Diamond-based models for scientific visualization

Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains including scientific visualization, finite element analysis and shape modeling and analysis. A popular class of such approaches is based on the regular simplex bisection operator, which bisects simplices (e.g. line segments, triangles, tetrahedra) along the midpoint of a predetermined edge. Regular simplex bisection produces adaptive simplicial meshes of high geometric quality, while simplifying the extraction of crack-free, or conforming, approximations to the original dataset. Efficient multiresolution representations for such models have been achieved in 2D and 3D by clustering sets of simplices sharing the same bisection edge into structures called diamonds. In this thesis, we introduce several diamond-based approaches for scientific visualization. We first formalize the notion of diamonds in arbitrary dimensions in terms of two related simplicial decompositions of hypercubes. This enables us to enumerate the vertices, simplices, parents and children of a diamond. In particular, we identify the number of simplices involved in conforming updates to be factorial in the dimension and group these into a linear number of subclusters of simplices that are generated simultaneously. The latter form the basis for a compact pointerless representation for conforming meshes generated by regular simplex bisection and for efficiently navigating the topological connectivity of these meshes. Secondly, we introduce the supercube as a high-level primitive on such nested meshes based on the atomic units within the underlying triangulation grid. We propose the use of supercubes to associate information with coherent subsets of the full hierarchy and demonstrate the effectiveness of such a representation for modeling multiresolution terrain and volumetric datasets. Next, we introduce Isodiamond Hierarchies, a general framework for spatial access structures on a hierarchy of diamonds that exploits the implicit hierarchical and geometric relationships of the diamond model. We use an isodiamond hierarchy to encode irregular updates to a multiresolution isosurface or interval volume in terms of regular updates to diamonds. Finally, we consider nested hypercubic meshes, such as quadtrees, octrees and their higher dimensional analogues, through the lens of diamond hierarchies. This allows us to determine the relationships involved in generating balanced hypercubic meshes and to propose a compact pointerless representation of such meshes. We also provide a local diamond-based triangulation algorithm to generate high-quality conforming simplicial meshes

Doctor of Philosophy

dissertationOne of the fundamental building blocks of many computational sciences is the construction and use of a discretized, geometric representation of a problem domain, often referred to as a mesh. Such a discretization enables an otherwise complex domain to be represented simply, and computation to be performed over that domain with a finite number of basis elements. As mesh generation techniques have become more sophisticated over the years, focus has largely shifted to quality mesh generation techniques that guarantee or empirically generate numerically well-behaved elements. In this dissertation, the two complementary meshing subproblems of vertex placement and element creation are analyzed, both separately and together. First, a dynamic particle system achieves adaptivity over domains by inferring feature size through a new information passing algorithm. Second, a new tetrahedral algorithm is constructed that carefully combines lattice-based stenciling and mesh warping to produce guaranteed quality meshes on multimaterial volumetric domains. Finally, the ideas of lattice cleaving and dynamic particle systems are merged into a unified framework for producing guaranteed quality, unstructured and adaptive meshing of multimaterial volumetric domains

Dynamic Multivariate Simplex Splines For Volume Representation And Modeling

Volume representation and modeling of heterogeneous objects acquired from real world are very challenging research tasks and playing fundamental roles in many potential applications, e.g., volume reconstruction, volume simulation and volume registration. In order to accurately and efficiently represent and model the real-world objects, this dissertation proposes an integrated computational framework based on dynamic multivariate simplex splines (DMSS) that can greatly improve the accuracy and efficacy of modeling and simulation of heterogenous objects. The framework can not only reconstruct with high accuracy geometric, material, and other quantities associated with heterogeneous real-world models, but also simulate the complicated dynamics precisely by tightly coupling these physical properties into simulation. The integration of geometric modeling and material modeling is the key to the success of representation and modeling of real-world objects. The proposed framework has been successfully applied to multiple research areas, such as volume reconstruction and visualization, nonrigid volume registration, and physically based modeling and simulation

On the Real-Time Performance, Robustness and Accuracy of Medical Image Non-Rigid Registration

