Arbitrary topology meshes in geometric design and vector graphics

Meshes are a powerful means to represent objects and shapes both in 2D and 3D, but the techniques based on meshes can only be used in certain regular settings and restrict their usage. Meshes with an arbitrary topology have many interesting applications in geometric design and (vector) graphics, and can give designers more freedom in designing complex objects. In the first part of the thesis we look at how these meshes can be used in computer aided design to represent objects that consist of multiple regular meshes that are constructed together. Then we extend the B-spline surface technique from the regular setting to work on extraordinary regions in meshes so that multisided B-spline patches are created. In addition, we show how to render multisided objects efficiently, through using the GPU and tessellation. In the second part of the thesis we look at how the gradient mesh vector graphics primitives can be combined with procedural noise functions to create expressive but sparsely defined vector graphic images. We also look at how the gradient mesh can be extended to arbitrary topology variants. Here, we compare existing work with two new formulations of a polygonal gradient mesh. Finally we show how we can turn any image into a vector graphics image in an efficient manner. This vectorisation process automatically extracts important image features and constructs a mesh around it. This automatic pipeline is very efficient and even facilitates interactive image vectorisation

Geometric Data Analysis: Advancements of the Statistical Methodology and Applications

Data analysis has become fundamental to our society and comes in multiple facets and approaches. Nevertheless, in research and applications, the focus was primarily on data from Euclidean vector spaces. Consequently, the majority of methods that are applied today are not suited for more general data types. Driven by needs from fields like image processing, (medical) shape analysis, and network analysis, more and more attention has recently been given to data from non-Euclidean spaces–particularly (curved) manifolds. It has led to the field of geometric data analysis whose methods explicitly take the structure (for example, the topology and geometry) of the underlying space into account. This thesis contributes to the methodology of geometric data analysis by generalizing several fundamental notions from multivariate statistics to manifolds. We thereby focus on two different viewpoints. First, we use Riemannian structures to derive a novel regression scheme for general manifolds that relies on splines of generalized Bézier curves. It can accurately model non-geodesic relationships, for example, time-dependent trends with saturation effects or cyclic trends. Since Bézier curves can be evaluated with the constructive de Casteljau algorithm, working with data from manifolds of high dimensions (for example, a hundred thousand or more) is feasible. Relying on the regression, we further develop a hierarchical statistical model for an adequate analysis of longitudinal data in manifolds, and a method to control for confounding variables. We secondly focus on data that is not only manifold- but even Lie group-valued, which is frequently the case in applications. We can only achieve this by endowing the group with an affine connection structure that is generally not Riemannian. Utilizing it, we derive generalizations of several well-known dissimilarity measures between data distributions that can be used for various tasks, including hypothesis testing. Invariance under data translations is proven, and a connection to continuous distributions is given for one measure. A further central contribution of this thesis is that it shows use cases for all notions in real-world applications, particularly in problems from shape analysis in medical imaging and archaeology. We can replicate or further quantify several known findings for shape changes of the femur and the right hippocampus under osteoarthritis and Alzheimer's, respectively. Furthermore, in an archaeological application, we obtain new insights into the construction principles of ancient sundials. Last but not least, we use the geometric structure underlying human brain connectomes to predict cognitive scores. Utilizing a sample selection procedure, we obtain state-of-the-art results

