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Research Papers

Generation of Segmented Triangular Meshes From CT Images Based on Centroidal Voronoi Tessellation and the Graph Cut Method

[+] Author and Article Information
Caiyun Yang

Institute of Automation,
Chinese Academy of Sciences,
Beijing 100864, China
e-mail: caiyun.yang@ia.ac.cn

Yutaka Ohtake

RCAST (Research Center for Advanced
Science and Technology),
The University of Tokyo,
Tokyo 13-8654, Japan
e-mail: yu-ohtake@den.rcast.u-tokyo.ac.jp

Masaki Moriguchi

Computer Science,
Chuo University,
Tokyo 112-0003, Japan
e-mail: moriguchi@ise.chuo-u.ac.jp

Hiromasa Suzuki

RCAST (Research Center for Advanced
Science and Technology),
The University of Tokyo,
Tokyo 13-8654, Japan
e-mail: suzuki@den.rcast.u-tokyo.ac.jp

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINNERING. Manuscript received August 8, 2013; final manuscript received December 9, 2013; published online January 29, 2014. Assoc. Editor: Xiaoping Qian.

J. Comput. Inf. Sci. Eng 14(1), 011009 (Jan 29, 2014) (7 pages) Paper No: JCISE-13-1150; doi: 10.1115/1.4026292 History: Received August 08, 2013; Revised December 09, 2013

Mesh generation from X-ray computed tomography (CT) images of mechanical parts is an important consideration in industrial application, and boundary surface meshes in multimaterial parts can be extracted by generating segmented meshes from segmented images. In this paper, the authors outline a new approach for achieving segmented mesh generation. The image is first subjected to centroidal Voronoi tessellation and Delaunay tessellation steered by a density map to create a triangular mesh while maintaining discontinuities between materials. Given an input domain and a number of initial sites, the energy function is minimized automatically by iteratively updating the Voronoi tessellation and relocating sites to produce optimized domain discretization and form the mesh. Thus, the mesh in question is effectively and quickly segmented into different parts via this new graph cut method. The proposed approach is considered more efficient because there are fewer triangles than pixels, which reduces computation time and memory usage.

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Figures

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Fig. 1

Outline of the proposed method. CVT, centroidal Voronoi tessellation; DT, Delaunay triangulation

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Fig. 2

Mesh generation based on CVT (a): the input image with a gray value (500*700 pixels) (b): the corresponding density map (c): the final CVT diagram with 1200 sites (d): the corresponding triangular mesh associated with the final CVT diagram

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Fig. 3

Graph of G = (V,Ξ).V represents all triangles t1,t2,t3,…,tm,tn in one model and the source node s0/the sink node s1. Ξ denotes the edges between the centroids of any two adjacent triangles and the edges linking triangles and the source node/sink node. E1 and E2 are, respectively, the cost of the edges linking triangles and the source node/sink node and the cost of the edges between the centroids of any two adjacent triangles. The graph is segmented into two parts by a min cut consisting of edges.

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Fig. 4

Mesh segmentation. The image on the left shows the triangular mesh, the one in the middle presents the average gray value for all triangles, and the one on the right illustrates the segmented mesh model with individual materials represented in different colors.

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Fig. 5

2D example: Cs1 consisting of 512 * 512 pixels with 1000 sites. (a) Shows the input image with the gray value. In line with this value, the density map shown in (b) is generated. (c) Presents the final optimized CVT, (d) gives the corresponding triangular mesh associated with CVT, (e) shows the average gray value for all triangles, and (f) indicates the segmented meshes created using the novel graph cut method.

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Fig. 6

Engine head 2 consisting of 500 * 700 pixels with 1000 sites. (a) Shows the input image with the gray value. In line with this value, the density map shown in (b) is generated. (c) Presents the final optimized CVT, (d) gives the corresponding triangular mesh, (e) shows the average gray value for all triangles, and (f) indicates the segmented mesh created using the novel graph cut method.

Grahic Jump Location
Fig. 7

Engine head 3 consisting of 500 * 700 pixels with 1000 sites. (a) Shows the input image with the gray value. In line with this value, the density map described in (b) is generated. (c) Presents the final optimized CVT, (d) gives the corresponding triangular mesh, (e) shows the average gray value for all triangles, and (f) indicates the segmented meshes created using the novel graph cut method.

Grahic Jump Location
Fig. 8

2D example: Cs2 consisting of 512 * 512 pixels with 1200 sites. (a) Shows the input image with the gray value, (b) presents the final optimized CVT, (c) gives the corresponding triangular mesh, and (d) illustrates the segmented meshes created using the novel graph cut method.

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