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Item Dynamic 2D/3D Registration(The Eurographics Association, 2014) Bouaziz, Sofien; Tagliasacchi, Andrea; Pauly, Mark; Nicolas Holzschuch and Karol MyszkowskiImage and geometry registration algorithms are an essential component of many computer graphics and computer vision systems. With recent technological advances in RGB-D sensors, such as the Microsoft Kinect or Asus Xtion Live, robust algorithms that combine 2D image and 3D geometry registration have become an active area of research. The goal of this course is to introduce the basics of 2D/3D registration algorithms and to provide theoretical explanations and practical tools to design computer vision and computer graphics systems based on RGB-D devices. To illustrate the theory and demonstrate practical relevance, we briefly discuss three applications: rigid scanning, non-rigid modeling, and realtime face tracking. Our course targets researchers and computer graphics practitioners with a background in computer graphics and/or computer vision. An up-to-date version of the course notes as well as slides and source code can be found at http://lgg.epfl.ch/2d3dRegistration.Item PriMo: Coupled Prisms for Intuitive Surface Modeling(The Eurographics Association, 2006) Botsch, Mario; Pauly, Mark; Gross, Markus; Kobbelt, Leif; Alla Sheffer and Konrad PolthierWe present a new method for 3D shape modeling that achieves intuitive and robust deformations by emulating physically plausible surface behavior inspired by thin shells and plates. The surface mesh is embedded in a layer of volumetric prisms, which are coupled through non-linear, elastic forces. To deform the mesh, prisms are rigidly transformed to satisfy user constraints while minimizing the elastic energy. The rigidity of the prisms prevents degenerations even under extreme deformations, making the method numerically stable. For the underlying geometric optimization we employ both local and global shape matching techniques. Our modeling framework allows for the specification of various geometrically intuitive parameters that provide control over the physical surface behavior. While computationally more involved than previous methods, our approach significantly improves robustness and simplifies user interaction for large, complex deformations.Item Sparse Iterative Closest Point(The Eurographics Association and Blackwell Publishing Ltd., 2013) Bouaziz, Sofien; Tagliasacchi, Andrea; Pauly, Mark; Yaron Lipman and Hao ZhangRigid registration of two geometric data sets is essential in many applications, including robot navigation, surface reconstruction, and shape matching. Most commonly, variants of the Iterative Closest Point (ICP) algorithm are employed for this task. These methods alternate between closest point computations to establish correspondences between two data sets, and solving for the optimal transformation that brings these correspondences into alignment. A major difficulty for this approach is the sensitivity to outliers and missing data often observed in 3D scans. Most practical implementations of the ICP algorithm address this issue with a number of heuristics to prune or reweight correspondences. However, these heuristics can be unreliable and difficult to tune, which often requires substantial manual assistance. We propose a new formulation of the ICP algorithm that avoids these difficulties by formulating the registration optimization using sparsity inducing norms. Our new algorithm retains the simple structure of the ICP algorithm, while achieving superior registration results when dealing with outliers and incomplete data. The complete source code of our implementation is provided at http://lgg.epfl.ch/sparseicp.Item Curvature-Domain Shape Processing(The Eurographics Association and Blackwell Publishing Ltd, 2008) Eigensatz, Michael; Sumner, Robert W.; Pauly, MarkWe propose a framework for 3D geometry processing that provides direct access to surface curvature to facilitate advanced shape editing, filtering, and synthesis algorithms. The central idea is to map a given surface to the curvature domain by evaluating its principle curvatures, apply filtering and editing operations to the curvature distribution, and reconstruct the resulting surface using an optimization approach. Our system allows the user to prescribe arbitrary principle curvature values anywhere on the surface. The optimization solves a nonlinear least-squares problem to find the surface that best matches the desired target curvatures while preserving important properties of the original shape. We demonstrate the effectiveness of this processing metaphor with several applications, including anisotropic smoothing, feature enhancement, and multi-scale curvature editing.Item State of the Art on Computational Design of Assemblies with Rigid Parts(The Eurographics Association and John Wiley & Sons Ltd., 2021) Wang, Ziqi; Song, Peng; Pauly, Mark; Bühler, Katja and Rushmeier, HollyAn assembly refers to a collection of parts joined together to achieve a specific form and/or functionality. Designing assemblies is a non-trivial task as a slight local modification on a part's geometry or its joining method could have a global impact on the structural and/or functional performance of the whole assembly. Assemblies can be classified as structures that transmit force to carry loads and mechanisms that transfer motion and force to perform mechanical work. In this state-of-the-art report, we focus on computational design of structures with rigid parts, which generally can be formulated as a geometric modeling and optimization problem. We broadly classify existing computational design approaches, mainly from the computer graphics community, according to high-level design objectives, including fabricability, structural stability, reconfigurability, and tileability. Computational analysis of various aspects of assemblies is an integral component in these design approaches. We review different classes of computational analysis and design methods, discuss their strengths and limitations, make connections among them, and propose possible directions for future research.Item Self Tuning Texture Optimization(The Eurographics Association and John Wiley & Sons Ltd., 2015) Kaspar, Alexandre; Neubert, Boris; Lischinski, Dani; Pauly, Mark; Kopf, Johannes; Olga Sorkine-Hornung and Michael WimmerThe goal of example-based texture synthesis methods is to generate arbitrarily large textures from limited exemplars in order to fit the exact dimensions and resolution required for a specific modeling task. The challenge