18 research outputs found
ZoomOut: Spectral Upsampling for Efficient Shape Correspondence
International audienceWe 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
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Multiphysics simulations: challenges and opportunities.
This report is an outcome of the workshop Multiphysics Simulations: Challenges and Opportunities, sponsored by the Institute of Computing in Science (ICiS). Additional information about the workshop, including relevant reading and presentations on multiphysics issues in applications, algorithms, and software, is available via https://sites.google.com/site/icismultiphysics2011/. We consider multiphysics applications from algorithmic and architectural perspectives, where 'algorithmic' includes both mathematical analysis and computational complexity and 'architectural' includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities. We also initiate a modest suite of test problems encompassing features present in many applications