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 Generation of Segmented Triangular Meshes From CT Images Based on Centroidal Voronoi Tessellation and the Graph Cut Method 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 dis- continuities between materials. Given an input domain and a number of initial sites, the energy function is minimized automatically by iteratively updating the Voronoi tessella- tion 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. [DOI: 10.1115/1.4026292] Keywords: Mesh generation, centroidal Voronoi tessellation, mesh segmentation, graph cut 1 Introduction X-ray CT scanning is commonly adopted in industry to detect internal voids and cavities in manufactured parts. Thanks to recent advances in the field, the technique can now be used to generate object shapes with sufficient accuracy for industrial application [1]. Against this background, there is a need for a method to gen- erate models of shapes such as boundary surface meshes and finite element meshes to support engineering simulation. CT scanners output images of objects with pixels, whose CT values are roughly proportional to the actual density of the materi- als they represent. The top-left image in Fig. 1 shows a typical example of such a CT image with a number of segments indicat- ing different materials. The pixels in each segment have a uniform gray color. Surface meshes for single-material objects can be extracted using an iso-surfacing method such as Marching Cubes. However, pixels in multimaterial objects need to be classified into material segments, and boundary meshes between different materials must be generated. This process is known as segmentation in the field of image processing. Thus, a common way of generating meshes involves the two steps of image segmentation and iso- surfacing [2]. In the novel approach proposed here, the image is first sub- jected to centroidal Voronoi tessellation (CVT) [3] (see Fig. 1) and Delaunay tessellation to create a mesh of triangles, which is then segmented into different components representing different materials using the graph cut method [4]. Although this method provides powerful segmentation performance, it is time- consuming (approximately Oðn 2 log n) where n is the number of elements such as pixels) and memory-intensive. With this in mind, the graph cut approach is applied not to the image itself but to the tessellated triangles because there are significantly fewer triangles than pixels in the image. The technique is also expected to be beneficial for extending the application of the proposed approach to 3D volumetric CT images in the future. Based on the proposed method, a nonsegmented CT image with gray values is transformed into a mesh with discontinuities between different materials preserved using CVT. For this purpose, an energy function reflecting the image gradient is intro- duced. The image in the bottom right of Fig. 1 shows small trian- gles generated along the material boundaries. The graph cut method is subsequently applied to the mesh to segment the trian- gles into different components representing different materials with reference to the gray values of the triangles. 2 Paper Overview In the rest of this paper, Sec. 2 outlines related work, Sec. 3 introduces CVT, Sec. 4 presents the CVT-based mesh generation method, Sec. 5 highlights the new graph cut approach developed to segment generated meshes, Sec. 6 details the results of the study’s experiments, and Sec. 7 concludes the work. 3 Related Work 3.1 Mesh Generation. Meshes are extensively adopted to provide solutions to various application problems. Due to the wide range of mesh generation approaches proposed in recent dec- ades, an exhaustive review of all such methods is outside the scope of this paper. In general meshing, Delaunay-based techni- ques [5–11] are quite popular. For a given set of sample points in a 2D domain, CVT can be used to generate mass center points of corresponding Voronoi regions with respect to a given density 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. Journal of Computing and Information Science in Engineering MARCH 2014, Vol. 14 / 011009-1 Copyright V C 2014 by ASME Downloaded From: http://computingengineering.asmedigitalcollection.asme.org/ on 03/03/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use