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PDE-BASED MEDIAL AXIS EXTRACTION AND SHAPE MANIPULATION OF ARBITRARY meshes

Journal of Systems Science & Complexity 2008年第4期21卷 609-625页

作者： Haixia DU Terry YOO Hong QIN Sterne Kessler Goldstein & Fox P.L.L.C. Washington 20005 USA. National Library of Medicine National Institutes of Health Bethesda 20894 USA. Computer Science Department Stony Brook University Stony Brook NY 11794 USA.

Shape skeletonization （i.e., medial axis extraction） is powerful in many visual computing applications, such as pattern recognition, object segmentation, registration, and animation. In this paper, the authors expand the use of diffusion equations combined with distance field information to approximate medial axes of arbitrary 3D differential properties. It offers an alternative solids represented by polygonal meshes based on their but natural way for medial axis extraction for commonly used 3D polygonal models. By solving the PDE along time axis, this system can not only quickly extract diffusion-based medial axes of input meshes, but also allow users to visualize the extraction process at each time step. In addition, the proposed model provides users a set of manipulation toolkits to sculpt extracted medial axes, then use diffusion-based techniques to recover corresponding deformed shapes according to the original input datasets. This skeleton-based shape manipulation offers a fast and easy way for animation and deformation of complicated mesh objects.

关键词： Diffusion Equation Medial Axis Extraction PDE techniques polygonal meshes Shape Manipulation.

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A VARIATIONAL APPROACH FOR DETECTING FEATURE LINES ON meshes

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Journal of Computational Mathematics 2016年第1期34卷 87-112页

作者： Weihua Tong Xuecheng Tai School of Mathematical Sciences University of Science and Technology of China Hefei 230026 China Department of Mathematics University of Bergen P.O. Box 7800 N-5020 Bergen Norway

Feature lines are fundamental shape descriptors and have been extensively applied to computer graphics, computer-aided design, image processing, and non-photorealistic renderingi This paper introduces a unified variational framework for detecting generic feature lines on polygonal meshes. The classic Mumford-Shah model is extended to surfaces. Using F-convergence method and discrete differential geometry, we discretize the proposed variational model to sequential coupled sparse linear systems. Through quadratic polyno- mials fitting, we develop a method for extracting valleys of functions defined on surfaces. Our approach provides flexible and intuitive control over the detecting procedure, and is easy to implement. Several measure functions are devised for different types of feature lines, and we apply our approach to various polygonal meshes ranging from synthetic to measured models. The experiments demonstrate both the effectiveness of our algorithms and the visual quality of results.

关键词： Feature lines Variational approach polygonal meshes The Mumford-Shah model Discrete operators Valleys of functions

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A unified framework for isotropic meshing based on narrowband Euclidean distance transformation

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Computational Visual Media 2015年第3期1卷 239-251页

作者： Yuen-Shan Leung Xiaoning Wang Ying He Yong-Jin Liu Charlie C.L.Wang School of Computer Engineering Nanyang Technological University Department of Computer Science and Technology Tsinghua University Department of Mechanical and Automation Engineering The Chinese University of Hong Kong

In this paper, we propose a simpleyet-effective method for isotropic meshing relying on Euclidean distance transformation based centroidal Voronoi tessellation(CVT). Our approach improves the performance and robustness of computing CVT on curved domains while simultaneously providing highquality output meshes. While conventional extrinsic methods compute CVTs in the entire volume bounded by the input model, we restrict the computation to a 3D shell of user-controlled thickness. Taking voxels which contain surface samples as sites, we compute the exact Euclidean distance transform on the GPU. Our algorithm is parallel and memory-efficient,and can construct the shell space for resolutions up to 20483 at interactive speed. The 3D centroidal Voronoi tessellation and restricted Voronoi diagrams are also computed efficiently on the GPU. Since the shell space can bridge holes and gaps smaller than a certain tolerance, and tolerate non-manifold edges and degenerate triangles, our algorithm can handle models with such defects, which typically cause conventional remeshing methods to fail. Our method can process implicit surfaces, polyhedral surfaces, and point clouds in a unified framework. Computational results show that our GPU-based isotropic meshing algorithm produces results comparable to state-ofthe-art techniques, but is significantly faster than conventional CPU-based implementations.

关键词： centroidal Voronoi tessellation(CVT) Euclidean distance transformation GPU isotropic meshing polygonal meshes point clouds implicit surfaces

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