 Decomposition of bone structures Segmentation of 3D-Images Wiens: Reeb Graph Segmentation 3 May 6, 2013
4 Touching / Interlocking Structures Challenges a) Wiens: Reeb Graph Segmentation 4 May 6, 2013
5 Touching / Interlocking Structures Challenges a) b) Wiens: Reeb Graph Segmentation 5 May 6, 2013
6 Touching / Interlocking Structures Challenges a) b) Wiens: Reeb Graph Segmentation 6 May 6, 2013
7 Challenges Fuzzy region-borders - Adjacent regions with similar scalar values - Resolution errors Image adopted from [Pham et al. 2000] Wiens: Reeb Graph Segmentation 7 May 6, 2013
8 Manual Segmentation [Xiao et al. BMC Medical Imaging 2010] Related Work Wiens: Reeb Graph Segmentation 8 May 6, 2013
9 Manual Segmentation [Xiao et al. BMC Medical Imaging 2010] Related Work Wiens: Reeb Graph Segmentation 9 May 6, 2013
10 Graph-Cut [Krcah et al. IEEE 2011] Related Work Wiens: Reeb Graph Segmentation 10 May 6, 2013
11 Graph-Cut [Krcah et al. IEEE 2011] Related Work Wiens: Reeb Graph Segmentation 11 May 6, 2013
12 Related Work - Segmentation of a human body using Reeb Graph [Xiao, 3DIM 2003] - Point-Clouds Wiens: Reeb Graph Segmentation 12 May 6, 2013
13 Overview Wiens: Reeb Graph Segmentation 13 May 6, 2013
14 Classic Reeb Graph Topological structure of an object Scalar function µ Critical points indicating change in topology Image adopted from [Hilaga et. al SIGGRAPH 2001] Wiens: Reeb Graph Segmentation 14 May 6, 2013
15 Discrete Reeb Graph - Nodes correspond to pixel regions (in a slice) - Connections correspond to overlapping regions (between slices) Wiens: Reeb Graph Segmentation 15 May 6, 2013
16 Influence of Scalar Function - Topological structure on behalf of the scalar function - Simplest scalar function µ( v(x,y,z) ) = z - Responsible for Reeb graph layout a) Wiens: Reeb Graph Segmentation 16 May 6, 2013
17 Influence of Scalar Function - Topological structure on behalf of the scalar function - Simplest scalar function µ( v(x,y,z) ) = z - Responsible for Reeb graph layout a) b) Wiens: Reeb Graph Segmentation 17 May 6, 2013
18 Vertex refinement Wiens: Reeb Graph Segmentation 18 May 6, 2013
19 Vertex refinement - Connected components segmentation Wiens: Reeb Graph Segmentation 19 May 6, 2013
20 Vertex refinement - Connected components segmentation - Traversal direction Wiens: Reeb Graph Segmentation 20 May 6, 2013
21 Vertex refinement - Connected components segmentation - Traversal direction classifies nodes Wiens: Reeb Graph Segmentation 21 May 6, 2013
22 Vertex refinement - Connected components segmentation - Traversal direction classifies nodes - Potential vertex splits at critical nodes Wiens: Reeb Graph Segmentation 22 May 6, 2013
23 Vertex refinement - Connected components segmentation - Traversal direction classifies nodes - Potential vertex splits at critical nodes Wiens: Reeb Graph Segmentation 23 May 6, 2013
24 Vertex refinement - Connected components segmentation - Traversal direction classifies nodes - Potential vertex splits at critical nodes Wiens: Reeb Graph Segmentation 24 May 6, 2013
25 Vertex refinement - Connected components segmentation - Traversal direction classifies nodes - Potential vertex splits at critical nodes Wiens: Reeb Graph Segmentation 25 May 6, 2013
26 Thresholding - Global threshold not sufficient - Local threshold required Wiens: Reeb Graph Segmentation 26 May 6, 2013
27 When to split? - Search for smallest λ such that split is consistent Wiens: Reeb Graph Segmentation 27 May 6, 2013
28 Overview Wiens: Reeb Graph Segmentation 28 May 6, 2013
29 Example Based Segmentation Wiens: Reeb Graph Segmentation 29 May 6, 2013
30 Example Based Segmentation Wiens: Reeb Graph Segmentation 30 May 6, 2013
31 Example Based Segmentation Rough cutout - Interested structure (Largest connected component) Wiens: Reeb Graph Segmentation 31 May 6, 2013
32 Rough cutout by example Example Based Segmentation Wiens: Reeb Graph Segmentation 32 May 6, 2013
33 - Touching regions - Generated through cutout Example Based Segmentation Wiens: Reeb Graph Segmentation 33 May 6, 2013
