3D Reconstruction Using High Resolution Implicit Surface Representations and Memory Management Strategies

La disponibilité de capteurs de numérisation 3D rapides et précis a permis de capturer de très grands ensembles de points à la surface de différents objets qui véhiculent la géométrie des objets. La métrologie appliquée consiste en l'application de mesures dans différents domaines tels que le contrôle qualité, l'inspection, la conception de produits et la rétroingénierie. Une fois que le nuage de points 3D non organisés couvrant toute la surface de l'objet a été capturé, un modèle de la surface doit être construit si des mesures métrologiques doivent être effectuées sur l'objet. Dans la reconstruction 3D en temps réel, à l'aide de scanners 3D portables, une représentation de surface implicite très efficace est le cadre de champ vectoriel, qui suppose que la surface est approchée par un plan dans chaque voxel. Le champ vectoriel contient la normale à la surface et la matrice de covariance des points tombant à l'intérieur d'un voxel. L'approche globale proposée dans ce projet est basée sur le cadre Vector Field. Le principal problème abordé dans ce projet est la résolution de l'incrément de consommation de mémoire et la précision du modèle reconstruit dans le champ vectoriel. Ce tte approche effectue une sélection objective de la taille optimale des voxels dans le cadre de champ vectoriel pour maintenir la consommation de mémoire aussi faible que possible et toujours obtenir un modèle précis de la surface. De plus, un ajustement d e surface d'ordre élevé est utilisé pour augmenter la précision du modèle. Étant donné que notre approche ne nécessite aucune paramétrisation ni calcul complexe, et qu'au lieu de travailler avec chaque point, nous travaillons avec des voxels dans le champ vectoriel, cela réduit la complexité du calcul.The availability of fast and accurate 3D scanning sensors has made it possible to capture very large sets of points at the surface of different objects that convey the geometry of the objects. A pplied metrology consists in the application of measurements in different fields such as quality control, inspection, product design and reverse engineering. Once the cloud of unorganized 3D points covering the entire surface of the object has been capture d, a model of the surface must be built if metrologic measurements are to be performed on the object. In realtime 3D reconstruction, using handheld 3D scanners a very efficient implicit surface representation is the Vector Field framework, which assumes that the surface is approximated by a plane in each voxel. The vector field contains the normal to the surface and the covariance matrix of the points falling inside a voxel. The proposed global approach in this project is based on the Vector Field framew ork. The main problem addressed in this project is solving the memory consumption increment and the accuracy of the reconstructed model in the vector field. This approach performs an objective selection of the optimal voxels size in the vector field frame work to keep the memory consumption as low as possible and still achieve an accurate model of the surface. Moreover, a highorder surface fitting is used to increase the accuracy of the model. Since our approach do not require any parametrization and compl ex calculation, and instead of working with each point we are working with voxels in the vector field, then it reduces the computational complexity

Memetic electromagnetism algorithm for surface reconstruction with rational bivariate Bernstein basis functions

Surface reconstruction is a very important issue with outstanding applications in fields such as medical imaging (computer tomography, magnetic resonance), biomedical engineering (customized prosthesis and medical implants), computer-aided design and manufacturing (reverse engineering for the automotive, aerospace and shipbuilding industries), rapid prototyping (scale models of physical parts from CAD data), computer animation and film industry (motion capture, character modeling), archaeology (digital representation and storage of archaeological sites and assets), virtual/augmented reality, and many others. In this paper we address the surface reconstruction problem by using rational Bézier surfaces. This problem is by far more complex than the case for curves we solved in a previous paper. In addition, we deal with data points subjected to measurement noise and irregular sampling, replicating the usual conditions of real-world applications. Our method is based on a memetic approach combining a powerful metaheuristic method for global optimization (the electromagnetism algorithm) with a local search method. This method is applied to a benchmark of five illustrative examples exhibiting challenging features. Our experimental results show that the method performs very well, and it can recover the underlying shape of surfaces with very good accuracy.This research is kindly supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project #TIN2012-30768, Toho University, and the University of Cantabria. The authors are particularly grateful to the Department of Information Science of Toho University for all the facilities given to carry out this work. We also thank the Editor and the two anonymous reviewers who helped us to improve our paper with several constructive comments and suggestions

