Template-based quadrilateral mesh generation from imaging data

This paper describes a novel template-based meshing approach for generating good quality quadrilateral meshes from 2D digital images. This approach builds upon an existing image-based mesh generation technique called Imeshp, which enables us to create a segmented triangle mesh from an image without the need for an image segmentation step. Our approach generates a quadrilateral mesh using an indirect scheme, which converts the segmented triangle mesh created by the initial steps of the Imesh technique into a quadrilateral one. The triangle-to-quadrilateral conversion makes use of template meshes of triangles. To ensure good element quality, the conversion step is followed by a smoothing step, which is based on a new optimization-based procedure. We show several examples of meshes generated by our approach, and present a thorough experimental evaluation of the quality of the meshes given as examples.

Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation

A new mesh adaptivity algorithm that combines a posteriori error estimation with bubble-type local mesh generation (BLMG) strategy for elliptic differential equations is proposed. The size function used in the BLMG is defined on each vertex during the adaptive process based on the obtained error estimator. In order to avoid the excessive coarsening and refining in each iterative step, two factor thresholds are introduced in the size function. The advantages of the BLMG-based adaptive finite element method, compared with other known methods, are given as follows: the refining and coarsening are obtained fluently in the same framework; the local a posteriori error estimation is easy to implement through the adjacency list of the BLMG method; at all levels of refinement, the updated triangles remain very well shaped, even if the mesh size at any particular refinement level varies by several orders of magnitude. Several numerical examples with singularities for the elliptic problems, where the explicit error estimators are used, verify the efficiency of the algorithm. The analysis for the parameters introduced in the size function shows that the algorithm has good flexibility.

Mesh-based vs. Image-based Statistical Appearance Model of the Human Femur: a Preliminary Comparison Study for the Creation of Finite Element Meshes

Statistical models have been recently introduced in computational orthopaedics to investigate the bone mechanical properties across several populations. A fundamental aspect for the construction of statistical models concerns the establishment of accurate anatomical correspondences among the objects of the training dataset. Various methods have been proposed to solve this problem such as mesh morphing or image registration algorithms. The objective of this study is to compare a mesh-based and an image-based statistical appearance model approaches for the creation of nite element(FE) meshes. A computer tomography (CT) dataset of 157 human left femurs was used for the comparison. For each approach, 30 finite element meshes were generated with the models. The quality of the obtained FE meshes was evaluated in terms of volume, size and shape of the elements. Results showed that the quality of the meshes obtained with the image-based approach was higher than the quality of the mesh-based approach. Future studies are required to evaluate the impact of this finding on the final mechanical simulations.

Image-based vs. mesh-based statistical appearance models of the human femur: Implications for finite element simulations.

Statistical appearance models have recently been introduced in bone mechanics to investigate bone geometry and mechanical properties in population studies. The establishment of accurate anatomical correspondences is a critical aspect for the construction of reliable models. Depending on the representation of a bone as an image or a mesh, correspondences are detected using image registration or mesh morphing. The objective of this study was to compare image-based and mesh-based statistical appearance models of the femur for finite element (FE) simulations. To this aim, (i) we compared correspondence detection methods on bone surface and in bone volume; (ii) we created an image-based and a mesh-based statistical appearance models from 130 images, which we validated using compactness, representation and generalization, and we analyzed the FE results on 50 recreated bones vs. original bones; (iii) we created 1000 new instances, and we compared the quality of the FE meshes. Results showed that the image-based approach was more accurate in volume correspondence detection and quality of FE meshes, whereas the mesh-based approach was more accurate for surface correspondence detection and model compactness. Based on our results, we recommend the use of image-based statistical appearance models for FE simulations of the femur.

A practical demonstration of scalable, parallel mesh generation

Cambridge Flow Solutions Ltd, Compass House, Vision Park, Cambridge, CB4 9AD, UK Real-world simulation challenges are getting bigger: virtual aero-engines with multistage blade rows coupled with their secondary air systems & with fully featured geometry; environmental flows at meta-scales over resolved cities; synthetic battlefields. It is clear that the future of simulation is scalable, end-to-end parallelism. To address these challenges we have reported in a sequence of papers a series of inherently parallel building blocks based on the integration of a Level Set based geometry kernel with an octree-based cut-Cartesian mesh generator, RANS flow solver, post-processing and geometry management & editing. The cut-cells which characterize the approach are eliminated by exporting a body-conformal mesh driven by the underpinning Level Set and managed by mesh quality optimization algorithms; this permits third party flow solvers to be deployed. This paper continues this sequence by reporting & demonstrating two main novelties: variable depth volume mesh refinement enabling variable surface mesh refinement and a radical rework of the mesh generation into a bottom-up system based on Space Filling Curves. Also reported are the associated extensions to body-conformal mesh export. Everything is implemented in a scalable, parallel manner. As a practical demonstration, meshes of guaranteed quality are generated for a fully resolved, generic aircraft carrier geometry, a cooled disc brake assembly and a B747 in landing configuration. Copyright © 2009 by W.N.Dawes.

Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.