Modelado jerárquico de objetos 3D con superficies de subdivisión

Las SSs (Superficies de Subdivisión) son un potente paradigma de modelado de objetos 3D (tridimensionales) que establece un puente entre los dos enfoques tradicionales a la aproximación de superficies, basados en mallas poligonales y de parches alabeados, que conllevan problemas uno y otro. Los esquemas de subdivisión permiten definir una superficie suave (a tramos), como las más frecuentes en la práctica, como el límite de un proceso recursivo de refinamiento de una malla de control burda, que puede ser descrita muy compactamente. Además, la recursividad inherente a las SSs establece naturalmente una relación de anidamiento piramidal entre las mallas / NDs (Niveles de Detalle) generadas/os sucesivamente, por lo que las SSs se prestan extraordinariamente al AMRO (Análisis Multiresolución mediante Ondículas) de superficies, que tiene aplicaciones prácticas inmediatas e interesantísimas, como la codificación y la edición jerárquicas de modelos 3D. Empezamos describiendo los vínculos entre las tres áreas que han servido de base a nuestro trabajo (SSs, extracción automática de NDs y AMRO) para explicar como encajan estas tres piezas del puzzle del modelado jerárquico de objetos de 3D con SSs. El AMRO consiste en descomponer una función en una versión burda suya y un conjunto de refinamientos aditivos anidados jerárquicamente llamados "coeficientes ondiculares". La teoría clásica de ondículas estudia las señales clásicas nD: las definidas sobre dominios paramétricos homeomorfos a R" o (0,1)n como el audio (n=1), las imágenes (n=2) o el vídeo (n=3). En topologías menos triviales, como las variedades 2D) (superficies en el espacio 3D), el AMRO no es tan obvio, pero sigue siendo posible si se enfoca desde la perspectiva de las SSs. Basta con partir de una malla burda que aproxime a un bajo ND la superficie considerada, subdividirla recursivamente y, al hacerlo, ir añadiendo los coeficientes ondiculares, que son los detalles 3D necesarios para obtener aproximaciones más y más finas a la superficie original. Pasamos después a las aplicaciones prácticas que constituyen nuestros principal desarrollo original y, en particular, presentamos una técnica de codificación jerárquica de modelos 3D basada en SSs, que actúa sobre los detalles 3D mencionados: los expresa en un referencial normal loscal; los organiza según una estructura jerárquica basada en facetas; los cuantifica dedicando menos bits a sus componentes tangenciales, menos energéticas, y los "escalariza"; y los codifica dinalmente gracias a una técnica similar al SPIHT (Set Partitioning In Hierarchical Tress) de Said y Pearlman. El resultado es un código completamente embebido y al menos dos veces más compacto, para superficies mayormente suaves, que los obtenidos con técnicas de codificación progresiva de mallas 3D publicadas previamente, en las que además los NDs no están anidados piramidalmente. Finalmente, describimos varios métodos auxiliares que hemos desarrollado, mejorando técnicas previas y creando otras propias, ya que una solución completa al modelado de objetos 3D con SSs requiere resolver otros dos problemas. El primero es la extracción de una malla base (triangular, en nuestro caso) de la superficie original, habitualmente dada por una malla triangular fina con conectividad arbitraria. El segundo es la generación de un remallado recursivo con conectividad de subdivisión de la malla original/objetivo mediante un refinamiento recursivo de la malla base, calculando así los detalles 3D necesarios para corregir las posiciones predichas por la subdivisión para nuevos vértices

Représentation hybride pour la modélisation géométrique interactive

De nos jours, les objets virtuels sont devenus omniprésents. On les trouve dans de nombreux domaines comme le divertissement (cinéma, jeux vidéo, etc.), la conception assistée par ordinateur ou encore la réalité virtuelle. Nous nous intéressons en particulier à la modélisation d'objets 3D dans le domaine de la création artistique. Ici, la création d'images riches nécessite de faire appel à des modèles très détaillés et donc extrêmement complexes. Les surfaces de subdivision, traditionnellement utilisées dans ces domaines, voient leur complexité croître rapidement lorsqu'on ajoute des détails, et la gestion de la connectivité du maillage de contrôle devient trop contraignante. Une approche standard pour gérer la complexité de tels modèles est d'utiliser des représentations différentes pour la forme générale de la surface et les détails. Cependant, ces détails sont représentés par des cartes matricielles qui ne possèdent pas la plupart des avantages des représentations vectorielles, et cela complexifie certaines tâches, comme par exemple l'animation. Dans cette thèse, nous proposons deux nouvelles représentations vectorielles, la première pour les surfaces de base, la deuxième pour les détails. Nous utilisons pour cette dernière une représentation vectorielle appelée images de diffusion permettant de créer des variations lisses à l'aide d'un ensemble réduit de contraintes. Cela nous permet de représenter aussi bien la géométrie que la couleur ou d'autres paramètres nécessaires au rendu de façon purement vectoriel, en conservant des contrôles de haut niveau.Notre première contribution est une représentation de surfaces, baptisée LS3, issue de la combinaison entre surfaces de subdivision et -point set surfaces. Cette approche réduit notablement les artefacts des surfaces de subdivision aux alentours de sommets dits extraordinaires, qui sont connus pour poser problème. Nous présentons une analyse numérique des propriétés de ces surfaces, qui tend à montrer que du point de vue de la continuité elles se comportent au moins aussi bien que les schémas de subdivision linéaires traditionnels. Notre deuxième contribution est un solveur pour les images de diffusion dont le principal avantage est de produire en sortie une autre représentation vectorielle légère et très rapide à évaluer. Nous illustrons la force de note solveur sur de nombreux exemples difficiles ou impossibles à réaliser avec les méthodes précédentes. Pour conclure, nous montrons comment combiner nos deux contributions pour obtenir une représentation de surface entièrement vectorielle capable de représenter des détails sans avoir à manipuler la connectivité d'un maillage.Nowadays, virtual objects have become omnipresent. We can find them in various domains such as entertainment (movies, video games, etc.), computer-aided design or virtual reality. Our main focus in this document is the modeling of 3D objects in the domain of artistic creation, where rich images creation requires highly detailed and complex models.Subdivision surfaces, the most used surface representation in this domain, quickly become very dense as the user add details, and manual handling of the connectivity becomes too cumbersome. A standard approach to handle the complexity of such models is to separate the overall shape of the surface and the details. Although, these detail maps are often stored in bitmap images that does not provide the advantages of vectorial representation, which complicate some tasks, like animation.In this document, we present two new vectorial representations: the first one for the base surface, the second one for the detail maps. For the later, we use a vectorial representation called diffusion images that allow to create smooth or sharp variations from a small set of constraints. This enables us to represent geometry as well as color or any other parameter required for rendering, while keeping high-level controls.Our first contribution is a surface representation, called LS3, based on the combination of subdivision surfaces and point set surfaces. This approach reduces notably artifacts that subdivision surfaces produce around so called extraordinary vertices. We also present a numerical analysis of the mathematical properties of these surfaces, that show that they behave at least as well as classical subdivision schemes.Our second contribution is a solver for diffusion images that has the particularity to produce as output a denser vectorial representation which is light and fast to evaluate. We show the advantages of this approach on several examples that would be hard or impossible to produce with former methods.To conclude, we show how these two contributions can be used together to obtain a fully vectorial surface representation able to produce detailed surfaces without needing to deal with complex connectivity.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF

