Nonlinear Spectral Geometry Processing via the TV Transform

We introduce a novel computational framework for digital geometry processing, based upon the derivation of a nonlinear operator associated to the total variation functional. Such operator admits a generalized notion of spectral decomposition, yielding a sparse multiscale representation akin to Laplacian-based methods, while at the same time avoiding undesirable over-smoothing effects typical of such techniques. Our approach entails accurate, detail-preserving decomposition and manipulation of 3D shape geometry while taking an especially intuitive form: non-local semantic details are well separated into different bands, which can then be filtered and re-synthesized with a straightforward linear step. Our computational framework is flexible, can be applied to a variety of signals, and is easily adapted to different geometry representations, including triangle meshes and point clouds. We showcase our method throughout multiple applications in graphics, ranging from surface and signal denoising to detail transfer and cubic stylization.Comment: 16 pages, 20 figure

Geometric Surface Processing and Virtual Modeling

In this work we focus on two main topics "Geometric Surface Processing" and "Virtual Modeling". The inspiration and coordination for most of the research work contained in the thesis has been driven by the project New Interactive and Innovative Technologies for CAD (NIIT4CAD), funded by the European Eurostars Programme. NIIT4CAD has the ambitious aim of overcoming the limitations of the traditional approach to surface modeling of current 3D CAD systems by introducing new methodologies and technologies based on subdivision surfaces in a new virtual modeling framework. These innovations will allow designers and engineers to transform quickly and intuitively an idea of shape in a high-quality geometrical model suited for engineering and manufacturing purposes. One of the objective of the thesis is indeed the reconstruction and modeling of surfaces, representing arbitrary topology objects, starting from 3D irregular curve networks acquired through an ad-hoc smart-pen device. The thesis is organized in two main parts: "Geometric Surface Processing" and "Virtual Modeling". During the development of the geometric pipeline in our Virtual Modeling system, we faced many challenges that captured our interest and opened new areas of research and experimentation. In the first part, we present these theories and some applications to Geometric Surface Processing. This allowed us to better formalize and give a broader understanding on some of the techniques used in our latest advancements on virtual modeling and surface reconstruction. The research on both topics led to important results that have been published and presented in articles and conferences of international relevance

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

Higher-order nonlinear priors for surface reconstruction

Journal ArticleAbstract-For surface reconstruction problems with noisy and incomplete range data, a Bayesian estimation approach can improve the overall quality of the surfaces. The Bayesian approach to surface estimation relies on a likelihood term, which ties the surface estimate to the input data, and the prior, which ensures surface smoothness or continuity. This paper introduces a new high-order, nonlinear prior for surface reconstruction. The proposed prior can smooth complex, noisy surfaces, while preserving sharp, geometric features, and it is a natural generalization of edge-preserving methods in image processing, such as anisotropic diffusion. An exact solution would require solving a fourth-order partial differential equation (PDE), which can be difficult with conventional numerical techniques. Our approach is to solve a cascade system of two second-order PDEs, which resembles the original fourth-order system. This strategy is based on the observation that the generalization of image processing to surfaces entails filtering the surface normals. We solve one PDE for processing the normals and one for refitting the surface to the normals. Furthermore, we implement the associated surface deformations using level sets. Hence, the algorithm can accommodate very complex shapes with arbitrary and changing topologies. This paper gives the mathematical formulation and describes the numerical algorithms. We also show results using range and medical data

Adaptive Methods for Point Cloud and Mesh Processing

Point clouds and 3D meshes are widely used in numerous applications ranging from games to virtual reality to autonomous vehicles. This dissertation proposes several approaches for noise removal and calibration of noisy point cloud data and 3D mesh sharpening methods. Order statistic filters have been proven to be very successful in image processing and other domains as well. Different variations of order statistics filters originally proposed for image processing are extended to point cloud filtering in this dissertation. A brand-new adaptive vector median is proposed in this dissertation for removing noise and outliers from noisy point cloud data. The major contributions of this research lie in four aspects: 1) Four order statistic algorithms are extended, and one adaptive filtering method is proposed for the noisy point cloud with improved results such as preserving significant features. These methods are applied to standard models as well as synthetic models, and real scenes, 2) A hardware acceleration of the proposed method using Microsoft parallel pattern library for filtering point clouds is implemented using multicore processors, 3) A new method for aerial LIDAR data filtering is proposed. The objective is to develop a method to enable automatic extraction of ground points from aerial LIDAR data with minimal human intervention, and 4) A novel method for mesh color sharpening using the discrete Laplace-Beltrami operator is proposed. Median and order statistics-based filters are widely used in signal processing and image processing because they can easily remove outlier noise and preserve important features. This dissertation demonstrates a wide range of results with median filter, vector median filter, fuzzy vector median filter, adaptive mean, adaptive median, and adaptive vector median filter on point cloud data. The experiments show that large-scale noise is removed while preserving important features of the point cloud with reasonable computation time. Quantitative criteria (e.g., complexity, Hausdorff distance, and the root mean squared error (RMSE)), as well as qualitative criteria (e.g., the perceived visual quality of the processed point cloud), are employed to assess the performance of the filters in various cases corrupted by different noisy models. The adaptive vector median is further optimized for denoising or ground filtering aerial LIDAR data point cloud. The adaptive vector median is also accelerated on multi-core CPUs using Microsoft Parallel Patterns Library. In addition, this dissertation presents a new method for mesh color sharpening using the discrete Laplace-Beltrami operator, which is an approximation of second order derivatives on irregular 3D meshes. The one-ring neighborhood is utilized to compute the Laplace-Beltrami operator. The color for each vertex is updated by adding the Laplace-Beltrami operator of the vertex color weighted by a factor to its original value. Different discretizations of the Laplace-Beltrami operator have been proposed for geometrical processing of 3D meshes. This work utilizes several discretizations of the Laplace-Beltrami operator for sharpening 3D mesh colors and compares their performance. Experimental results demonstrated the effectiveness of the proposed algorithms