A framework for hull form reverse engineering and geometry integration into numerical simulations

The thesis presents a ship hull form specific reverse engineering and CAD integration framework. The reverse engineering part proposes three alternative suitable reconstruction approaches namely curves network, direct surface fitting, and triangulated surface reconstruction. The CAD integration part includes surface healing, region identification, and domain preparation strategies which used to adapt the CAD model to downstream application requirements. In general, the developed framework bridges a point cloud and a CAD model obtained from IGES and STL file into downstream applications

Feature-Based Models for Three-Dimensional Data Fitting.

There are numerous techniques available for fitting a surface to any supplied data set. The feature-based modeling technique takes advantage of the known, geometric shape of the data by deforming a model having this generic shape to approximate the data. The model is constructed as a rational B-spline surface with characteristic features superimposed on its definition. The first step in the fitting process is to align the model with a data set using the center of mass, principal axes and/or landmarks. Using this initial orientation, the position, rotation and scale parameters are optimized using a Newton-type optimization of a least squares cost function. Once aligned, features embedded within the model, corresponding to pertinent characteristics of the shape, are used to improve the fit of the model to the data. Finally, the control vertex weights and positions of the rational B-spline model are optimized to approximate the data to within a specified tolerance. Since the characteristic features are defined within the model a creation, important measures are easily extracted from a data set, once fit. The feature-based modeling approach is demonstrated in two-dimensions by the fitting of five facial, silhouette profiles and in three-dimensions by the fitting of eleven human foot scans. The algorithm is tested for sensitivity to data distribution and structure and the extracted measures are tested for repeatability and accuracy. Limitations within the current implementation, future work and potential applications are also provided

Curve Skeleton and Moments of Area Supported Beam Parametrization in Multi-Objective Compliance Structural Optimization