Three critical issues about medical image non-rigid registration are performance, robustness and accuracy. A registration method, which is capable of responding timely with an accurate alignment, robust against the variation of the image intensity and the missing data, is desirable for its clinical use. This work addresses all three of these issues. Unacceptable execution time of Non-rigid registration (NRR) often presents a major obstacle to its routine clinical use. We present a hybrid data partitioning method to parallelize a NRR method on a cooperative architecture, which enables us to get closer to the goal: accelerating using architecture rather than designing a parallel algorithm from scratch. to further accelerate the performance for the GPU part, a GPU optimization tool is provided to automatically optimize GPU execution configuration.;Missing data and variation of the intensity are two severe challenges for the robustness of the registration method. A novel point-based NRR method is presented to resolve mapping function (deformation field) with the point correspondence missing. The novelty of this method lies in incorporating a finite element biomechanical model into an Expectation and Maximization (EM) framework to resolve the correspondence and mapping function simultaneously. This method is extended to deal with the deformation induced by tumor resection, which imposes another challenge, i.e. incomplete intra-operative MRI. The registration is formulated as a three variable (Correspondence, Deformation Field, and Resection Region) functional minimization problem and resolved by a Nested Expectation and Maximization framework. The experimental results show the effectiveness of this method in correcting the deformation in the vicinity of the tumor. to deal with the variation of the intensity, two different methods are developed depending on the specific application. For the mono-modality registration on delayed enhanced cardiac MRI and cine MRI, a hybrid registration method is designed by unifying both intensity- and feature point-based metrics into one cost function. The experiment on the moving propagation of suspicious myocardial infarction shows effectiveness of this hybrid method. For the multi-modality registration on MRI and CT, a Mutual Information (MI)-based NRR is developed by modeling the underlying deformation as a Free-Form Deformation (FFD). MI is sensitive to the variation of the intensity due to equidistant bins. We overcome this disadvantage by designing a Top-to-Down K-means clustering method to naturally group similar intensities into one bin. The experiment shows this method can increase the accuracy of the MI-based registration.;In image registration, a finite element biomechanical model is usually employed to simulate the underlying movement of the soft tissue. We develop a multi-tissue mesh generation method to build a heterogeneous biomechanical model to realistically simulate the underlying movement of the brain. We focus on the following four critical mesh properties: tissue-dependent resolution, fidelity to tissue boundaries, smoothness of mesh surfaces, and element quality. Each mesh property can be controlled on a tissue level. The experiments on comparing the homogeneous model with the heterogeneous model demonstrate the effectiveness of the heterogeneous model in improving the registration accuracy

On Volumetric Shape Reconstruction from Implicit Forms

International audienceIn this paper we report on the evaluation of volumetric shape reconstruction methods that consider as input implicit forms in 3D. Many visual applications build implicit representations of shapes that are converted into explicit shape representations using geometric tools such as the Marching Cubes algorithm. This is the case with image based reconstructions that produce point clouds from which implicit functions are computed, with for instance a Poisson reconstruction approach. While the Marching Cubes method is a versatile solution with proven efficiency, alternative solutions exist with different and complementary properties that are of interest for shape modeling. In this paper, we propose a novel strategy that builds on Centroidal Voronoi Tessellations (CVTs). These tessellations provide volumetric and surface representations with strong regularities in addition to provably more accurate approximations of the implicit forms considered. In order to compare the existing strategies, we present an extensive evaluation that analyzes various properties of the main strategies for implicit to explicit volumetric conversions: Marching cubes, Delaunay refinement and CVTs, including accuracy and shape quality of the resulting shape mesh

Tetrahedral Image-to-Mesh Conversion Software for Anatomic Modeling of Arteriovenous Malformations

We describe a new implementation of an adaptive multi-tissue tetrahedral mesh generator targeting anatomic modeling of Arteriovenous Malformation (AVM) for surgical simulations. Our method, initially constructs an adaptive Body-Centered Cubic (BCC) mesh of high quality elements. Then, it deforms the mesh surfaces to their corresponding physical image boundaries, hence, improving the mesh fidelity and smoothness. Our deformation scheme, which builds upon the ITK toolkit, is based on the concept of energy minimization, and relies on a multi-material point-based registration. It uses non-connectivity patterns to implicitly control the number of the extracted feature points needed for the registration, and thus, adjusts the trade-off between the achieved mesh fidelity and the deformation speed. While many medical imaging applications require robust mesh generation, there are few codes available to the public. We compare our implementation with two similar open-source image-to-mesh conversion codes: (1) Cleaver from US, and (2) CGAL from EU. Our evaluation is based on five isotropic/anisotropic segmented images, and relies on metrics like geometric & topologic fidelity, mesh quality, gradation and smoothness. The implementation we describe is open- source and it will be available within: (i) the 3D Slicer package for visualization and image analysis from Harvard Medical School, and (ii) an interactive simulator for neurosurgical procedures involving vasculature using SOFA, a framework for real-time medical simulation developed by INRIA