Toward Controllable and Robust Surface Reconstruction from Spatial Curves

Reconstructing surface from a set of spatial curves is a fundamental problem in computer graphics and computational geometry. It often arises in many applications across various disciplines, such as industrial prototyping, artistic design and biomedical imaging. While the problem has been widely studied for years, challenges remain for handling different type of curve inputs while satisfying various constraints. We study studied three related computational tasks in this thesis. First, we propose an algorithm for reconstructing multi-labeled material interfaces from cross-sectional curves that allows for explicit topology control. Second, we addressed the consistency restoration, a critical but overlooked problem in applying algorithms of surface reconstruction to real-world cross-sections data. Lastly, we propose the Variational Implicit Point Set Surface which allows us to robustly handle noisy, sparse and non-uniform inputs, such as samples from spatial curves

Multi-scale Geometric Modeling of Ambiguous Shapes with Toleranced Balls and Compoundly Weighted alpha-shapes

Dealing with ambiguous data is a challenge in Science in general and geometry processing in particular. One route of choice to extract information from such data consists of replacing the ambiguous input by a continuum, typically a one-parameter family, so as to mine stable geometric and topological features within this family. This work follows this spirit and introduces a novel framework to handle 3D ambiguous geometric data which are naturally modeled by balls. First, we introduce {\em toleranced balls} to model ambiguous geometric objects. A toleranced ball consists of two concentric balls, and interpolating between their radii provides a way to explore a range of possible geometries. We propose to model an ambiguous shape by a collection of toleranced balls, and show that the aforementioned radius interpolation is tantamount to the growth process associated with an additively-multiplicatively weighted Voronoi diagram (also called compoundly weighted or CW). Second and third, we investigate properties of the CW diagram and the associated CW $\alpha$-complex, which provides a filtration called the $\lambda$-complex. Fourth, we propose a naive algorithm to compute the CW VD. Finally, we use the $\lambda$-complex to assess the quality of models of large protein assemblies, as these models inherently feature ambiguities

Quantification of the pore size distribution of soils:assessment of existing software using tomographic and synthetic 3D images

The pore size distribution (PSD) of the void space is widely used to predict a range of processes in soils. Recent advances in X-ray computed tomography (CT) now afford novel ways to obtain exact data on pore geometry, which has stimulated the development of algorithms to estimate the pore size distribution from 3D data sets. To date there is however no clear consensus on how PSDs should be estimated, and in what form PSDs are best presented. In this article, we first review the theoretical principles shared by the various methods for PSD estimation. Then we select methods that are widely adopted in soil science and geoscience, and we use a robust statistical method to compare their application to synthetic image samples, for which analytical solutions of PSDs are available, and X-ray CT images of soil samples selected from different treatments to obtain wide ranging PSDs. Results indicate that, when applied to the synthetic images, all methods presenting PSDs as pore volume per class size (i.e., Avizo, CTAnalyser, BoneJ, Quantim4, and DTM), perform well. Among them, the methods based on Maximum Inscribed Balls (Bone J, CTAnalyser, Quantim4) also produce similar PSDs for the soil samples, whereas the Delaunay Triangulation Method (DTM) produces larger estimates of the pore volume occupied by small pores, and Avizo yields larger estimates of the pore volume occupied by large pores. By contrast, the methods that calculate PSDs as object population fraction per volume class (Avizo, 3DMA, DFS-FIJI) perform inconsistently on the synthetic images and do not appear well suited to handle the more complex geometries of soils. It is anticipated that the extensive evaluation of method performance carried out in this study, together with the recommendations reached, will be useful to the porous media community to make more informed choices relative to suitable PSD estimation methods, and will help improve current practice, which is often ad hoc and heuristic

Spatial relationship based scene analysis and synthesis

In this thesis, we propose a new representation, which we name Interaction Bisector Surface (IBS), that can describe the general nature of spatial relationship. We show that the IBS can be applied in 3D scene analysis, retrieval and synthesis. Despite the fact that the spatial relationship between different objects plays a significant role in describing the context, few works have focused on elaborating a representation that can describe arbitrary interactions between different objects. Previous methods simply concatenate the individual state vectors to produce a joint space, or only use simple representations such as relative vectors or contacts to describe the context. Such representations do not contain detailed information of spatial relationships. They cannot describe complex interactions such as hooking and enclosure. The IBS is a data structure with rich information about the interaction. It provides the topological, geometric and correspondence features that can be used to classify and recognize interactions. The topological features are at the most abstract level and it can be used to recognize spatial relationships such as enclosure, hooking and surrounding. The geometric features encode the fine details of interactions. The correspondence feature describes which parts of the scene elements contribute to the interaction and is especially useful for recognizing character-object interactions. We show examples of successful classification and retrieval of different types of data including indoor static scenes and dynamic scenes which contain character-object interactions. We also conduct an exhaustive comparison which shows that our method outperforms existing approaches. We also propose a novel approach to automatically synthesizing new interactions from example scenes and new objects. Given an example scene composed of two objects, the open space between the objects is abstracted by the IBS. Then, an translation, rotation and scale equivariant feature called shape coverage feature, which encodes how the point in the open space is surrounded by the environment, is computed near the IBS and around the open space of the new objects. Finally, a novel scene is synthesized by conducting a partial matching of the open space around the new objects with the IBS. Using our approach, new scenes can be automatically synthesized from example scenes and new objects without relying on label information, which is especially useful when the data of scenes and objects come from multiple sources

