A Low-Dimensional Representation for Robust Partial Isometric Correspondences Computation

Intrinsic isometric shape matching has become the standard approach for pose invariant correspondence estimation among deformable shapes. Most existing approaches assume global consistency, i.e., the metric structure of the whole manifold must not change significantly. While global isometric matching is well understood, only a few heuristic solutions are known for partial matching. Partial matching is particularly important for robustness to topological noise (incomplete data and contacts), which is a common problem in real-world 3D scanner data. In this paper, we introduce a new approach to partial, intrinsic isometric matching. Our method is based on the observation that isometries are fully determined by purely local information: a map of a single point and its tangent space fixes an isometry for both global and the partial maps. From this idea, we develop a new representation for partial isometric maps based on equivalence classes of correspondences between pairs of points and their tangent spaces. From this, we derive a local propagation algorithm that find such mappings efficiently. In contrast to previous heuristics based on RANSAC or expectation maximization, our method is based on a simple and sound theoretical model and fully deterministic. We apply our approach to register partial point clouds and compare it to the state-of-the-art methods, where we obtain significant improvements over global methods for real-world data and stronger guarantees than previous heuristic partial matching algorithms.Comment: 17 pages, 12 figure

Learning-based intrinsic reflectional symmetry detection

Reflectional symmetry is a ubiquitous pattern in nature. Previous works usually solve this problem by voting or sampling, suffering from high computational cost and randomness. In this paper, we propose a learning-based approach to intrinsic reflectional symmetry detection. Instead of directly finding symmetric point pairs, we parametrize this self-isometry using a functional map matrix, which can be easily computed given the signs of Laplacian eigenfunctions under the symmetric mapping. Therefore, we manually label the eigenfunction signs for a variety of shapes and train a novel neural network to predict the sign of each eigenfunction under symmetry. Our network aims at learning the global property of functions and consequently converts the problem defined on the manifold to the functional domain. By disentangling the prediction of the matrix into separated bases, our method generalizes well to new shapes and is invariant under perturbation of eigenfunctions. Through extensive experiments, we demonstrate the robustness of our method in challenging cases, including different topology and incomplete shapes with holes. By avoiding random sampling, our learning-based algorithm is over 20 times faster than state-of-the-art methods, and meanwhile, is more robust, achieving higher correspondence accuracy in commonly used metrics

Shape Completion from a Single RGBD Image

We present a novel approach for constructing a complete 3D model for an object from a single RGBD image. Given an image of an object segmented from the background, a collection of 3D models of the same category are non-rigidly aligned with the input depth, to compute a rough initial result. A volumetric-patch-based optimization algorithm is then performed to refine the initial result to generate a 3D model that not only is globally consistent with the overall shape expected from the input image but also possesses geometric details similar to those in the input image. The optimization with a set of high-level constraints, such as visibility, surface confidence and symmetry, can achieve more robust and accurate completion over state-of-the art techniques. We demonstrate the efficiency and robustness of our approach with multiple categories of objects with various geometries and details, including busts, chairs, bikes, toys, vases and tables

Structure-aware content creation : detection, retargeting and deformation

Nowadays, access to digital information has become ubiquitous, while three-dimensional visual representation is becoming indispensable to knowledge understanding and information retrieval. Three-dimensional digitization plays a natural role in bridging connections between the real and virtual world, which prompt the huge demand for massive three-dimensional digital content. But reducing the effort required for three-dimensional modeling has been a practical problem, and long standing challenge in compute graphics and related fields. In this thesis, we propose several techniques for lightening up the content creation process, which have the common theme of being structure-aware, ie maintaining global relations among the parts of shape. We are especially interested in formulating our algorithms such that they make use of symmetry structures, because of their concise yet highly abstract principles are universally applicable to most regular patterns. We introduce our work from three different aspects in this thesis. First, we characterized spaces of symmetry preserving deformations, and developed a method to explore this space in real-time, which significantly simplified the generation of symmetry preserving shape variants. Second, we empirically studied three-dimensional offset statistics, and developed a fully automatic retargeting application, which is based on verified sparsity. Finally, we made step forward in solving the approximate three-dimensional partial symmetry detection problem, using a novel co-occurrence analysis method, which could serve as the foundation to high-level applications.Jetzt hat die Zugang zu digitalen Informationen allgegenwärtig geworden. Dreidimensionale visuelle Darstellung wird immer zum Einsichtsverständnis und Informationswiedergewinnung unverzichtbar. Dreidimensionale Digitalisierung verbindet die reale und virtuelle Welt auf natürliche Weise, die prompt die große Nachfrage nach massiven dreidimensionale digitale Inhalte. Es ist immer noch ein praktisches Problem und langjährige Herausforderung in Computergrafik und verwandten Bereichen, die den Aufwand für die dreidimensionale Modellierung reduzieren. In dieser Dissertation schlagen wir verschiedene Techniken zur Aufhellung der Erstellung von Inhalten auf, im Rahmen der gemeinsamen Thema der struktur-bewusst zu sein, d.h. globalen Beziehungen zwischen den Teilen der Gestalt beibehalten wird. Besonders interessiert sind wir bei der Formulierung unserer Algorithmen, so dass sie den Einsatz von Symmetrische Strukturen machen, wegen ihrer knappen, aber sehr abstrakten Prinzipien für die meisten regelmäßigen Mustern universell einsetzbar sind. Wir stellen unsere Arbei aus drei verschiedenen Aspekte in dieser Dissertation. Erstens befinden wir Räume der Verformungen, die Symmetrien zu erhalten, und entwickelten wir eine Methode, diesen Raum in Echtzeit zu erkunden, die deutlich die Erzeugung von Gestalten vereinfacht, die Symmetrien zu bewahren. Zweitens haben wir empirisch untersucht dreidimensionale Offset Statistiken und entwickelten eine vollautomatische Applikation für Retargeting, die auf den verifizierte Seltenheit basiert. Schließlich treten wir uns auf die ungefähre dreidimensionalen Teilsymmetrie Erkennungsproblem zu lösen, auf der Grundlage unserer neuen Kookkurrenz Analyseverfahren, die viele hochrangige Anwendungen dienen verwendet werden könnten

