Conference Paper

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

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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: 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.
    International Journal of Computational Geometry & Applications 02/2005; 15:55-98. DOI:10.1142/S0218195905001609 · 0.08 Impact Factor
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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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Jun 1, 2014