Ship Hull Representation by Non-Uniform Rational B-Spline Surface Patches

The purpose of this work is to propose a new method for representing the ship hull shape with mathematic surfaces so that geometric data can be generated for any point on the hull where required to assist the production process. An extensive survey of previous work is presented covering both the use of parametric curves and surfaces to model the ship hull and also the most relevant software systems developed for that purpose. The main methods and algorithms available for the generation and edition of curves and surfaces are presented and compared taking into consideration the intended application. From the analysis of the formulations available it was concluded that the most adequate one, which however had not yet been extensively used to model ship hulls was the Non-Uniform Rational B-Splines (NURBS), due to the potential of their capability to represent exactly conic curves and surfaces. Therefore these surfaces were selected as the basis of the method developed in this thesis. A procedure is proposed for the representation of a given hull form in a two step approach, creating first a wireframe model over which the surface patches are generated. Both curves and surfaces are based on the NURBS formulation. To create the wireframe model, first a set of longitudinal boundary lines is selected, dividing the surface into areas of similar shape. Then, these lines are fitted by curves and faired to some extent. Next, transverse sections are defined and split by the boundary lines. Surface patches are then generated over the transverse section curves within the limits of each patch. Finally, to obtain the traditional representation of the ship surface by transverse sections, buttocks and waterlines, contour lines are generated for constant values of x, y and z coordinates. A computer system has been developed incorporating an interface that allows the visualization of the curves and surfaces being modeled. The system incorporates several algorithms for generation and edition of curves and surfaces, in addition to the main contribution of this thesis which is the use of NURBS to represent the ship hull surface. The system also incorporates curve and surface analysis tools and some basic fairing algorithms so that during the several steps of the creation of the model, the fairness of the curves and surfaces can be evaluated and improved to some extent. The procedure is tested and compared with an existing commercial system through some application examples, of a complete hull and in more detail in the bow region, showing that good results can be obtained with the system presented here

Thermal-structural combined loads design criteria study

A study was conducted to determine methodology for combining thermal structural loads and assessing the effects of the combined loads on the design of a thermal protection system and a hot structure of a high cross range delta wing space shuttle orbiter vehicle. The study presents guidelines for establishing a basis for predicting thermal and pressure environments and for determining limit and ultimate design loads on the vehicle during reentry. Limit trajectories were determined by using dispersions on a representative nominal mission and system parameters expected during the life of the vehicle. Nine chosen locations on the vehicle surface having TPS or hot structures were examined, and weight sensitivity analyses were performed for each location

Integrated modeling and analysis methodologies for architecture-level vehicle design.

In order to satisfy customer expectations, a ground vehicle must be designed to meet a broad range of performance requirements. A satisfactory vehicle design process implements a set of requirements reflecting necessary, but perhaps not sufficient conditions for assuring success in a highly competitive market. An optimal architecture-level vehicle design configuration is one of the most important of these requirements. A basic layout that is efficient and flexible permits significant reductions in the time needed to complete the product development cycle, with commensurate reductions in cost. Unfortunately, architecture-level design is the most abstract phase of the design process. The high-level concepts that characterize these designs do not lend themselves to traditional analyses normally used to characterize, assess, and optimize designs later in the development cycle. This research addresses the need for architecture-level design abstractions that can be used to support ground vehicle development. The work begins with a rigorous description of hierarchical function-based abstractions representing not the physical configuration of the elements of a vehicle, but their function within the design space. The hierarchical nature of the abstractions lends itself to object orientation - convenient for software implementation purposes - as well as description of components, assemblies, feature groupings based on non-structural interactions, and eventually, full vehicles. Unlike the traditional early-design abstractions, the completeness of our function-based hierarchical abstractions, including their interactions, allows their use as a starting point for the derivation of analysis models. The scope of the research in this dissertation includes development of meshing algorithms for abstract structural models, a rigid-body analysis engine, and a fatigue analysis module. It is expected that the results obtained in this study will move systematic design and analysis to the earliest phases of the vehicle development process, leading to more highly optimized architectures, and eventually, better ground vehicles. This work shows that architecture level abstractions in many cases are better suited for life cycle support than geometric CAD models. Finally, substituting modeling, simulation, and optimization for intuition and guesswork will do much to mitigate the risk inherent in large projects by minimizing the possibility of incorporating irrevocably compromised architecture elements into a vehicle design that no amount of detail-level reengineering can undo