Desarrollo de herramienta de visualización para la reparación de piezas arqueológicas basado en su simetría

La simetría es la correspondencia exacta en la disposición regular de las partes o puntos de un cuerpo con relación a un centro, un eje o un plano. Esta característica está presente en la naturaleza y en objetos fabricados por el hombre. Asimismo, en el caso de objetos simétricos realizados por el hombre, existen vasijas de la cultura inca conocidos como keros que representan una simetría rotacional. Sin embargo, muchos de estos cerámicos no se encuentran en óptimas condiciones, debido a que fueron deteriorados por la tierra y por las piedras. Además, muchos de estos estuvieron enterrados o fueron parcialmente dañados en guerras. En años recientes, el estudio de la simetría ha captado la atención de las comunidades de computación gráfica. La simetría puede facilitar el entendimiento computacional de algunas representaciones de manera visual, por lo tanto esta característica ubicua puede brindar una gran ayuda en la reconstrucción de objetos. Uno de los problemas está relacionado con la verificación y detección de la simetría en un objeto. Algunos métodos encontrados en la literatura, tales como Momentos generalizados y Curvas del eje de simetría, para poder realizar la verificación de la simetría en un objeto necesita que este posea una estructura completa, dejando de esta manera inaplicable estos métodos para la reconstrucción de restos arqueológicos. Otro problema encontrado es el recurso computacional que se necesita para realizar los cálculos, debido a que se componen de pasos muy complejos computacionalmente. Además, al ser algoritmos complejos, estos pueden poseer un tiempo de ejecución mayor a 15 minutos, siendo esto un factor negativo debido a que se espera que la reconstrucción de los objetos arqueológicos sea interactiva y rápida.Desde el punto de vista de los arqueólogos, el proceso de reconstrucción de objetos arqueológicos de manera manual puede tomar varios días. Sumado a esto, en la mayoría de los casos, la reconstrucción no es precisa, porque se realizan muchas maquetas hasta obtener un modelo final con la posible reconstrucción del objeto. Existen distintos métodos como alternativa para el tratamiento de reconstrucción de objetos, claro que la precisión dependerá de qué tan completo se pueda tener a estos. En el presente proyecto de fin de carrera se pretende plantear una interfaz gráfica en la cual el usuario pueda interactuar con el método extraído de aproximación de detección de simetrías en Mallas 3D (Sipiran, Gregor, & Schreck, 2014). Como objetivo se busca reducir el campo de análisis del método anteriormente mencionado, por lo cual se plantea el uso de una interfaz gráfica para la interacción entre el usuario con el uso de una herramienta OpenGL, para de esta manera reducir el tiempo de respuesta que presenta este método. Esta reducción se realizó con la interacción que brindó el usuario usando la interfaz gráfica, donde el usuario podrá brindar información indicando dónde es posible que se encuentren los ejes de simetría o planos de simetría que servirán como entrada para el método a utilizar para la reconstrucción de los objetos arqueológicos.Tesi

Investigating human-perceptual properties of "shapes" using 3D shapes and 2D fonts

Shapes are generally used to convey meaning. They are used in video games, films and other multimedia, in diverse ways. 3D shapes may be destined for virtual scenes or represent objects to be constructed in the real-world. Fonts add character to an otherwise plain block of text, allowing the writer to make important points more visually prominent or distinct from other text. They can indicate the structure of a document, at a glance. Rather than studying shapes through traditional geometric shape descriptors, we provide alternative methods to describe and analyse shapes, from a lens of human perception. This is done via the concepts of Schelling Points and Image Specificity. Schelling Points are choices people make when they aim to match with what they expect others to choose but cannot communicate with others to determine an answer. We study whole mesh selections in this setting, where Schelling Meshes are the most frequently selected shapes. The key idea behind image Specificity is that different images evoke different descriptions; but ‘Specific’ images yield more consistent descriptions than others. We apply Specificity to 2D fonts. We show that each concept can be learned and predict them for fonts and 3D shapes, respectively, using a depth image-based convolutional neural network. Results are shown for a range of fonts and 3D shapes and we demonstrate that font Specificity and the Schelling meshes concept are useful for visualisation, clustering, and search applications. Overall, we find that each concept represents similarities between their respective type of shape, even when there are discontinuities between the shape geometries themselves. The ‘context’ of these similarities is in some kind of abstract or subjective meaning which is consistent among different people

