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Item Object Completion using k-Sparse Optimization(The Eurographics Association and John Wiley & Sons Ltd., 2015) Mavridis, Pavlos; Sipiran, Ivan; Andreadis, Anthousis; Papaioannou, Georgios; Stam, Jos and Mitra, Niloy J. and Xu, KunWe present a new method for the completion of partial globally-symmetric 3D objects, based on the detection of partial and approximate symmetries in the incomplete input dataset. In our approach, symmetry detection is formulated as a constrained sparsity maximization problem, which is solved efficiently using a robust RANSACbased optimizer. The detected partial symmetries are then reused iteratively, in order to complete the missing parts of the object. A global error relaxation method minimizes the accumulated alignment errors and a nonrigid registration approach applies local deformations in order to properly handle approximate symmetry. Unlike previous approaches, our method does not rely on the computation of features, it uniformly handles translational, rotational and reflectional symmetries and can provide plausible object completion results, even on challenging cases, where more than half of the target object is missing. We demonstrate our algorithm in the completion of 3D scans with varying levels of partiality and we show the applicability of our approach in the repair and completion of heavily eroded or incomplete cultural heritage objects.Item Hierarchical Multiview Rigid Registration(The Eurographics Association and John Wiley & Sons Ltd., 2015) Tang, Yizhi; Feng, Jieqing; Mirela Ben-Chen and Ligang LiuRegistration is a key step in the 3D reconstruction of real-world objects. In this paper, we propose a hierarchical method for the rigid registration of multiple views. The multiview registration problem is solved via hierarchical optimization defined on an undirected graph. Each node or edge in this graph represents a single view or a connection between two overlapped views, respectively. The optimizations are performed hierarchically on the edges, the loops, and the entire graph. First, each overlapped pair of views is locally aligned. Then, a loop-based incremental registration algorithm is introduced to refine the initial pairwise alignments. After a loop is registered, the views in the loop are merged into a metaview in the graph. Finally, global error diffusion is applied to the entire graph to evenly distribute the accumulated errors to all views. In addition, a new objective function is defined to describe the loop closure problem; it improves the accuracy and robustness of registration by simultaneously considering transformation and registration errors. The experimental results show that the proposed hierarchical approach is accurate, efficient and robust for initial view states that are not well posed.Item Projective Feature Learning for 3D Shapes with Multi-View Depth Images(The Eurographics Association and John Wiley & Sons Ltd., 2015) Xie, Zhige; Xu, Kai; Shan, Wen; Liu, Ligang; Xiong, Yueshan; Huang, Hui; Stam, Jos and Mitra, Niloy J. and Xu, KunFeature learning for 3D shapes is challenging due to the lack of natural paramterization for 3D surface models. We adopt the multi-view depth image representation and propose Multi-View Deep Extreme Learning Machine (MVD-ELM) to achieve fast and quality projective feature learning for 3D shapes. In contrast to existing multiview learning approaches, our method ensures the feature maps learned for different views are mutually dependent via shared weights and in each layer, their unprojections together form a valid 3D reconstruction of the input 3D shape through using normalized convolution kernels. These lead to a more accurate 3D feature learning as shown by the encouraging results in several applications. Moreover, the 3D reconstruction property enables clear visualization of the learned features, which further demonstrates the meaningfulness of our feature learning.Item Layer-Based Procedural Design of Façades(The Eurographics Association and John Wiley & Sons Ltd., 2015) IlcĂk, Martin; Musialski, Przemyslaw; Auzinger, Thomas; Wimmer, Michael; Olga Sorkine-Hornung and Michael WimmerWe present a novel procedural framework for interactively modeling building façades. Common procedural approaches, such as shape grammars, assume that building façades are organized in a tree structure, while in practice this is often not the case. Consequently, the complexity of their layout description becomes unmanageable for interactive editing. In contrast, we obtain a façade by composing multiple overlapping layers, where each layer contains a single rectilinear grid of façade elements described by two simple generator patterns. This way, the design process becomes more intuitive and the editing effort for complex layouts is significantly reduced. To achieve this, we present a method for the automated merging of different layers in the form of a mixed discrete and continuous optimization problem. Finally, we provide several modeling examples and a comparison to shape grammars in order to highlight the advantages of our method when designing realistic building façades.Item Fast and Exact (Poisson) Solvers on Symmetric Geometries(The Eurographics Association and John Wiley & Sons Ltd., 2015) Kazhdan, Misha; Mirela Ben-Chen and Ligang LiuIn computer graphics, numerous geometry processing applications reduce to the solution of a Poisson equation. When considering geometries with symmetry, a natural question to consider is whether and how the symmetry can be leveraged to derive an efficient solver for the underlying system of linear equations. In this work we provide a simple representation-theoretic analysis that demonstrates how symmetries of the geometry translate into block diagonalization of the linear operators and we show how this results in efficient linear solvers for surfaces of revolution with and without angular boundaries.Item Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data(The Eurographics Association and John Wiley & Sons Ltd., 2015) Carr, Hamish; Geng, Zhao; Tierny, Julien; Chattopadhyay, Amit; Knoll, Aaron; H. Carr, K.