Conference Paper

A New Algorithm for Generating Quadrilateral Meshes and its Application to FE-Based Image Registration.

Source: DBLP

ABSTRACT The use of finite element (FE) analysis in the simulation of physical phenomena over the human body has necessitated the construc-tion of meshes from images. Despite the availability of several tools for generating meshes for FE-based applications, most cannot deal directly with the raw pixel-wise representation of image data. Additionally, some are optimized for the construction of much simpler shapes than those encountered within the human body. In this work, we introduce a new algorithm to obtain strictly convex quadrilateral meshes of bounded size from triangulations of polygonal regions with or without polygonal holes. We present an approach to construct quadrilateral meshes from segmented images using the aforementioned algorithm, and a quantitative analysis of the quality of the meshes generated by our algorithm with respect to the performance of a FE-based image registration method that takes image meshes as input.

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    ABSTRACT: Digital images from computerized tomography (CT) and magnetic resonance (MR) scanners can be used to create computer models of anatomical shapes. These models are typically used in biomedical applications for the purpose of physical simulation and visualization. In this thesis, we describe new algorithms for creating models from 2D and 3D binary digital images. Our models are meshes of 2D shapes represented by 2D binary digital images, and meshes of the surface of 3D shapes represented by 3D binary digital images. More specifically, this thesis contains the following two contributions: First, we give an algorithm for converting constrained triangular meshes of polygonal domains into constrained and strictly convex quadrilateral meshes of the same domain. Our algorithm has linear time in the number of triangles of the input triangular mesh, produces a bounded number of quadrilaterals, offers better bounds than similar algorithms that also produce strictly convex quadrilateral meshes of bounded size, and tends to preserve the grading of the input triangular mesh. We also present examples to demonstrate that our algorithm can be successfully used to create quadrilateral meshes from 2D binary digital images of anatomical shapes, such as the human brain. Second, we provide a new algorithm for generating simplicial surface meshes that approximate the boundary of 3D shapes represented by 3D binary digital images. Our algorithm is based on a simplified version of one of two known algorithms for generating provably good quality simplicial approximations of smooth, implicit surfaces. Provably good quality simplicial surfaces are very desirable for visualization purposes, and the main advantage of our algorithm is to offer this provable quality guarantee.
    Dissertations available from ProQuest. 01/2006;
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    ABSTRACT: Medical image segmentation and 3D mesh generation are the two critical challenges for numerical analysis based on medical images. Seamlessly linking different segmented results to appropriate mesh generation algorithms should be greatly beneficial for automatic and rapid finite element modeling from medical images. We present the interface representation models between segmentation and mesh generation algorithms and briefly discuss the input requirements of several well-established meshing algorithms.
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    ABSTRACT: We introduce a new algorithm to convert triangular meshes of polygonal regions, with or without holes, into strictly convex quadrilateral meshes of small bounded size. Our algorithm includes all vertices of the triangular mesh in the quadrilateral mesh, but may add extra vertices (called Steiner points). We show that if the input triangular mesh has t triangles, our algorithm produces a mesh with at most b 3t 2 c + 2 quadrilaterals by adding at most t + 2 Steiner points, one of which may be placed outside the triangular mesh domain. We also describe an extension of our algorithm to convert constrained triangular meshes into constrained quadrilateral ones. We show that if the input con- strained triangular mesh has t triangles and its dual graph has h connected components, the resulting constrained quadrilateral mesh has at most b 3t 2 c + 4h quadrilaterals and at most t + 3h Steiner points, one of which may be placed outside the triangular mesh domain. Examples of meshes generated by our algorithm, and an evaluation of the qual- ity of these meshes with respect to a quadrilateral shape quality criterion are presented as well.
    Int. J. Comput. Geometry Appl. 01/2005; 15:55-98.

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