Of assembling small sculptures and disassembling large geometry

This thesis describes the research results and contributions that have been achieved during the author’s doctoral work. It is divided into two independent parts, each of which is devoted to a particular research aspect. The first part covers the true-to-detail creation of digital pieces of art, so-called relief sculptures, from given 3D models. The main goal is to limit the depth of the contained objects with respect to a certain perspective without compromising the initial three-dimensional impression. Here, the preservation of significant features and especially their sharpness is crucial. Therefore, it is necessary to overemphasize fine surface details to ensure their perceptibility in the more complanate relief. Our developments are aimed at amending the flexibility and user-friendliness during the generation process. The main focus is on providing real-time solutions with intuitive usability that make it possible to create precise, lifelike and aesthetic results. These goals are reached by a GPU implementation, the use of efficient filtering techniques, and the replacement of user defined parameters by adaptive values. Our methods are capable of processing dynamic scenes and allow the generation of seamless artistic reliefs which can be composed of multiple elements. The second part addresses the analysis of repetitive structures, so-called symmetries, within very large data sets. The automatic recognition of components and their patterns is a complex correspondence problem which has numerous applications ranging from information visualization over compression to automatic scene understanding. Recent algorithms reach their limits with a growing amount of data, since their runtimes rise quadratically. Our aim is to make even massive data sets manageable. Therefore, it is necessary to abstract features and to develop a suitable, low-dimensional descriptor which ensures an efficient, robust, and purposive search. A simple inspection of the proximity within the descriptor space helps to significantly reduce the number of necessary pairwise comparisons. Our method scales quasi-linearly and allows a rapid analysis of data sets which could not be handled by prior approaches because of their size.Die vorgelegte Arbeit beschreibt die wissenschaftlichen Ergebnisse und Beiträge, die während der vergangenen Promotionsphase entstanden sind. Sie gliedert sich in zwei voneinander unabhängige Teile, von denen jeder einem eigenen Forschungsschwerpunkt gewidmet ist. Der erste Teil beschäftigt sich mit der detailgetreuen Erzeugung digitaler Kunstwerke, sogenannter Reliefplastiken, aus gegebenen 3D-Modellen. Das Ziel ist es, die Objekte, abhängig von der Perspektive, stark in ihrer Tiefe zu limitieren, ohne dass der Eindruck der räumlichen Ausdehnung verloren geht. Hierbei kommt dem Aufrechterhalten der Schärfe signifikanter Merkmale besondere Bedeutung zu. Dafür ist es notwendig, die feinen Details der Objektoberfläche überzubetonen, um ihre Sichtbarkeit im flacheren Relief zu gewährleisten. Unsere Weiterentwicklungen zielen auf die Verbesserung der Flexibilität und Benutzerfreundlichkeit während des Enstehungsprozesses ab. Der Fokus liegt dabei auf dem Bereitstellen intuitiv bedienbarer Echtzeitlösungen, die die Erzeugung präziser, naturgetreuer und visuell ansprechender Resultate ermöglichen. Diese Ziele werden durch eine GPU-Implementierung, den Einsatz effizienter Filtertechniken sowie das Ersetzen benutzergesteuerter Parameter durch adaptive Werte erreicht. Unsere Methoden erlauben das Verarbeiten dynamischer Szenen und die Erstellung nahtloser, kunstvoller Reliefs, die aus mehreren Elementen und Perspektiven zusammengesetzt sein können. Der zweite Teil behandelt die Analyse wiederkehrender Stukturen, sogenannter Symmetrien, innerhalb sehr großer Datensätze. Das automatische Erkennen von Komponenten und deren Muster ist ein komplexes Korrespondenzproblem mit zahlreichen Anwendungen, von der Informationsvisualisierung über Kompression bis hin zum automatischen Verstehen. Mit zunehmender Datenmenge geraten die etablierten Algorithmen an ihre Grenzen, da ihre Laufzeiten quadratisch ansteigen. Unser Ziel ist es, auch massive Datensätze handhabbar zu machen. Dazu ist es notwendig, Merkmale zu abstrahieren und einen passenden niedrigdimensionalen Deskriptor zu entwickeln, der eine effiziente, robuste und zielführende Suche erlaubt. Eine simple Betrachtung der Nachbarschaft innerhalb der Deskriptoren hilft dabei, die Anzahl notwendiger paarweiser Vergleiche signifikant zu reduzieren. Unser Verfahren skaliert quasi-linear und ermöglicht somit eine rasche Auswertung auch auf Daten, die für bisherige Methoden zu groß waren