From Segmented Medical Images to Surface and Volume Meshes, Using Existing Tools and Algorithms
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Compression and Streaming of Polygon Meshes
Compression and Streaming of Polygon Meshes by Martin Isenburg A dissertation submitted to the faculty of the University of North Carolina at Chapel Hill in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Computer Science. Chapel Hill 2005 Approved by: Jack Snoeyink, Advisor Craig Gotsman, Reader Peter Lindstrom, Reader Dinesh Manocha, Committee Member Ming Lin, Committee Member ii iii ABSTRACT MARTIN ISENBURG: Compression and Streaming of Polygon Meshes (Under the direction of Jack Snoeyink) Polygon meshes provide a simple way to represent three-dimensional surfaces and are the de-facto standard for interactive visualization of geometric models. Storing large polygon meshes in standard indexed formats results in files of substantial size. Such formats allow listing vertices and polygons in any order so that not only the mesh is stored but also the particular ordering of its elements. Mesh compression rearranges vertices and polygons into an order that allows more compact coding of the incidence between vertices and predictive compression of their positions. Previous schemes were designed for triangle meshes and polygonal faces were triangulated prior to compression. I show that polygon models can be encoded more compactly by avoiding the initial triangulation step. I describe two compression schemes that achieve better compression by encoding meshes directly in their polygonal representation. I demonstrate that the same holds true for volume meshes by extending one scheme to hexahedral meshes. Nowadays scientists create polygonal meshes of incredible size. Ironically, com- pression schemes are not capable|at least not on common desktop PCs|to deal with giga-byte size meshes that need compression the most. -
MASTER THESIS Generating Hollow Offset Surface Meshes From
Department of Information and Computing Sciences Utrecht University The Netherlands MASTER THESIS ICA-3746356 Generating hollow offset surface meshes from segmented CT volumes using distance fields Submitted on 20th August 2019 By M.F.A. Martens Project supervisor (first examiner): prof. dr. R.C. Veltkamp Second examiner: dr. ir. A.F. van der Stappen Daily supervisor: Jan de Vaan Abstract We propose a method to generate hollow offset surface meshes from CT data using distance fields, in general and in the context of the 3mensio software package. Our method improves on several shortcomings of the currently implemented morpholo- gical offsetting method, like a blocky appearance of the offset surface, and uneven distance between the original surface and the offset surface. Our distance field ap- proach is very robust, and performs consistently for a wide range of tested anatomy and across different levels of CT voxel scaling. Our new method is able to return an offset mesh from CT segmentation data in an acceptable amount of time: mostly below 20 seconds, even for very large segmentations. Acknowledgements I want to thank 3mensio Medical Imaging B.V, and my daily supervisor Jan de Vaan in particular, for providing the opportunity to do an internship at their company, and for the support throughout the writing of this thesis report. I also want to thank my main supervisor and first examiner, prof. dr. Remco Veltkamp, for the help with all of my questions and for the feedback on earlier versions of this report. Also I would like to thank dr. ir. Frank van der Stappen, who agreed to by my second examiner. -
Voronoi Meshing Without Clipping
VoroCrust: Voronoi Meshing Without Clipping AHMED ABDELKADER, University of Maryland, College Park CHANDRAJIT L. BAJAJ, University of Texas, Austin MOHAMED S. EBEIDA∗, Sandia National Laboratories AHMED H. MAHMOUD, University of California, Davis SCOTT A. MITCHELL, Sandia National Laboratories JOHN D. OWENS, University of California, Davis AHMAD A. RUSHDI, Sandia National Laboratories 0.00 0.99 0.41 1.00 0.0 0.2 0.4 0.6 0.8 1.0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fig. 1. State-of-the-art methods for conforming Voronoi meshing clip Voronoi cells at the bounding surface. The Restricted Voronoi Diagram [Yan et al. 2013] (left) is sensitive to the input tessellation and produces surface elements of very low quality, per the shortest-to-longest edge ratio distribution shown in the inset. In contrast, VoroCrust (right) generates an unclipped Voronoi mesh conforming to a high-quality surface mesh. Polyhedral meshes are increasingly becoming an attractive option algorithm that can handle broad classes of domains exhibiting with particular advantages over traditional meshes for certain arbitrarily curved boundaries and sharp features. In addition, the applications. What has been missing is a robust polyhedral meshing power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous ∗ Correspondence address: [email protected]. Author names are listed in alphabetical order. formulations. The VoroCrust algorithm is the first provably-correct This material is based upon work supported by the U.S. Department algorithm for conforming polyhedral Voronoi meshing for non- of Energy, Office of Science, Office of Advanced Scientific Computing convex and non-manifold domains with guarantees on the quality Research (ASCR), Applied Mathematics Program, and the Laboratory of both surface and volume elements. -