A depth-integrated 2D coastal and estuarine model with conformal boundary-fitted mesh generation

Details are given of the development and application of a 2D depth-integrated, conformal boundary-fitted, curvilinear model for predicting the depth-mean velocity field and the spatial concentration distribution in estuarine and coastal waters. A numerical method for conformal mesh generation, based on a boundary integral equation formulation, has been developed. By this method a general polygonal region with curved edges can be mapped onto a regular polygonal region with the same number of horizontal and vertical straight edges and a multiply connected region can be mapped onto a regular region with the same connectivity. A stretching transformation on the conformally generated mesh has also been used to provide greater detail where it is needed close to the coast, with larger mesh sizes further offshore, thereby minimizing the computing effort whilst maximizing accuracy. The curvilinear hydrodynamic and solute model has been developed based on a robust rectilinear model. The hydrodynamic equations are approximated using the ADI finite difference scheme with a staggered grid and the solute transport equation is approximated using a modified QUICK scheme. Three numerical examples have been chosen to test the curvilinear model, with an emphasis placed on complex practical applications

Comparison of the meccano method with standard mesh generation techniques

[EN]The meccano method is a novel and promising mesh generation technique for simultaneously creating adaptive tetrahedral meshes and volume parameterizations of a complex solid. The method combines several former procedures: a mapping from the meccano boundary to the solid surface, a 3-D local refinement algorithm and a simultaneous mesh untangling and smoothing. In this paper we present the main advantages of our method against other standard mesh generation techniques. We show that our method constructs meshes that can be locally refined by using the Kossaczky bisection rule and maintaining a high mesh quality. Finally, we generate volume T-mesh for isogeometric analysis, based on the volume parameterization obtained by the method…

Influence of Smoothing on Voxel-Based Mesh Accuracy in Micro-Finite Element

The interest in automatic volume meshing for finite element analysis (FEA) has grown more since the appearance of microfocus CT (μCT), due to its high resolution, which allows for the assessment of mechanical behaviour at a high precision. Nevertheless, the basic meshing approach of generating one hexahedron per voxel produces jagged edges. To prevent this effect, smoothing algorithms have been introduced to enhance the topology of the mesh. However, whether smoothing also improves the accuracy of voxel-based meshes in clinical applications is still under question. There is a trade-off between smoothing and quality of elements in the mesh. Distorted elements may be produced by excessive smoothing and reduce accuracy of the mesh. In the present work, influence of smoothing on the accuracy of voxel-based meshes in micro-FE was assessed. An accurate 3D model of a trabecular structure with known apparent mechanical properties was used as a reference model. Virtual CT scans of this reference model (with resolutions of 16, 32 and 64 μm) were then created and used to build voxel-based meshes of the microarchitecture. Effects of smoothing on the apparent mechanical properties of the voxel-based meshes as compared to the reference model were evaluated. Apparent Young’s moduli of the smooth voxel-based mesh were significantly closer to those of the reference model for the 16 and 32 μm resolutions. Improvements were not significant for the 64 μm, due to loss of trabecular connectivity in the model. This study shows that smoothing offers a real benefit to voxel-based meshes used in micro-FE. It might also broaden voxel-based meshing to other biomechanical domains where it was not used previously due to lack of accuracy. As an example, this work will be used in the framework of the European project ContraCancrum, which aims at providing a patient-specific simulation of tumour development in brain and lungs for oncologists. For this type of clinical application, such a fast, automatic, and accurate generation of the mesh is of great benefit.

An image-based method to automatically propagate bony landmarks: application to computational spine biomechanics.

In attempts to elucidate the underlying mechanisms of spinal injuries and spinal deformities, several experimental and numerical studies have been conducted to understand the biomechanical behavior of the spine. However, numerical biomechanical studies suffer from uncertainties associated with hard- and soft-tissue anatomies. Currently, these parameters are identified manually on each mesh model prior to simulations. The determination of soft connective tissues on finite element meshes can be a tedious procedure, which limits the number of models used in the numerical studies to a few instances. In order to address these limitations, an image-based method for automatic morphing of soft connective tissues has been proposed. Results showed that the proposed method is capable to accurately determine the spatial locations of predetermined bony landmarks. The present method can be used to automatically generate patient-specific models, which may be helpful in designing studies involving a large number of instances and to understand the mechanical behavior of biomechanical structures across a given population.

Choice of image features for depth-axis control in image based visual servo control

This paper is concerned with choosing image features for image based visual servo control and how this choice influences the closed-loop dynamics of the system. In prior work, image features tend to be chosen on the basis of image processing simplicity and noise sensitivity. In this paper we show that the choice of feature directly influences the closed-loop dynamics in task-space. We focus on the depth axis control of a visual servo system and compare analytically various approaches that have been reported recently in the literature. The theoretical predictions are verified by experiment.

Adaptive depth estimation in image based visual servo control of dynamic systems

This paper considers the question of designing a fully image based visual servo control for a dynamic system. The work is motivated by the ongoing development of image based visual servo control of small aerial robotic vehicles. The observed targets considered are coloured blobs on a flat surface to which the normal direction is known. The theoretical framework is directly applicable to the case of markings on a horizontal floor or landing field. The image features used are a first order spherical moment for position and an image flow measurement for velocity. A fully non-linear adaptive control design is provided that ensures global stability of the closed-loop system. © 2005 IEEE.