An Adjectival Interface for procedural content generation

Includes abstract.Includes bibliographical references.In this thesis, a new interface for the generation of procedural content is proposed, in which the user describes the content that they wish to create by using adjectives. Procedural models are typically controlled by complex parameters and often require expert technical knowledge. Since people communicate with each other using language, an adjectival interface to the creation of procedural content is a natural step towards addressing the needs of non-technical and non-expert users. The key problem addressed is that of establishing a mapping between adjectival descriptors, and the parameters employed by procedural models. We show how this can be represented as a mapping between two multi-dimensional spaces, adjective space and parameter space, and approximate the mapping by applying novel function approximation techniques to points of correspondence between the two spaces. These corresponding point pairs are established through a training phase, in which random procedural content is generated and then described, allowing one to map from parameter space to adjective space. Since we ultimately seek a means of mapping from adjective space to parameter space, particle swarm optimisation is employed to select a point in parameter space that best matches any given point in adjective space. The overall result, is a system in which the user can specify adjectives that are then used to create appropriate procedural content, by mapping the adjectives to a suitable set of procedural parameters and employing the standard procedural technique using those parameters as inputs. In this way, none of the control offered by procedural modelling is sacrificed â although the adjectival interface is simpler, it can at any point be stripped away to reveal the standard procedural model and give users access to the full set of procedural parameters. As such, the adjectival interface can be used for rapid prototyping to create an approximation of the content desired, after which the procedural parameters can be used to fine-tune the result. The adjectival interface also serves as a means of intermediate bridging, affording users a more comfortable interface until they are fully conversant with the technicalities of the underlying procedural parameters. Finally, the adjectival interface is compared and contrasted to an interface that allows for direct specification of the procedural parameters. Through user experiments, it is found that the adjectival interface presented in this thesis is not only easier to use and understand, but also that it produces content which more accurately reflects usersâ intentions

Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop

3D model reconstruction using neural gas accelerated on GPU

In this work, we propose the use of the neural gas (NG), a neural network that uses an unsupervised Competitive Hebbian Learning (CHL) rule, to develop a reverse engineering process. This is a simple and accurate method to reconstruct objects from point clouds obtained from multiple overlapping views using low-cost sensors. In contrast to other methods that may need several stages that include downsampling, noise filtering and many other tasks, the NG automatically obtains the 3D model of the scanned objects. To demonstrate the validity of our proposal we tested our method with several models and performed a study of the neural network parameterization computing the quality of representation and also comparing results with other neural methods like growing neural gas and Kohonen maps or classical methods like Voxel Grid. We also reconstructed models acquired by low cost sensors that can be used in virtual and augmented reality environments for redesign or manipulation purposes. Since the NG algorithm has a strong computational cost we propose its acceleration. We have redesigned and implemented the NG learning algorithm to fit it onto Graphics Processing Units using CUDA. A speed-up of 180× faster is obtained compared to the sequential CPU version.This work was partially funded by the Spanish Government DPI2013-40534-R grant

AutoGraff: towards a computational understanding of graffiti writing and related art forms.

The aim of this thesis is to develop a system that generates letters and pictures with a style that is immediately recognizable as graffiti art or calligraphy. The proposed system can be used similarly to, and in tight integration with, conventional computer-aided geometric design tools and can be used to generate synthetic graffiti content for urban environments in games and in movies, and to guide robotic or fabrication systems that can materialise the output of the system with physical drawing media. The thesis is divided into two main parts. The first part describes a set of stroke primitives, building blocks that can be combined to generate different designs that resemble graffiti or calligraphy. These primitives mimic the process typically used to design graffiti letters and exploit well known principles of motor control to model the way in which an artist moves when incrementally tracing stylised letter forms. The second part demonstrates how these stroke primitives can be automatically recovered from input geometry defined in vector form, such as the digitised traces of writing made by a user, or the glyph outlines in a font. This procedure converts the input geometry into a seed that can be transformed into a variety of calligraphic and graffiti stylisations, which depend on parametric variations of the strokes