Dynamic data structures and saliency-influenced rendering

With increasing heterogeneity of modern hardware, different requirements for 3d applications arise. Despite the fact that real-time rendering of photo-realistic images is possible using today’s graphics cards, still large computational effort is required. Furthermore, smart-phones or computers with older, less powerful graphics cards may not be able to reproduce these results. To retain interactive rendering, usually the detail of a scene is reduced, and so less data needs to be processed. This removal of data, however, may introduce errors, so called artifacts. These artifacts may be distracting for a human spectator when gazing at the display. Thus, the visual quality of the presented scene is reduced. This is counteracted by identifying features of an object that can be removed without introducing artifacts. Most methods utilize geometrical properties, such as distance or shape, to rate the quality of the performed reduction. This information used to generate so called Levels Of Detail (LODs), which are made available to the rendering system. This reduces the detail of an object using the precalculated LODs, e.g. when it is moved into the back of the scene. The appropriate LOD is selected using a metric, and it is replaced with the current displayed version. This exchange must be made smoothly, requiring both LOD-versions to be drawn simultaneously during a transition. Otherwise, this exchange will introduce discontinuities, which are easily discovered by a human spectator. After completion of the transition, only the newly introduced LOD-version is drawn and the previous overhead removed. These LOD-methods usually operate with discrete levels and exploit limitations of both the display and the spectator: the human. Humans are limited in their vision. This ranges from being unable to distinct colors at varying illumination scenarios to the limitation to focus only at one location at a time. Researchers have developed many applications to exploit these limitations to increase the quality of an applied compression. Some popular methods of vision-based compression are MPEG or JPEG. For example, a JPEG compression exploits the reduced sensitivity of humans regarding color and so encodes colors with a lower resolution. Also, other fields, such as auditive perception, allow the exploitation of human limitations. The MP3 compression, for example, reduces the quality of stored frequencies if other frequencies are masking it. For representation of perception various computer models exist. In our rendering scenario, a model is advantageous that cannot be influenced by a human spectator, such as the visual salience or saliency. Saliency is a notion from psycho-physics that determines how an object “pops out” of its surrounding. These outstanding objects (or features) are important for the human vision and are directly evaluated by our Human Visual System (HVS). Saliency combines multiple parts of the HVS and allows an identification of regions where humans are likely to look at. In applications, saliency-based methods have been used to control recursive or progressive rendering methods. Especially expensive display methods, such as pathtracing or global illumination calculations, benefit from a perceptual representation as recursions or calculations can be aborted if only small or unperceivable errors are expected to occur. Yet, saliency is commonly applied to 2d images, and an extension towards 3d objects has only partially been presented. Some issues need to be addressed to accomplish a complete transfer. In this work, we present a smart rendering system that not only utilizes a 3d visual salience model but also applies the reduction in detail directly during rendering. As opposed to normal LOD-methods, this detail reduction is not limited to a predefined set of levels, but rather a dynamic and continuous LOD is created. Furthermore, to apply this reduction in a human-oriented way, a universal function to compute saliency of a 3d object is presented. The definition of this function allows to precalculate and store object-related visual salience information. This stored data is then applicable in any illumination scenario and allows to identify regions of interest on the surface of a 3d object. Unlike preprocessed methods, which generate a view-independent LOD, this identification includes information of the scene as well. Thus, we are able to define a perception-based, view-specific LOD. Performance measures of a prototypical implementation on computers with modern graphic cards achieved interactive frame rates, and several tests have proven the validity of the reduction. The adaptation of an object is performed with a dynamic data structure, the TreeCut. It is designed to operate on hierarchical representations, which define a multi-resolution object. In such a hierarchy, the leaf nodes contain the highest detail while inner nodes are approximations of their respective subtree. As opposed to classical hierarchical rendering methods, a cut is stored and re-traversal of a tree during rendering is avoided. Due to the explicit cut representation, the TreeCut can be altered using only two core operations: refine and coarse. The refine-operation increases detail by replacing a node of the tree with its children while the coarse-operation removes the node along with its siblings and replaces them with their parent node. These operations do not rely on external information and can be performed in a local manner. These only require direct successor or predecessor information. Different strategies to evolve the TreeCut are presented, which adapt the representation using only information given by the current cut. These evaluate the cut by assigning either a priority or a target-level (or bucket) to each cut-node. The former is modelled as an optimization problem that increases the average priority of a cut while being restricted in some way, e.g. in size. The latter evolves the cut to match a certain distribution. This is applied in cases where a prioritization of nodes is not applicable. Both evaluation strategies operate with linear time complexity with respect to the size of the current TreeCut. The data layout is chosen to separate rendering data and hierarchy to enable multi-threaded evaluation and display. The object is adapted over multiple frames while the rendering is not interrupted by the used evaluation strategy. Therefore, we separate the representation of the hierarchy from the rendering data. Due to its design, this overhead imposed to the TreeCut data structure does not influence rendering performance, and a linear time complexity for rendering is retained. The TreeCut is not only limited to alter geometrical detail of an object. The TreeCut has successfully been applied to create a non-photo-realistic stippling display, which draws the object with equal sized points in varying density. In this case the bucket-based evaluation strategy is utilized, which determines the distribution of the cut based on local illumination information. As an alternative, an attention drawing mechanism is proposed, which applies the TreeCut evaluation strategies to define the display style of a notification icon. A combination of external priorities is used to derive the appropriate icon version. An application for this mechanism is a messaging system that accounts for the