Mesh Generation
Mesh Generation Pierre Alliez Inria Sophia Antipolis - Mediterranee 2D Delaunay Refinement 2D Triangle Mesh Generation Input: . PSLG C (planar straight line graph) . Domain bounded by edges of C Output: . triangle mesh T of such that . vertices of C are vertices of T . edges of C are union of edges in T . triangles of T inside have controlled size and quality Key Idea . Break bad elements by inserting circumcenters (Voronoi vertices) [Chew, Ruppert, Shewchuk,...] “bad” in terms of size or shape Basic Notions C: PSLG describing the constraints T: Triangulation to be refined Respect of the PSLG . Edges a C are split until constrained subedges are edges of T . Constrained subedges are required to be Gabriel edges . An edge of a triangulation is a Gabriel edge if its smallest circumcirle encloses no vertex of T . An edge e is encroached by point p if the smallest circumcirle of e encloses p. Refinement Algorithm C: PSLG bounding the domain to be meshed. T: Delaunay triangulation of the current set of vertices T|: T Constrained subedges: subedges of edges of C Initialise with T = Delaunay triangulation of vertices of C Refine until no rule apply . Rule 1 if there is an encroached constrained subedge e insert c = midpoint(e) in T (refine-edge) . Rule 2 if there is a bad facet f in T| c = circumcenter(f) if c encroaches a constrained subedge e refine-edge(e). else insert(c) in T 2D Delaunay Refinement PSLG Background Constrained Delaunay Triangulation Delaunay Edge An edge is said to be a Delaunay edge, if it is inscribed in an empty circle -
Mesh Generation for Voxel -Based Objects
Graduate Theses, Dissertations, and Problem Reports 2005 Mesh generation for voxel -based objects Hanzhou Zhang West Virginia University Follow this and additional works at: https://researchrepository.wvu.edu/etd Recommended Citation Zhang, Hanzhou, "Mesh generation for voxel -based objects" (2005). Graduate Theses, Dissertations, and Problem Reports. 2676. https://researchrepository.wvu.edu/etd/2676 This Dissertation is protected by copyright and/or related rights. It has been brought to you by the The Research Repository @ WVU with permission from the rights-holder(s). You are free to use this Dissertation in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you must obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/ or on the work itself. This Dissertation has been accepted for inclusion in WVU Graduate Theses, Dissertations, and Problem Reports collection by an authorized administrator of The Research Repository @ WVU. For more information, please contact [email protected]. Mesh Generation for Voxel-Based Objects Hanzhou Zhang Dissertation submitted to the College of Engineering and Mineral Resources at West Virginia University in partial ful¯llment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering Dr. Andrei V. Smirnov, Chair Dr. Ismail Celik Dr. Victor H. Mucino Dr. Ibrahim Yavuz Dr. Frances L.Van Scoy Department of Mechanical and Aerospace Engineering Morgantown, West Virginia 2005 ABSTRACT Mesh Generation for Voxel-Based Objects Hanzhou Zhang A new physically-based approach to unstructured mesh generation via Monte-Carlo simulation is proposed. -
A Robust Smoothed Voxel Representation for the Generation of Finite Element Models for Computational Urban Physics
FICUP An International Conference on Urban Physics B. Beckers, T. Pico, S. Jimenez (Eds.) Quito – Galápagos, Ecuador, 26 – 30 September 2016 A robust smoothed voxel representation for the generation of finite element models for computational urban physics Alain Rassineux1, Benoit Beckers1 1 Sorbonne universités, Université de Technologie de Compiègne, CNRS Laboratoire Roberval UMR 7337 CNRS/UTC 7337, Centre de Recherche de Royallieu, BP 20529, F60205 Compiègne e-mail: [email protected] Keywords: Mesh generation, finite element analysis, large scale city models. Abstract. A voxel based methodology to create high quality finite element meshes of large city models for urban computational physics is proposed. Initial data are limited to 3D points cloud or STL files. A voxel grid which provides a rough representation of the outer (visible) surfaces of geometry is first created. The voxel model is then smoothed by a subdivision technique which provides a better representation of the normal vector to the surface than the voxel model. The points smoothed models are thereafter projected on the initial data. The ground, building blocks and the air are identified as volumes and their corresponding closed conforming surface mesh is created. Examples of complex reconstructions are presented. 