-L. Ma, and G. SantucciScientific visualization has many effective methods for examining and exploring scalar and vector fields, but rather fewer for bivariate fields. We report the first general purpose approach for the interactive extraction of geometric separating surfaces in bivariate fields. This method is based on fiber surfaces: surfaces constructed from sets of fibers, the multivariate analogues of isolines. We show simple methods for fiber surface definition and extraction. In particular, we show a simple and efficient fiber surface extraction algorithm based on Marching Cubes. We also show how to construct fiber surfaces interactively with geometric primitives in the range of the function. We then extend this to build user interfaces that generate parameterized families of fiber surfaces with respect to arbitrary polygons. In the special case of isovalue-gradient plots, fiber surfaces capture features geometrically for quantitative analysis that have previously only been analysed visually and qualitatively using multi-dimensional transfer functions in volume rendering. We also demonstrate fiber surface extraction on a variety of bivariate data.Item Composition-Aware Scene Optimization for Product Images(The Eurographics Association and John Wiley & Sons Ltd., 2015) Liu, Tianqiang; McCann, Jim; Li, Wilmot; Funkhouser, Thomas; Olga Sorkine-Hornung and Michael WimmerIncreasingly, companies are creating product advertisements and catalog images using computer renderings of 3D scenes. A common goal for these companies is to create aesthetically appealing compositions that highlight objects of interest within the context of a scene. Unfortunately, this goal is challenging, not only due to the need to balance the trade-off among aesthetic principles and design constraints, but also because of the huge search space induced by possible camera parameters, object placement, material choices, etc. Previous methods have investigated only optimization of camera parameters. In this paper, we develop a tool that starts from an initial scene description and a set of high-level constraints provided by a stylist and then automatically generates an optimized scene whose 2D composition is improved. It does so by locally adjusting the 3D object transformations, surface materials, and camera parameters. The value of this tool is demonstrated in a variety of applications motivated by product catalogs, including rough layout refinement, detail image creation, home planning, cultural customization, and text inlay placement. Results of a perceptual study indicate that our system produces images preferable for product advertisement compared to a more traditional camera-only optimization.Item Analysis and Synthesis of 3D Shape Families via Deep-learned Generative Models of Surfaces(The Eurographics Association and John Wiley & Sons Ltd., 2015) Huang, Haibin; Kalogerakis, Evangelos; Marlin, Benjamin; Mirela Ben-Chen and Ligang LiuWe present a method for joint analysis and synthesis of geometrically diverse 3D shape families. Our method first learns part-based templates such that an optimal set of fuzzy point and part correspondences is computed between the shapes of an input collection based on a probabilistic deformation model. In contrast to previous template-based approaches, the geometry and deformation parameters of our part-based templates are learned from scratch. Based on the estimated shape correspondence, our method also learns a probabilistic generative model that hierarchically captures statistical relationships of corresponding surface point positions and parts as well as their existence in the input shapes. A deep learning procedure is used to capture these hierarchical relationships. The resulting generative model is used to produce control point arrangements that drive shape synthesis by combining and deforming parts from the input collection. The generative model also yields compact shape descriptors that are used to perform fine-grained classification. Finally, it can be also coupled with the probabilistic deformation model to further improve shape correspondence. We provide qualitative and quantitative evaluations of our method for shape correspondence, segmentation, fine-grained classification and synthesis. Our experiments demonstrate superior correspondence and segmentation results than previous state-of-the-art approaches.Item Quaternion Julia Set Shape Optimization(The Eurographics Association and John Wiley & Sons Ltd., 2015) Kim, Theodore; Mirela Ben-Chen and Ligang LiuWe present the first 3D algorithm capable of answering the question: what would a Mandelbrot-like set in the shape of a bunny look like? More concretely, can we find an iterated quaternion rational map whose potential field contains an isocontour with a desired shape? We show that it is possible to answer this question by casting it as a shape optimization that discovers novel, highly complex shapes. The problem can be written as an energy minimization, the optimization can be made practical by using an efficient method for gradient evaluation, and convergence can be accelerated by using a variety of multi-resolution strategies. The resulting shapes are not invariant under common operations such as translation, and instead undergo intricate, non-linear transformations.Item T-SAH: Animation Optimized Bounding Volume Hierarchies(The Eurographics Association and John Wiley & Sons Ltd., 2015) Bittner, JirĂ; Meister, Daniel; Olga Sorkine-Hornung and Michael WimmerWe propose a method for creating a bounding volume hierarchy (BVH) that is optimized for all frames of a given animated scene. The method is based on a novel extension of surface area heuristic to temporal domain (T-SAH). We perform iterative BVH optimization using T-SAH and create a single BVH accounting for scene geometry distribution at different frames of the animation. Having a single optimized BVH for the whole animation makes our method extremely easy to integrate to any application using BVHs, limiting the per-frame overhead only to refitting the bounding volumes.We evaluated the T-SAH optimized BVHs in the scope of real-time GPU ray tracing. We demonstrate, that our method can handle even highly complex inputs with large deformations and significant topology changes. The results show, that in a vast majority of tested scenes our method provides significantly better run-time performance than traditional SAH and also better performance than GPU based per-frame BVH rebuild.