ZoomOut: Spectral Upsampling for Efficient Shape Correspondence

Abstract: We present a simple and efficient method for refining maps or correspondences by iterative upsampling in the spectral domain that can be implemented in a few lines of code. Our main observation is that high quality maps can be obtained even if the input correspondences are noisy or are encoded by a small number of coefficients in a spectral basis. We show how this approach can be used in conjunction with existing initialization techniques across a range of application scenarios, including symmetry detection, map refinement across complete shapes, non-rigid partial shape matching and function transfer. In each application we demonstrate an improvement with respect to both the quality of the results and the computational speed compared to the best competing methods, with up to two orders of magnitude speed-up in some applications. We also demonstrate that our method is both robust to noisy input and is scalable with respect to shape complexity. Finally, we present a theoretical justification for our approach, shedding light on structural properties of functional maps.

Authors/Presenter(s): Simone Melzi, University of Verona, Italy
Jing Ren, KAUST, Saudi Arabia
Emanuele Rodolà, Sapienza University of Rome, Italy
Abhishek Sharma, Laboratoire d'informatique de l'École Polytechnique (LIX), France
Peter Wonka, KAUST, Saudi Arabia
Maks Ovsjanikov, Laboratoire d'informatique de l'École Polytechnique (LIX), France

Distortion-Minimizing Injective Maps Between Surfaces

Abstract: The problem of discrete surface parametrization, i.e. mapping a mesh to a planar domain, has been investigated extensively. We address the more general problem of mapping between surfaces. In particular, we provide a formulation that yields a map between two disk-topology meshes, which is continuous and injective by construction and which locally minimizes intrinsic distortion. A common approach is to express such a map as the composition of two maps via a simple intermediate domain such as the plane, and to independently optimize the individual maps. However, even if both individual maps are of minimal distortion, there is potentially high distortion in the composed map. In contrast to many previous works, we minimize distortion in an end-to-end manner, directly optimizing the quality of the composed map. This setting poses additional challenges due to the discrete nature of both the source and the target domain. We propose a formulation that, despite the combinatorial aspects of the problem, allows for a purely continuous optimization. Further, our approach addresses the non-smooth nature of discrete distortion measures in this context which hinders straightforward application of off-the-shelf optimization techniques. We demonstrate that, despite the challenges inherent to the more involved setting, discrete surface-to-surface maps can be optimized effectively.

Authors/Presenter(s): Patrick Schmidt, RWTH Aachen University, Germany
Janis Born, RWTH Aachen University, Germany
Marcel Campen, Osnabrück University, Germany
Leif Kobbelt, RWTH Aachen University, Germany

X-CAD: Optimizing CAD Models with Extended Finite Elements

Abstract: We propose a novel generic shape optimization method for CAD models based on the eXtended Finite Element Method (XFEM). Our method works directly on the intersection between the model and a regular simulation grid, without the need to mesh or remesh, thus removing a bottleneck of classical shape optimization strategies. This is made possible by a novel hierarchical integration scheme that accurately integrates finite element quantities with sub-element precision. For optimization, we efficiently compute analytical shape derivatives of the entire framework, from model intersection to integration rule generation and XFEM simulation. Moreover, we describe a differentiable projection of shape parameters onto a constraint manifold spanned by user-specified shape preservation, consistency, and manufacturability constraints. We demonstrate the utility of our approach by optimizing mass distribution, strength-to-weight ratio, and inverse elastic shape design objectives directly on parameterized 3D CAD models.

Authors/Presenter(s): Christian Hafner, Institute of Science and Technology Austria, Disney Research, Austria
Christian Schumacher, Disney Research, Switzerland
Espen Knoop, Disney Research, Switzerland
Thomas Auzinger@ist.ac.at, Institute of Science and Technology Austria, Austria
Bernd Bickel, Institute of Science and Technology Austria, Austria
Moritz Bächer, Disney Research, Switzerland

Repairing Man-Made Meshes via Visual Driven Global Optimization with Minimum Intrusion

Abstract: 3D mesh models created by human users and shared through online platforms and datasets flourish recently. While the creators generally have spent large efforts in modeling the visually appealing shapes with both large scale structures and intricate details, a majority of the meshes are unfortunately flawed in terms of having duplicate faces, mis-oriented regions, disconnected patches, etc., due to multiple factors involving both human errors and software inconsistencies. All these artifacts have severely limited the possible low-level and high-level processing tasks that can be applied to the rich datasets. In this work, we present a novel approach to fix these man-made meshes such that the outputs are guaranteed to be oriented manifold meshes that preserve the original structures, big and small, as much as possible. Our key observation is that the models all visually look meaningful, which leads to our strategy of repairing the flaws while always preserving the visual quality. We apply local refinements and removals only where necessary to achieve minimal intrusion of the original meshes, and global adjustments through robust optimization to ensure the outputs are valid manifold meshes with optimal connections. We test the approach on large-scale 3D datasets, and obtain quality meshes that are more readily usable for further geometry processing tasks.

Authors/Presenter(s): Lei Chu, The University of Hong Kong, Microsoft Research Asia, Hong Kong
Hao Pan, Microsoft Research Asia, China
Yang Liu, Microsoft Research Asia, China
Wenping Wang, The University of Hong Kong, Hong Kong

SceneGit: A Practical System for Diffing and Merging 3D Environments

Abstract: Version control systems are at the base of collaborative workflows for text documents. For 3D environments though, version control is still an open problem due to the heterogeneous data of 3D scenes and their size. In this paper, we present a practical version control system for 3D scenes comprised of shapes, materials, textures, and animations, combined together in scene graphs. We version objects at their finest granularity, to make repositories smaller and to allow artists to work concurrently on the same object. Since, for some scene data, computing an optimal set of changes between versions is not computationally feasible, version control systems use heuristics. Compared to prior work, we propose heuristics that are efficient, robust, and independent of the application. We test our system on a variety of large scenes edited with different workflows, and show that our approach can handle all cases well while remaining efficient as scene size increases. Compared to prior work, we are significantly faster and more robust. A user study confirms that our system aids collaboration.

Authors/Presenter(s): Edoardo Carra, Sapienza University of Rome, Italy
Fabio Pellacini, Sapienza University of Rome, Italy