current user situation. When optimizing an object or scene, perceptual methods allow to account for or exploit human limitations. Therefore, visual salience approaches derive a saliency map, which encodes regions of interest in a 2d map. Rendering algorithms extract importance from such a map and adapt the rendering accordingly, e.g. abort a recursion when the current location is unsalient. The visual salience depends on multiple factors including the view and the illumination of the scene. We extend the existing definition of the 2d saliency and propose a universal function for 3d visual salience: the Bidirectional Saliency Weight Distribution Function (BSWDF). Instead of extracting the saliency from 2d image and approximate 3d information, we directly compute this information using the 3d data. We derive a list of equivalent features for the 3d scenario and add them to the BSWDF. As the BSWDF is universal, also 2d images are covered with the BSWDF, and the calculation of the important regions within images is possible. To extract the individual features that contribute to visual salience, capabilities of modern graphics card in combination with an accumulation method for rendering is utilized. Inspired from point-based rendering methods local features are summed up in a single surface element (surfel) and are compared with their surround to determine whether they “pop out”. These operations are performed with a shader-program that is executed on the Graphics Processing Unit (GPU) and has direct access to the 3d data. This increases processing speed because no transfer of the data is required. After computation, each of these object-specific features can be combined to derive a saliency map for this object. Surface specific information, e.g. color or curvature, can be preprocessed and stored onto disk. We define a sampling scheme to determine the views that need to be evaluated for each object. With these schemes, the features can be interpolated for any view that occurs during rendering, and the according surface data is reconstructed. These sampling schemes compose a set of images in form of a lookup table. This is similar to existing rendering techniques, which extract illumination information from a lookup. The size of the lookup table increases only with the number of samples or the image size used for creation as the images are of equal size. Thus, the quality of the saliency data is independent of the object’s geometrical complexity. The computation of a BSWDF can be performed either on a Central Processing Unit (CPU) or a GPU, and an implementation requires only a few instructions when using a shader program. If the surface features have been stored during a preprocess, a reprojection of the data is performed and combined with the current information of the object. Once the data is available, the computation of the saliency values is done using a specialized illumination model, and a priority for each primitive is extracted. If the GPU is used, the calculated data has to be transferred from the graphics card. We therefore use the “transform feedback” capabilities, which allow high transfer rates and preserve the order of processed primitives. So, an identification of regions of interest based on the currently used primitives is achieved. The TreeCut evaluation strategies are then able to optimize the representation in an perception-based manner. As the adaptation utilizes information of the current scene, each change to an object can result in new visual salience information. So, a self-optimizing system is defined: the Feedback System. The output generated by this system converges towards a perception-optimized solution. To proof the saliency information to be useful, user tests have been performed with the results generated by the proposed Feedback System. We compared a saliency-enhanced object compression to a pure geometrical approach, common for LOD-generation. One result of the tests is that saliency information allows to increase compression even further as possible with the pure geometrical methods. The participants were not able to distinguish between objects even if the saliency-based compression had only 60% of the size of the geometrical reduced object. If the size ratio is greater, saliency-based compression is rated, on average, with higher score and these results have a high significance using statistical tests. The Feedback System extends an 3d object with the capability of self-optimization. Not only geometrical detail but also other properties can be limited and optimized using the TreeCut in combination with a BSWDF. We present a dynamic animation, which utilizes a Software Development Kit (SDK) for physical simulations. This was chosen, on the one hand, to show the universal applicability of the proposed system, and on the other hand, to focus on the connection between the TreeCut and the SDK. We adapt the existing framework, and include the SDK within our design. In this case, the TreeCut-operations not only alter geometrical but also simulation detail. This increases calculation performance because both the rendering and the SDK operate on less data after the reduction has been completed. The selected simulation type is a soft-body simulation. Soft-bodies are deformable in a certain degree but retain their internal connection. An example is a piece of cloth that smoothly fits the underlying surface without tearing apart. Other types are rigid bodies, i.e. idealistic objects that cannot be deformed, and fluids or gaseous materials, which are well suited for point-based simulations. Any of these simulations scales with the number of simulation nodes used, and a reduction of detail increases performance significantly. We define a specialized BSWDF to evaluate simulation specific features, such as motion. The Feedback System then increases detail in highly salient regions, e.g. those with large motion, and saves computation time by reducing detail in static parts of the simulation. So, detail of the simulation is preserved while less nodes are simulated. The incorporation of perception in real-time rendering is an important part of recent research. Today, the HVS is well understood, and valid computer models have been derived. These models are frequently used in commercial and free software, e.g. JPEG compression. Within this thesis, the Tree-Cut is presented to change the LOD of an object in a dynamic and continuous manner. No definition of the individual levels in advance is required, and the transitions are performed locally. Furthermore, in combination with an identification of important regions by the BSWDF, a perceptual evaluation of a 3d object is achieved. As opposed to existing methods, which approximate data from 2d images, the perceptual information is directly acquired from 3d data. Some of this data can be preprocessed if necessary, to defer additional computations during rendering. The Feedback System, created by the TreeCut and the BSWDF, optimizes the representation and is not limited to visual data alone. We have shown with our prototype that interactive frame rates can be achieved with modern hardware, and we have proven the validity of the reductions by performing several user tests. However, the presented system only focuses on specific aspects, and more research is required to capture even more capabilities that a perception-based rendering system can provide