This work addresses the end-to-end virtual automation of structural optimization up to the derivation of a parametric geometry model that can be used for application areas such as additive manufacturing or the verification of the structural optimization result with the finite element method. A holistic design in structural optimization can be achieved with the weighted sum method, which can be automatically parameterized with curve skeletonization and cross-section regression to virtually verify the result and control the local size for additive manufacturing. is investigated in general. In this paper, a holistic design is understood as a design that considers various compliances as an objective function. This parameterization uses the automated determination of beam parameters by so-called curve skeletonization with subsequent cross-section shape parameter estimation based on moments of area, especially for multi-objective optimized shapes. An essential contribution is the linking of the parameterization with the results of the structural optimization, e.g., to include properties such as boundary conditions, load conditions, sensitivities or even density variables in the curve skeleton parameterization. The parameterization focuses on guiding the skeletonization based on the information provided by the optimization and the finite element model. In addition, the cross-section detection considers circular, elliptical, and tensor product spline cross-sections that can be applied to various shape descriptors such as convolutional surfaces, subdivision surfaces, or constructive solid geometry. The shape parameters of these cross-sections are estimated using stiffness distributions, moments of area of 2D images, and convolutional neural networks with a tailored loss function to moments of area. Each final geometry is designed by extruding the cross-section along the appropriate curve segment of the beam and joining it to other beams by using only unification operations. The focus of multi-objective structural optimization considering 1D, 2D and 3D elements is on cases that can be modeled using equations by the Poisson equation and linear elasticity. This enables the development of designs in application areas such as thermal conduction, electrostatics, magnetostatics, potential flow, linear elasticity and diffusion, which can be optimized in combination or individually. Due to the simplicity of the cases defined by the Poisson equation, no experts are required, so that many conceptual designs can be generated and reconstructed by ordinary users with little effort. Specifically for 1D elements, a element stiffness matrices for tensor product spline cross-sections are derived, which can be used to optimize a variety of lattice structures and automatically convert them into free-form surfaces. For 2D elements, non-local trigonometric interpolation functions are used, which should significantly increase interpretability of the density distribution. To further improve the optimization, a parameter-free mesh deformation is embedded so that the compliances can be further reduced by locally shifting the node positions. Finally, the proposed end-to-end optimization and parameterization is applied to verify a linear elasto-static optimization result for and to satisfy local size constraint for the manufacturing with selective laser melting of a heat transfer optimization result for a heat sink of a CPU. For the elasto-static case, the parameterization is adjusted until a certain criterion (displacement) is satisfied, while for the heat transfer case, the manufacturing constraints are satisfied by automatically changing the local size with the proposed parameterization. This heat sink is then manufactured without manual adjustment and experimentally validated to limit the temperature of a CPU to a certain level.:TABLE OF CONTENT III I LIST OF ABBREVIATIONS V II LIST OF SYMBOLS V III LIST OF FIGURES XIII IV LIST OF TABLES XVIII 1. INTRODUCTION 1 1.1 RESEARCH DESIGN AND MOTIVATION 6 1.2 RESEARCH THESES AND CHAPTER OVERVIEW 9 2. PRELIMINARIES OF TOPOLOGY OPTIMIZATION 12 2.1 MATERIAL INTERPOLATION 16 2.2 TOPOLOGY OPTIMIZATION WITH PARAMETER-FREE SHAPE OPTIMIZATION 17 2.3 MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE WEIGHTED SUM METHOD 18 3. SIMULTANEOUS SIZE, TOPOLOGY AND PARAMETER-FREE SHAPE OPTIMIZATION OF WIREFRAMES WITH B-SPLINE CROSS-SECTIONS 21 3.1 FUNDAMENTALS IN WIREFRAME OPTIMIZATION 22 3.2 SIZE AND TOPOLOGY OPTIMIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 27 3.3 PARAMETER-FREE SHAPE OPTIMIZATION EMBEDDED IN SIZE OPTIMIZATION 32 3.4 WEIGHTED SUM SIZE AND TOPOLOGY OPTIMIZATION 36 3.5 CROSS-SECTION COMPARISON 39 4. NON-LOCAL TRIGONOMETRIC INTERPOLATION IN TOPOLOGY OPTIMIZATION 41 4.1 FUNDAMENTALS IN MATERIAL INTERPOLATIONS 43 4.2 NON-LOCAL TRIGONOMETRIC SHAPE FUNCTIONS 45 4.3 NON-LOCAL PARAMETER-FREE SHAPE OPTIMIZATION WITH TRIGONOMETRIC SHAPE FUNCTIONS 49 4.4 NON-LOCAL AND PARAMETER-FREE MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION 54 5. FUNDAMENTALS IN SKELETON GUIDED SHAPE PARAMETRIZATION IN TOPOLOGY OPTIMIZATION 58 5.1 SKELETONIZATION IN TOPOLOGY OPTIMIZATION 61 5.2 CROSS-SECTION RECOGNITION FOR IMAGES 66 5.3 SUBDIVISION SURFACES 67 5.4 CONVOLUTIONAL SURFACES WITH META BALL KERNEL 71 5.5 CONSTRUCTIVE SOLID GEOMETRY 73 6. CURVE SKELETON GUIDED BEAM PARAMETRIZATION OF TOPOLOGY OPTIMIZATION RESULTS 75 6.1 FUNDAMENTALS IN SKELETON SUPPORTED RECONSTRUCTION 76 6.2 SUBDIVISION SURFACE PARAMETRIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 78 6.3 CURVE SKELETONIZATION TAILORED TO TOPOLOGY OPTIMIZATION WITH PRE-PROCESSING 82 6.4 SURFACE RECONSTRUCTION USING LOCAL STIFFNESS DISTRIBUTION 86 7. CROSS-SECTION SHAPE PARAMETRIZATION FOR PERIODIC B-SPLINES 96 7.1 PRELIMINARIES IN B-SPLINE CONTROL GRID ESTIMATION 97 7.2 CROSS-SECTION EXTRACTION OF 2D IMAGES 101 7.3 TENSOR SPLINE PARAMETRIZATION WITH MOMENTS OF AREA 105 7.4 B-SPLINE PARAMETRIZATION WITH MOMENTS OF AREA GUIDED CONVOLUTIONAL NEURAL NETWORK 110 8. FULLY AUTOMATED COMPLIANCE OPTIMIZATION AND CURVE-SKELETON PARAMETRIZATION FOR A CPU HEAT SINK WITH SIZE CONTROL FOR SLM 115 8.1 AUTOMATED 1D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINED SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 118 8.2 AUTOMATED 2D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINT SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 120 8.3 USING THE HEAT SINK PROTOTYPES COOLING A CPU 123 9. CONCLUSION 127 10. OUTLOOK 131 LITERATURE 133 APPENDIX 147 A PREVIOUS STUDIES 147 B CROSS-SECTION PROPERTIES 149 C CASE STUDIES FOR THE CROSS-SECTION PARAMETRIZATION 155 D EXPERIMENTAL SETUP 15