249 FICUP 2016 A. Rassineux, B. Beckers 1. Introduction The work proposed here is mostly based on the generation of finite element meshes of complex urban models. When dealing with complex geometry assembly, the major time of the finite element analysis (FEA) is spent on the creation of the mesh model. Mesh generation based on CAD for computational mechanics for instance has been widely investigated [De Cougny 1996]. -
Automatic and High-Quality Surface Mesh Generation for CAD Models
Automatic and High-quality Surface Mesh Generation for CAD Models Jianwei Guoa, Fan Dinga, Xiaohong Jiab,c,∗, Dong-Ming Yana aNational Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China bKLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China cSchool of Mathematical Science, University of Chinese Academy of Sciences, Beijing 100049, China Abstract In this paper, we present a fully automatic framework that tessellates industrial computer-aided design (CAD) models into high-quality triangular meshes. In contrast to previous approaches that are purely parametric or performed directly in 3D space, our method is based on a remeshing algorithm that can achieve accuracy and high-quality simultaneously. Given an input standard CAD model, which is represented by B-rep format, we first rebuild the parametric domain for each surface patch according to an initial triangulation, and then the boundaries of the parametric domain are retriangulated by exploiting the Constrained Delaunay Triangulation (CDT). In the second stage, the 2D triangulation is projected back to the 3D space, and a modified global isotropic remeshing process is applied, which further improves the regularity and angle quality of the tessellated meshes. Experiments demonstrate the validity of the proposed approach and its ability to generate high-quality meshes. Moreover, we evaluate our technique and compare it with state-of-the-art CAD model tessellation approaches. Keywords: CAD Tessellation, High-quality mesh, Remeshing. 1. Introduction (a) (b) Tessellating Computer-Aided Design (CAD) models into dis- crete representations is important in various downstream applica- tions [1, 2] ranging from engineering to scientific research, such as numerical simulations, rapid prototyping, computational fluid dynamics, and visualization, to name a few. -
Geometry from Imaging Data Part II: Geometry Reconstruction Computational Biomechanics Summer Term 2016 Lecture 5/12 Frank Niemeyer Geometry Reconstruction
Zhang et al. 2004 Geometry From Imaging Data Part II: Geometry Reconstruction Computational Biomechanics Summer Term 2016 Lecture 5/12 Frank Niemeyer Geometry Reconstruction Starting Point Note: intentionally reduced resolution Images made of pixels (DICOM, PNG, …) Stack Volume defined by wikimedia.org voxels , , Geometry Reconstruction Image Processing • Visualization • Multi-planar • Volume rendering • Iso-surface • Cropping (ROI) Iso-surface rendering of sheep femur • Windowing • De-noising • Artifact removal • Segmentation, labelling, classification: • Identify connected components Original Windowed, equalized • Locate object boundaries, interfaces • Manually or (semi-)automated, machine learning Segmented Geometry Reconstruction | Image Processing | Noise Suppression Linear (Low-Pass) Filtering • Replace each pixel with weighted average of surrounding pixels/voxels (2D or 3D) Original • Equivalent to suppressing high-frequency components as = • : kernel (weights), e.g. Gaussian, Lanczos… • Simple & fast • Removes noise … • … but also blurs edges Gaussian filter Geometry Reconstruction | Image Processing | Noise Suppression Rank Filters • Replace each pixel with min/max/median (or any other “rank”) of adjacent pixels/voxels Original • Arbitrary adjacency (box, diamond, cross, …) • Median: “robust” estimator → particularly useful against impulse-like noise (speckle, salt & pepper) • Better at preserving edges than Gaussian • Relatively expensive (sorting!) Median filter Geometry Reconstruction | Image Processing | Noise Suppression -
Techniques for the Generation of 3D Finite Element Meshes of Human Organs
