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

Ordered Statistics Vertex Extraction and Tracing Algorithm (OSVETA)

We propose an algorithm for identifying vertices from three dimensional (3D) meshes that are most important for a geometric shape creation. Extracting such a set of vertices from a 3D mesh is important in applications such as digital watermarking, but also as a component of optimization and triangulation. In the first step, the Ordered Statistics Vertex Extraction and Tracing Algorithm (OSVETA) estimates precisely the local curvature, and most important topological features of mesh geometry. Using the vertex geometric importance ranking, the algorithm traces and extracts a vector of vertices, ordered by decreasing index of importance.Comment: Accepted for publishing and Copyright transfered to Advances in Electrical and Computer Engineering, November 23th 201

A Comparative Study on Polygonal Mesh Simplification Algorithms

Polygonal meshes are a common way of representing three dimensional surface models in many different areas of computer graphics and geometry processing. However, with the evolution of the technology, polygonal models are becoming more and more complex. As the complexity of the models increase, the visual approximation to the real world objects get better but there is a trade-off between the cost of processing these models and better visual approximation. In order to reduce this cost, the number of polygons in a model can be reduced by mesh simplification algorithms. These algorithms are widely used such that nearly all of the popular mesh editing libraries include at least one of them. In this work, polygonal simplification algorithms that are embedded in open source libraries: CGAL, VTK and OpenMesh are compared with the Metro geometric error measuring tool. By this way we try to supply a guidance for developers for publicly available mesh libraries in order to implement polygonal mesh simplification

Efficient Decimation of Polygonal Models Using Normal Field Deviation

A simple and robust greedy algorithm has been proposed for efficient and quality decimation of polygonal models. The performance of a simplification algorithm depends on how the local geometric deviation caused by a local decimation operation is measured. As normal field of a surface plays key role in its visual appearance, exploiting the local normal field deviation in a novel way, a new measure of geometric fidelity has been introduced. This measure has the potential to identify and preserve the salient features of a surface model automatically. The resulting algorithm is simple to implement, produces approximations of better quality and is efficient in running time. Subjective and objective comparisons validate the assertion. It is suitable for applications where the focus is better speed-quality trade-off, and simplification is used as a processing step in other algorithms

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

Feature preserving decimation of urban meshes

1 online resource (vii, 72 pages) : illustrations (chiefly colour), charts (chiefly colour)Includes abstract.Includes bibliographical references (pages 65-72).Commercial buildings as well as residential houses represent core structures of any modern day urban or semi-urban areas. Consequently, 3D models of urban buildings are of paramount importance to a majority of digital urban applications such as city planning, 3D mapping and navigation, video games and movies, among others. However, current studies suggest that existing 3D modeling approaches often involve high computational cost and large storage volumes for processing the geometric details of the buildings. Therefore, it is essential to generate concise digital representations of urban buildings from the 3D measurements or images, so that the acquired information can be efficiently utilized for various urban applications. Such concise representations, often referred to as “lightweight” models, strive to capture the details of the physical objects with less computational storage. Furthermore, lightweight models consume less bandwidth for online applications and facilitate accelerated visualizations. In this thesis, we provide an assessment study on state-of-the-art data structures for storing lightweight urban buildings. Then we propose a method to generate lightweight yet highly detailed 3D building models from LiDAR scans. The lightweight modeling pipeline comprises the following stages: mesh reconstruction, feature points detection and mesh decimation through gradient structure tensors. The gradient of each vertex of the reconstructed mesh is obtained by estimating the vertex confidence through eigen analysis and further encoded into a 3 X 3 structure tensor. We analyze the eigenvalues of structure tensor representing gradient variations and use it to classify vertices into various feature classes, e.g., edges, and corners. While decimating the mesh, fea ture points are preserved through a mean cost-based edge collapse operation. The experiments on different building facade models show that our method is effective in generating simplified models with a trade-off between simplification and accuracy