34 Example Based Segmentation - Touching nodes are critical nodes - Iterative traversal of the graph (both directions) - Vertex-Split at critical nodes - Computation of largest connected component Wiens: Reeb Graph Segmentation 34 May 6, 2013
35 Example Based Segmentation - Touching nodes are critical nodes - Iterative traversal of the graph (both directions) - Vertex-Split at critical nodes - Computation of largest connected component Wiens: Reeb Graph Segmentation 35 May 6, 2013
36 Example Based Segmentation - Touching nodes are critical nodes - Iterative traversal of the graph (both directions) - Vertex-Split at critical nodes - Computation of largest connected component Wiens: Reeb Graph Segmentation 36 May 6, 2013
37 Example Based Segmentation - Touching nodes are critical nodes - Iterative traversal of the graph (both directions) - Vertex-Split at critical nodes - Computation of largest connected component Wiens: Reeb Graph Segmentation 37 May 6, 2013
38 - Applied to rodent skulls Example Based Segmentation Wiens: Reeb Graph Segmentation 38 May 6, 2013
39 - Applied to rodent skulls Example Based Segmentation Wiens: Reeb Graph Segmentation 39 May 6, 2013
40 - Applied to rodent skulls Example Based Segmentation Wiens: Reeb Graph Segmentation 40 May 6, 2013
41 - Applied to rodent skulls Example Based Segmentation Wiens: Reeb Graph Segmentation 41 May 6, 2013
42 - Applied to rodent skulls Example Based Segmentation Wiens: Reeb Graph Segmentation 42 May 6, 2013
43 Summary - Formulate segmentation in terms of graph operations (vertex splits) - Automatic - Exploiting information from given example Wiens: Reeb Graph Segmentation 43 May 6, 2013
44 Results - Separation of 193 µct datasets Segmentation Quality Very good Small artifacts Fail (64%) (8%) (28%) Wiens: Reeb Graph Segmentation 44 May 6, 2013
45 Results - Separation of 193 µct datasets Segmentation Quality Very good Small artifacts Fail (64%) (8%) (28%) Wiens: Reeb Graph Segmentation 45 May 6, 2013
46 Results - Separation of 193 µct datasets Segmentation Quality Very good Small artifacts Fail (64%) (8%) (28%) Wiens: Reeb Graph Segmentation 46 May 6, 2013
47 Results Results without example a) b) Wiens: Reeb Graph Segmentation 47 May 6, 2013
48 Future Work Investigate more scalar functions Graph matching Combination with graph-cut Wiens: Reeb Graph Segmentation 48 May 6, 2013
49 Thank You Wiens: Reeb Graph Segmentation 49 May 6, 2013
50 Acknowledgment We are grateful to Dr. Anja C. Schunke, MPI Plön, for providing the rodent skull mct dataset. Dataset: Human-Skull courtesy of Kitware. Dataset: Human-Foot courtesy of Philips Research. Wiens: Reeb Graph Segmentation 50 May 6, 2013
51 References [Pham et al. 2000] D. L. Pham, C. Xu, and J. L. Prince. A survey of current methods in medical image segmentation. In Annual Review of Biomedical Engineering, volume 2, pages [Xiao et al. BMC Medical Imaging 2010] Mei Xiao, Jung Soh, Oscar Meruvia- Pastor, Eric Schmidt, Benedikt Hallgrimsson, and Christoph Sensen. Building generic anatomical models using virtual model cutting and iterative registration.bmc Medical Imaging, 10(1):5,2010 [Krcah et al. IEEE 2011] M. Krcah, G.Szekely and R. Blanc. Fully automatic and fast segmentation of the femur bone from 3D-CT images with no shape prior. Biomedical Imaging: From Nano to Macro, 2011 IEEE International Symposium on, vol., no., pp.2087,2090, March April Wiens: Reeb Graph Segmentation 51 May 6, 2013
52 References(2) [Hilaga et. al SIGGRAPH 2001] Masaki Hilaga, Yoshihisa Shinagawa, Taku Kohmura, and Tosiyasu L. Kunii. Topology matching for fully automatic similarity estimation of 3D shapes. In SIGGRAPH, pages , New York, NY, USA, ACM Press. [Xiao, 3DIM 2003] Yijun Xiao, P. Siebert, and N. Werghi. A discrete Reeb graph approach for the segmentation of human body scans. 3-D Digital Imaging and Modeling, DIM Proceedings. Fourth International Conference on, vol., no., pp.378,385, 6-10 Oct Wiens: Reeb Graph Segmentation 52 May 6, 2013
53 Heuristics - Post-Processing heuristics 1) Labeling and splitting process Wiens: Reeb Graph Segmentation 53 May 6, 2013
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