3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques

3D Mesh Simplification. A survey of algorithms and CAD model simplification tests

Simplification of highly detailed CAD models is an important step when CAD models are visualized or by other means utilized in augmented reality applications. Without simplification, CAD models may cause severe processing and storage is- sues especially in mobile devices. In addition, simplified models may have other advantages like better visual clarity or improved reliability when used for visual pose tracking. The geometry of CAD models is invariably presented in form of a 3D mesh. In this paper, we survey mesh simplification algorithms in general and focus especially to algorithms that can be used to simplify CAD models. We test some commonly known algorithms with real world CAD data and characterize some new CAD related simplification algorithms that have not been surveyed in previous mesh simplification reviews.Siirretty Doriast

A Concept For Surface Reconstruction From Digitised Data

Reverse engineering and in particular the reconstruction of surfaces from digitized data is an important task in industry. With the development of new digitizing technologies such as laser or photogrammetry, real objects can be measured or digitized quickly and cost effectively. The result of the digitizing process is a set of discrete 3D sample points. These sample points have to be converted into a mathematical, continuous surface description, which can be further processed in different computer applications. The main goal of this work is to develop a concept for such a computer aided surface generation tool, that supports the new scanning technologies and meets the requirements in industry towards such a product. Therefore first, the requirements to be met by a surface reconstruction tool are determined. This marketing study has been done by analysing different departments of several companies. As a result, a catalogue of requirements is developed. The number of tasks and applications shows the importance of a fast and precise computer aided reconstruction tool in industry. The main result from the analysis is, that many important applications such as stereolithographie, copy milling etc. are based on triangular meshes or they are able to handle these polygonal surfaces. Secondly the digitizer, currently available on the market and used in industry are analysed. Any scanning system has its strength and weaknesses. A typical problem in digitizing is, that some areas of a model cannot be digitized due to occlusion or obstruction. The systems are also different in terms of accuracy, flexibility etc. The analysis of the systems leads to a second catalogue of requirements and tasks, which have to be solved in order to provide a complete and effective software tool. The analysis also shows, that the reconstruction problem cannot be solved fully automatically due to many limitations of the scanning technologies. Based on the two requirements, a concept for a software tool in order to process digitized data is developed and presented. The concept is restricted to the generation of polygonal surfaces. It combines automatic processes, such as the generation of triangular meshes from digitized data, as well as user interactive tools such as the reconstruction of sharp corners or the compensation of the scanning probe radius in tactile measured data. The most difficult problem in this reconstruction process is the automatic generation of a surface from discrete measured sample points. Hence, an algorithm for generating triangular meshes from digitized data has been developed. The algorithm is based on the principle of multiple view combination. The proposed approach is able to handle large numbers of data points (examples with up to 20 million data points were processed). Two pre-processing algorithm for triangle decimation and surface smoothing are also presented and part of the mesh generation process. Several practical examples, which show the effectiveness, robustness and reliability of the algorithm are presented

Automatic Linear and Curvilinear Mesh Generation Driven by Validity Fidelity and Topological Guarantees

Image-based geometric modeling and mesh generation play a critical role in computational biology and medicine. In this dissertation, a comprehensive computational framework for both guaranteed quality linear and high-order automatic mesh generation is presented. Starting from segmented images, a quality 2D/3D linear mesh is constructed. The boundary of the constructed mesh is proved to be homeomorphic to the object surface. In addition, a guaranteed dihedral angle bound of up to 19:47o for the output tetrahedra is provided. Moreover, user-specified guaranteed bounds on the distance between the boundaries of the mesh and the boundaries of the materials are allowed. The mesh contains a small number of mesh elements that comply with these guarantees, and the runtime is compatible in performance with other software. Then the curvilinear mesh generator allows for a transformation of straight-sided meshes to curvilinear meshes with C1 or C2 smooth boundaries while keeping all elements valid and with good quality as measured by their Jacobians. The mathematical proof shows that the meshes generated by our algorithm are guaranteed to be homeomorphic to the input images, and all the elements inside the meshes are guaranteed to be with good quality. Experimental results show that the mesh boundaries represent the objects\u27 shapes faithfully, and the accuracy of the representation is improved compared to the corresponding linear mesh

Curvature-enhanced Neural Subdivision

Subdivision is an important and widely used technique for obtaining dense meshes from coarse control (triangular) meshes for modelling and animation purposes. Most subdivision algorithms use engineered features (subdivisionrules). Recently, neural subdivision successfully applied machine learning to the subdivision of a triangular mesh. It uses a simple neural network to learn an optimal vertex positioning during a subdivision step. We propose an extension to the neural subdivision algorithm that introduces explicit curvature informationinto the network. This makes a larger amount of relevant information accessible which allows the network to yield better results. We demonstrate that this modification yields significant improvement over the original algorithm, in terms of both Hausdorff distance and mean squared error

Curvature-enhanced Neural Subdivision

Subdivision is an important and widely used technique for obtaining dense meshes from coarse control (triangular) meshes for modelling and animation purposes. Most subdivision algorithms use engineered features (subdivisionrules). Recently, neural subdivision successfully applied machine learning to the subdivision of a triangular mesh. It uses a simple neural network to learn an optimal vertex positioning during a subdivision step. We propose an extension to the neural subdivision algorithm that introduces explicit curvature informationinto the network. This makes a larger amount of relevant information accessible which allows the network to yield better results. We demonstrate that this modification yields significant improvement over the original algorithm, in terms of both Hausdorff distance and mean squared error

Surface segmentation for improved remeshing

Many remeshing techniques sample the input surface in a meaningful way and then triangulate the samples to produce an output triangulated mesh. One class of methods samples in a parametrization of the surface. Another class samples directly on the surface. These latter methods must have sufficient density of samples to achieve outputs that are homeomorphic to the input. In many datasets samples must be very dense even in some nearly planar regions due to small local feature size. We present an isotropic remeshing algorithm called κCVT that achieves topological correctness while sampling sparsely in all flat regions, regardless of local feature size. This is accomplished by segmenting the surface, remeshing the segmented subsurfaces individually and then stitching them back together. We show that κCVT produces quality meshes using fewer triangles than other methods. The output quality meshes are both homeomorphic and geometrically close to the input surface.postprin