A regularization approach for reconstruction and visualization of 3-D data

Esta tesis trata sobre reconstrucción de superficies a partir de imágenes de rango utilizando algunas extensiones de la Regularización de Tikhonov, que produce Splines aplicables a datos en n dimensiones. La idea central es que estos splines se pueden obtener mediante la teoría de regularización, utilizando un equilibrio entre la suavidad y la fidelidad a los datos, por tanto, serán aplicables tanto en la interpolación como en la aproximación de datos exactos o ruidosos. En esta tesis proponemos un enfoque variacional que incluye los datos e información a priori acerca de la solución, dada en forma de funcionales. Solucionamos problemas de optimización que resultan ser una extensión de la teoría de Tikhonov, con el propósito de incluir funcionales con propiedades locales y globales que pueden ser ajustadas mediante parámetros de regularización. El a priori es analizado en términos de las propiedades físicas y geométricas de los funcionales para luego ser agregados a la formulación variacional. Los resultados obtenidos se prueban con datos para reconstrucción de superficies, mostrando notables propiedades de reproducción y aproximación. En particular, utilizamos la reconstrucción de superficies para ilustrar las aplicaciones prácticas, pero nuestro enfoque tiene muchas más aplicaciones. En el centro de nuestra propuesta esta la teoría general de problemas inversos y las aplicaciones de algunas ideas provenientes del análisis funcional. Los splines que obtenemos son combinaciones lineales de las soluciones fundamentales de ciertos operadores en derivadas parciales, frecuentes en la teoría de la elasticidad y no se hace ninguna suposición previa sobre el modelo estadístico de los datos de entrada, de manera que se pueden tomar en términos de una inferencia estadística no paramétrica. Estos splines son implementables en una forma muy estable y se pueden aplicar en problemas de interpolación y suavizado. / Abstract: This thesis is about surface reconstruction from range images using some extensions of Tikhonov regularization that produces splines applicable on n-dimensional data. The central idea is that these splines can be obtained by regularization theory, using a trade-off between fidelity to data and smoothness properties; as a consequence, they are applicable both in interpolation and approximation of exact or noisy data. We propose a variational framework that includes data and a priori information about the solution, given in the form of functionals. We solve optimization problems which are extensions of Tikhonov theory, in order to include functionals with local and global features that can be tuned by regularization parameters. The a priori is thought in terms of geometric and physical properties of functionals and then added to the variational formulation. The results obtained are tested on data for surface reconstruction, showing remarkable reproducing and approximating properties. In this case we use surface reconstruction to illustrate practical applications; nevertheless, our approach has many other applications. In the core of our approach is the general theory of inverse problems and the application of some abstract ideas from functional analysis. The splines obtained are linear combinations of certain fundamental solutions of partial differential operators from elasticity theory and no prior assumption is made on a statistical model for the input data, so it can be thought in terms of nonparametric statistical inference. They are implementable in a very stable form and can be applied for both interpolation and smoothing problems.Doctorad