is to faithfully capture all of the visual characteristics of the exemplar texture, without introducing obvious repetitions or unnatural looking visual elements. While existing non-parametric synthesis methods have made remarkable progress towards this goal, most such methods have been demonstrated only on relatively low-resolution exemplars. Real-world high resolution textures often contain texture details at multiple scales, which these methods have difficulty reproducing faithfully. In this work, we present a new general-purpose and fully automatic selftuning non-parametric texture synthesis method that extends Texture Optimization by introducing several key improvements that result in superior synthesis ability. Our method is able to self-tune its various parameters and weights and focuses on addressing three challenging aspects of texture synthesis: (i) irregular large scale structures are faithfully reproduced through the use of automatically generated and weighted guidance channels; (ii) repetition and smoothing of texture patches is avoided by new spatial uniformity constraints; (iii) a smart initialization strategy is used in order to improve the synthesis of regular and near-regular textures, without affecting textures that do not exhibit regularities. We demonstrate the versatility and robustness of our completely automatic approach on a variety of challenging high-resolution texture exemplars.Item Positional, Metric, and Curvature Control for Constraint-Based Surface Deformation(The Eurographics Association and Blackwell Publishing Ltd, 2009) Eigensatz, Michael; Pauly, MarkWe present a geometry processing framework that allows direct manipulation or preservation of positional, metric, and curvature constraints anywhere on the surface of a geometric model. Target values for these properties can be specified point-wise or as integrated quantities over curves and surface patches embedded in the shape. For example, the user can draw several curves on the surface and specify desired target lengths, manipulate the normal curvature along these curves, or modify the area or principal curvature distribution of arbitrary surface patches. This user input is converted into a set of non-linear constraints. A global optimization finds the new deformed surface that best satisfies the constraints, while minimizing adaptable measures for metric and curvature distortion that provide explicit control of the deformation semantics. We illustrate how this approach enables flexible surface processing and shape editing operations not available in current systems.Item Geometric Modeling Based on Triangle Meshes(The Eurographics Association, 2006) Botsch, Mario; Pauly, Mark; Rössl, Christian; Bischoff, Stephan; Kobbelt, Leif; Nadia Magnenat-Thalmann and Katja BühlerIn the last years triangle meshes have become increasingly popular and are nowadays intensively used in many different areas of computer graphics and geometry processing. In classical CAGD irregular triangle meshes developed into a valuable alternative to traditional spline surfaces, since their conceptual simplicity allows for more flexible and highly efficient processing. Moreover, the consequent use of triangle meshes as surface representation avoids error-prone conversions, e.g., from CAD surfaces to meshbased input data of numerical simulations. Besides classical geometric modeling, other major areas frequently employing triangle meshes are computer games and movie production. In this context geometric models are often acquired by 3D scanning techniques and have to undergo postprocessing and shape optimization techniques before being actually used in production.This course discusses the whole geometry processing pipeline based on triangle meshes. We will first introduce general concepts of surface representations and point out the advantageous properties of triangle meshes in Section 2, and present efficient data structures for their implementation in Section 3. The different sources of input data and types of geometric and topological degeneracies and inconsistencies are described in Section 4, as well as techniques for their removal, resulting in clean two-manifold meshes suitable for further processing. Mesh quality criteria measuring geometric smoothness and element shape together with the corresponding analysis techniques are presented in Section 6. Mesh smoothing reduces noise in scanned surfaces by generalizing signal processing techniques to irregular triangle meshes (Section 7). Similarly, the underlying concepts from differential geometry are useful for surface parametrization as well (Section 8). Due to the enormous complexity of meshes acquired by 3D scanning, mesh decimation techniques are required for error-controlled simplification (Section 9). The shape of triangles, which is important for the robustness of numerical simulations, can be optimized by general remeshing methods (Section 10). After optimizing meshes with respect to the different quality criteria, we finally present techniques for intuitive and interactive shape deformation (Section 11). Since solving linear systems is a commonly required component for many of the presented mesh processing algorithms, we will discuss their efficient solution and compare several existing libraries in Section 12.Item Point-Based Computer Graphics(Eurographics Association, 2003) Alexa, Marc; Dachsbacher, Carsten; Gross, Markus; Pauly, Mark; van Baar, Jeroen; Zwicker, Matthias-Item Fabrication-aware Design with Intersecting Planar Pieces(The Eurographics Association and Blackwell Publishing Ltd., 2013) Schwartzburg, Yuliy; Pauly, Mark; I. Navazo, P. PoulinWe propose a computational design approach to generate 3D models composed of interlocking planar pieces. We show how intricate 3D forms can be created by sliding the pieces into each other along straight slits, leading to a simple construction that does not require glue, screws, or other means of support. To facilitate the design process, we present an abstraction model that formalizes the main geometric constraints imposed by fabrication and assembly, and incorporates conditions on the rigidity of the resulting structure.We show that the tight coupling of constraints makes manual design highly nontrivial and introduce an optimization method to automate constraint satisfaction based on an analysis of the constraint relation graph. This algorithm ensures that the planar parts can be fabricated and assembled. We demonstrate the versatility of our approach by creating 3D toy models, an architectural design study, and several examples of functional furniture.