Advances in Computer Recognition, Image Processing and Communications, Selected Papers from CORES 2021 and IP&C 2021

As almost all human activities have been moved online due to the pandemic, novel robust and efficient approaches and further research have been in higher demand in the field of computer science and telecommunication. Therefore, this (reprint) book contains 13 high-quality papers presenting advancements in theoretical and practical aspects of computer recognition, pattern recognition, image processing and machine learning (shallow and deep), including, in particular, novel implementations of these techniques in the areas of modern telecommunications and cybersecurity

Advances on Mechanics, Design Engineering and Manufacturing III

This open access book gathers contributions presented at the International Joint Conference on Mechanics, Design Engineering and Advanced Manufacturing (JCM 2020), held as a web conference on June 2–4, 2020. It reports on cutting-edge topics in product design and manufacturing, such as industrial methods for integrated product and process design; innovative design; and computer-aided design. Further topics covered include virtual simulation and reverse engineering; additive manufacturing; product manufacturing; engineering methods in medicine and education; representation techniques; and nautical, aeronautics and aerospace design and modeling. The book is organized into four main parts, reflecting the focus and primary themes of the conference. The contributions presented here not only provide researchers, engineers and experts in a range of industrial engineering subfields with extensive information to support their daily work; they are also intended to stimulate new research directions, advanced applications of the methods discussed and future interdisciplinary collaborations