High-performance geometric vascular modelling

Image-based high-performance geometric vascular modelling and reconstruction is an essential component of computer-assisted surgery on the diagnosis, analysis and treatment of cardiovascular diseases. However, it is an extremely challenging task to efficiently reconstruct the accurate geometric structures of blood vessels out of medical images. For one thing, the shape of an individual section of a blood vessel is highly irregular because of the squeeze of other tissues and the deformation caused by vascular diseases. For another, a vascular system is a very complicated network of blood vessels with different types of branching structures. Although some existing vascular modelling techniques can reconstruct the geometric structure of a vascular system, they are either time-consuming or lacking sufficient accuracy. What is more, these techniques rarely consider the interior tissue of the vascular wall, which consists of complicated layered structures. As a result, it is necessary to develop a better vascular geometric modelling technique, which is not only of high performance and high accuracy in the reconstruction of vascular surfaces, but can also be used to model the interior tissue structures of the vascular walls.This research aims to develop a state-of-the-art patient-specific medical image-based geometric vascular modelling technique to solve the above problems. The main contributions of this research are:- Developed and proposed the Skeleton Marching technique to reconstruct the geometric structures of blood vessels with high performance and high accuracy. With the proposed technique, the highly complicated vascular reconstruction task is reduced to a set of simple localised geometric reconstruction tasks, which can be carried out in a parallel manner. These locally reconstructed vascular geometric segments are then combined together using shape-preserving blending operations to faithfully represent the geometric shape of the whole vascular system.- Developed and proposed the Thin Implicit Patch method to realistically model the interior geometric structures of the vascular tissues. This method allows the multi-layer interior tissue structures to be embedded inside the vascular wall to illustrate the geometric details of the blood vessel in real world

