Geometric modeling and mesh generation from scanned images (Q2797099)

In recent years the finite element method and the scanning technology have been developed and advanced rapidly. Their applications are very broad from computational biology, medicine to materials science and engineering. So, there is an emerging need for quality mesh generation to enable the analysis, understanding and prediction of complex physical or biological phenomena. The book is devoted to such quality mesh generation methods. It covers all topics ranging from imaging, image processing, geometric modelling, and mesh generation, to simulation and applications. Students often just consider each topic in isolation but are not shown how the pieces fit together to make a whole. This book will give them the big picture. The material in this book is based on a course ''Computational Biomodeling \& Visualization'' that the author has conduced at Carnegie Mellon University and also on some research of the author.NEWLINENEWLINEChapter 1 gives an broad view of the pipelines that the author will use in the presented methods. Next, in Chapter 2, the author makes some review of basic numerical methods. The topics included in this chapter include: linear and nonlinear algebraic methods, curve fitting via interpolation and approximation, ordinary and partial differential equations, eigenvalue problem, numerical integration and Fourier analysis. Some overview of scanning techniques in biomedical imaging is made in Chapter 3. It starts from the review of medical imaging history. Then, computational tomography, magnetic resonance imaging, single photon emission computed tomography, positron emission tomography, ultrasound, fluoroscopy, cryo-electronic microscopy, electron backscatter diffraction and high-energy X-rays are introduced. Moreover, in this chapter, the author gives a concise introduction to image processing (basic operations, filtering, segmentation and registration). Chapter 4 is devoted to the fundamentals of geometric modelling and meshing. In the beginning the author introduces some basic notions from linear algebra, e.g., points, vectors, matrices, transformations etc. Next, some overview of curves and surfaces is made. The author focuses on Hermite, Bézier, B-spline parametric curves and surfaces, and on some subdivision techniques. The chapter ends with the introduction of the isocontouring methods: marching cubes and dual contouring.NEWLINENEWLINEThe main topic of the book starts in Chapter 5. This chapter is devoted to the image-based triangular and tetrahedral meshing. Firstly, the author reviews unstructured triangular and tetrahedral mesh generation. After that, she introduces octree-based mesh generation techniques from scanned images, their extension to multiple-material domains. Moreover, how to resolve topology ambiguities and improve the mesh quality, as well as dual contouring-based mesh generation with guaranteed angle range is presented. Chapter 6 starts with the review of unstructured quad and hex mesh generation, and then it introduces image-based meshing schemes, i.e., refinement templates, adaptive meshing using hybrid octree, meshing multiple-material domains, sharp feature preservation and RD-tree based hex meshing. At the end of the chapter, the author discusses various methods used to improve the quality of the mesh. Next, in Chapter 7, the author introduces volumetric T-spline modelling. Firstly, she reviews NURBS and T-spline surfaces. After that, several volumetric T-spline modelling techniques are introduced. The techniques cover: converting quad/hex meshes to standard and rational T-splines, polycube-based parametric mapping, feature preservation using eigenfunctions, Boolean operation and skeletons, truncated hierarchical Catmull-Clark subdivision, weighted T-splines, conformal T-spline modelling. In the last chapter, some overview of the application areas is discussed. Moreover, various applications of the techniques introduced in the book are presented, e.g., multiscale biomolecular modelling, construction of patient-specific cardiovascular model, critical feature determination of polycrystalline materials and bondline composites.NEWLINENEWLINEThe book is presented in a very accessible fashion. The author gives many examples presenting the notations and problems which are considered. Every chapter ends with exercises, both theoretical and programming. The book is suitable for senior undergraduate students and researchers in computer science, biomedical engineering, materials science. Moreover, it can be used as a professional reference.