Techniques for the generation of 3D Finite Element Meshes of human organs LOBOS, C. †, PAYAN, Y. †, and HITSCHFELD, N. ‡ † TIMC-IMAG Laboratory, UMR CNRS 5225, Joseph Fourier University, 38706 La Tronche CEDEX, France. ‡Universidad de Chile, FCFM, Departamento de Ciencias de la Computación, Blanco Encalada 2120, 837-0459 Santiago, Chile. INTRODUCTION Continuum mechanics (CM) is a branch of mechanics that deals with the analysis of the kinematic and mechanical behavior of materials modeled as a continuum, e.g., solids and fluids (i.e., liquids and gases). In a nutshell, CM assumes that matter is continuous (ignoring the fact that matter is actually made of atoms). This assumption allows the approximation of physical quantities over the materials, such as energy and momentum, at the infinitesimal limit. Differential equations can thus be employed in solving problems in CM. Let Ω be a volumetric domain defined in 3D and P a point inside Ω. A deformation occurs in Ω as external (surface or volumetric) forces ƒ are applied to some P in Ω. If Ω is considered as an elastic body, the deformation is characterized by: A displacement vector field u caused by ƒ applied over one or more P. An internal state of deformation, mathematically defined by a “strain tensor” for each P in Ω. The “force reaction” of the body to the external forces; this is mathematically defined by a “stress tensor” for each P in Ω. The Local Equilibrium of the Medium (LEM) is an expression defined for each P in Ω that links the displacement, the strain and the stress tensor through Partial Differential Equations (PDE). -
Mesh Generation
Mesh Generation Pierre Alliez Inria Sophia Antipolis - Mediterranee 2D Delaunay Refinement 2D Triangle Mesh Generation Input: . PSLG C (planar straight line graph) . Domain bounded by edges of C Output: . triangle mesh T of such that . vertices of C are vertices of T . edges of C are union of edges in T . triangles of T inside have controlled size and quality Key Idea . Break bad elements by inserting circumcenters (Voronoi vertices) [Chew, Ruppert, Shewchuk,...] “bad” in terms of size or shape Basic Notions C: PSLG describing the constraints T: Triangulation to be refined Respect of the PSLG . Edges a C are split until constrained subedges are edges of T . Constrained subedges are required to be Gabriel edges . An edge of a triangulation is a Gabriel edge if its smallest circumcirle encloses no vertex of T . An edge e is encroached by point p if the smallest circumcirle of e encloses p. Refinement Algorithm C: PSLG bounding the domain to be meshed. T: Delaunay triangulation of the current set of vertices T|: T Constrained subedges: subedges of edges of C Initialise with T = Delaunay triangulation of vertices of C Refine until no rule apply . Rule 1 if there is an encroached constrained subedge e insert c = midpoint(e) in T (refine-edge) . Rule 2 if there is a bad facet f in T| c = circumcenter(f) if c encroaches a constrained subedge e refine-edge(e). else insert(c) in T 2D Delaunay Refinement PSLG Background Constrained Delaunay Triangulation Pseudo-dual: Bounded Voronoi Diagram constrained Bounded Voronoi “blind” triangles diagram -
Hexahedral Mesh Generation from Volumetric Data by Dual Interval Volume
Hexahedral Mesh Generation from Volumetric Data by Dual Interval Volume Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Fei Xiao Graduate Program in Computer Science and Engineering The Ohio State University 2018 Thesis Committee Dr. Rephael Wenger, Advisor Dr. Tamal Dey Copyrighted by Fei Xiao 2018 Abstract Finite element methods play an important role in the field of scientific research and engineering applications. An important requirement of numerical methods is to discretize the model into a mesh composed of simple elements. In three-dimensional numerical analysis, tetrahedral and hexahedral elements are usually used. Tetrahedral meshes have the advantage of high efficiency, easy implementation, flexibility for adaptive mesh generation and (relatively) easy mesh regeneration. However, hexahedral meshes have an advantage over tetrahedron element meshes regarding the analysis accuracy and total number of elements. This makes hexahedral meshes an attractive choice for numerical analysis. In medical and industrial applications, X-ray computed tomography (CT) or magnetic resonance imaging (MRI) scanners are widely used in medical and industrial diagnostics. The CT and MRI produce a regular grid with scalar values at each grid vertex. This regular grid is called volumetric data. Hexahedral mesh generation for volumetric data provides an opportunity to exploit the structure provided in the volumetric data. One way to generate hexahedral meshes from the volumetric data is to extract the surface geometry first and then mesh the object. However, this two-step approach takes extra time and effort for mesh generation. Also, this approach does not take the advantage of the regular grid from which the surface is generated.