Surface Deformation Potentials on Meshes for Computer Graphics and Visualization

Shape deformation models have been used in computer graphics primarily to describe the dynamics of physical deformations like cloth draping, collisions of elastic bodies, fracture, or animation of hair. Less frequent is their application to problems not directly related to a physical process. In this thesis we apply deformations to three problems in computer graphics that do not correspond to physical deformations. To this end, we generalize the physical model by modifying the energy potential. Originally, the energy potential amounts to the physical work needed to deform a body from its rest state into a given configuration and relates material strain to internal restoring forces that act to restore the original shape. For each of the three problems considered, this potential is adapted to reflect an application specific notion of shape. Under the influence of further constraints, our generalized deformation results in shapes that balance preservation of certain shape properties and application specific objectives similar to physical equilibrium states. The applications discussed in this thesis are surface parameterization, interactive shape editing and automatic design of panorama maps. For surface parameterization, we interpret parameterizations over a planar domain as deformations from a flat initial configuration onto a given surface. In this setting, we review existing parameterization methods by analyzing properties of their potential functions and derive potentials accounting for distortion of geometric properties. Interactive shape editing allows an untrained user to modify complex surfaces, be simply grabbing and moving parts of interest. A deformation model interactively extrapolates the transformation from those parts to the rest of the surface. This thesis proposes a differential shape representation for triangle meshes leading to a potential that can be optimized interactively with a simple, tailored algorithm. Although the potential is not physically accurate, it results in intuitive deformation behavior and can be parameterized to account for different material properties. Panorama maps are blends between landscape illustrations and geographic maps that are traditionally painted by an artist to convey geographic surveyknowledge on public places like ski resorts or national parks. While panorama maps are not drawn to scale, the shown landscape remains recognizable and the observer can easily recover details necessary for self location and orientation. At the same time, important features as trails or ski slopes appear not occluded and well visible. This thesis proposes the first automatic panorama generation method. Its basis is again a surface deformation, that establishes the necessary compromise between shape preservation and feature visibility.Potentiale zur Flächendeformation auf Dreiecksnetzen für Anwendungen in der Computergrafik und Visualisierung Deformationsmodelle werden in der Computergrafik bislang hauptsächlich eingesetzt, um die Dynamik physikalischer Deformationsprozesse zu modellieren. Gängige Beispiele sind Bekleidungssimulationen, Kollisionen elastischer Körper oder Animation von Haaren und Frisuren. Deutlich seltener ist ihre Anwendung auf Probleme, die nicht direkt physikalischen Prozessen entsprechen. In der vorliegenden Arbeit werden Deformationsmodelle auf drei Probleme der Computergrafik angewandt, die nicht unmittelbar einem physikalischen Deformationsprozess entsprechen. Zu diesem Zweck wird das physikalische Modell durch eine passende Änderung der potentiellen Energie verallgemeinert. Die potentielle Energie entspricht normalerweise der physikalischen Arbeit, die aufgewendet werden muss, um einen Körper aus dem Ruhezustand in eine bestimmte Konfiguration zu verformen. Darüber hinaus setzt sie die aktuelle Verformung in Beziehung zu internen Spannungskräften, die wirken um die ursprüngliche Form wiederherzustellen. In dieser Arbeit passen wir für jedes der drei betrachteten Problemfelder die potentielle Energie jeweils so an, dass sie eine anwendungsspezifische Definition von Form widerspiegelt. Unter dem Einfluss weiterer Randbedingungen führt die so verallgemeinerte Deformation zu einer Fläche, die eine Balance zwischen der Erhaltung gewisser Formeigenschaften und Zielvorgaben der Anwendung findet. Diese Balance entspricht dem Equilibrium einer physikalischen Deformation. Die drei in dieser Arbeit diskutierten Anwendungen sind Oberflächenparameterisierung, interaktives Bearbeiten von Flächen und das vollautomatische Erzeugen von Panoramakarten im Stile von Heinrich Berann. Zur Oberflächenparameterisierung interpretieren wir Parameterisierungen über einem flachen Parametergebiet als Deformationen, die ein ursprünglich ebenes Flächenstück in eine gegebene Oberfläche verformen. Innerhalb dieses Szenarios vergleichen wir dann existierende Methoden zur planaren Parameterisierung, indem wir die resultierenden potentiellen Energien analysieren, und leiten weitere Potentiale her, die die Störung geometrischer Eigenschaften wie Fläche und Winkel erfassen. Verfahren zur interaktiven Flächenbearbeitung ermöglichen schnelle und intuitive Änderungen an einer komplexen Oberfläche. Dazu wählt der Benutzer Teile der Fläche und bewegt diese durch den Raum. Ein Deformationsmodell extrapoliert interaktiv die Transformation der gewählten Teile auf die restliche Fläche. Diese Arbeit stellt eine neue differentielle Flächenrepräsentation für diskrete Flächen vor, die zu einem einfach und interaktiv zu optimierendem Potential führt. Obwohl das vorgeschlagene Potential nicht physikalisch korrekt ist, sind die resultierenden Deformationen intuitiv. Mittels eines Parameters lassen sich außerdem bestimmte Materialeigenschaften einstellen. Panoramakarten im Stile von Heinrich Berann sind eine Verschmelzung von Landschaftsillustration und geographischer Karte. Traditionell werden sie so von Hand gezeichnet, dass bestimmt Merkmale wie beispielsweise Skipisten oder Wanderwege in einem Gebiet unverdeckt und gut sichtbar bleiben, was große Kunstfertigkeit verlangt. Obwohl diese Art der Darstellung nicht maßstabsgetreu ist, sind Abweichungen auf den ersten Blick meistens nicht zu erkennen. Dadurch kann der Betrachter markante Details schnell wiederfinden und sich so innerhalb des Gebietes orientieren. Diese Arbeit stellt das erste, vollautomatische Verfahren zur Erzeugung von Panoramakarten vor. Grundlage ist wiederum eine verallgemeinerte Oberflächendeformation, die sowohl auf Formerhaltung als auch auf die Sichtbarkeit vorgegebener geographischer Merkmale abzielt