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Item Symmetry in 3D Geometry: Extraction and Applications(The Eurographics Association and Blackwell Publishing Ltd., 2013) Mitra, Niloy J.; Pauly, Mark; Wand, Michael; Ceylan, Duygu; Holly Rushmeier and Oliver DeussenThe concept of symmetry has received significant attention in computer graphics and computer vision research in recent years. Numerous methods have been proposed to find, extract, encode and exploit geometric symmetries and high‐level structural information for a wide variety of geometry processing tasks. This report surveys and classifies recent developments in symmetry detection. We focus on elucidating the key similarities and differences between existing methods to gain a better understanding of a fundamental problem in digital geometry processing and shape understanding in general. We discuss a variety of applications in computer graphics and geometry processing that benefit from symmetry information for more effective processing. An analysis of the strengths and limitations of existing algorithms highlights the plenitude of opportunities for future research both in terms of theory and applications.The concept of symmetry has received significant attention in computer graphics and computer vision research in recent years. Numerous methods have been proposed to find, extract, encode, and exploit geometric symmetries and high‐level structural information for a wide variety of geometry processing tasks. This report surveys and classifies recent developments in symmetry detection. We focus on elucidating the key similarities and differences between existing methods to gain a better understanding of a fundamental problem in digital geometry processing and shape understanding in general.Item Enhancing Bayesian Estimators for Removing Camera Shake(The Eurographics Association and Blackwell Publishing Ltd., 2013) Wang, C.; Yue, Y.; Dong, F.; Tao, Y.; Ma, X.; Clapworthy, G.; Ye, X.; Holly Rushmeier and Oliver DeussenThe aim of removing camera shake is to estimate a sharp version x from a shaken image y when the blur kernel k is unknown. Recent research on this topic evolved through two paradigms called MAP(k) and MAP(x,k). MAP(k) only solves for k by marginalizing the image prior, while MAP(x,k) recovers both x and k by selecting the mode of the posterior distribution. This paper first systematically analyses the latent limitations of these two estimators through Bayesian analysis. We explain the reason why it is so difficult for image statistics to solve the previously reported MAP(x,k) failure. Then we show that the leading MAP(x,k) methods, which depend on efficient prediction of large step edges, are not robust to natural images due to the diversity of edges. MAP(k), although much more robust to diverse edges, is constrained by two factors: the prior variation over different images, and the ratio between image size and kernel size. To overcome these limitations, we introduce an inter‐scale prior prediction scheme and a principled mechanism for integrating the sharpening filter into MAP(k). Both qualitative results and extensive quantitative comparisons demonstrate that our algorithm outperforms state‐of‐the‐art methods.The aim of removing camera shake is to estimate a sharp version x from a shaken image y when the blur kernel k is unknown. Recent research on this topic evolved through two paradigms called MAP(k) and MAP(x,k). MAP(k) only solves for k by marginalizing the image prior, while MAP(x,k) recovers both x and k by selecting the mode of the posterior distribution. This paper first systematically analyzes the latent limitations of these two estimators through Bayesian analysis. We explain the reason why it is so difficult for image statistics to solve the previously reported MAP(x,k) failure. Then we show that the leading MAP(x,k) methods, which depend on efficient prediction of large step edges, are not robust to natural images due to the diversity of edges. MAP(k), although much more robust to diverse edges, is constrained by two factors: the prior variation over different images, and the ratio between image size and kernel size.Item InK‐Compact: In‐Kernel Stream Compaction and Its Application to Multi‐Kernel Data Visualization on General‐Purpose GPUs(The Eurographics Association and Blackwell Publishing Ltd., 2013) Hughes, D. M.; Lim, I. S.; Jones, M. W.; Knoll, A.; Spencer, B.; Holly Rushmeier and Oliver DeussenStream compaction is an important parallel computing primitive that produces a reduced (compacted) output stream consisting of only valid elements from an input stream containing both invalid and valid elements. Computing on this compacted stream rather than the mixed input stream leads to improvements in performance, load balancing and memory footprint. Stream compaction has numerous applications in a wide range of domains: e.g. deferred shading, isosurface extraction and surface voxelization in computer graphics and visualization. We present a novel In‐Kernel stream compaction method, where compaction is completed before leaving an operating kernel. This contrasts with conventional parallel compaction methods that require leaving the kernel and running a prefix sum kernel followed by a scatter kernel. We apply our compaction methods to ray‐tracing‐based visualization of volumetric data. We demonstrate that the proposed In‐Kernel compaction outperforms the standard out‐of‐kernel Thrust parallel‐scan method for performing stream compaction in this real‐world application. For the data visualization, we also propose a novel multi‐kernel ray‐tracing pipeline for increased thread coherency and show that it outperforms a conventional single‐kernel approach.Stream compaction is an important parallel computing primitive that produces a reduced (compacted) output stream consisting of only valid elements from an input stream containing both invalid and valid elements. Computing on this compacted stream rather than the mixed input stream leads to improvements in performance, load balancing, and memory footprint. Stream compaction has numerous applications in a wide range of domains: e.g., deferred shading, isosurface extraction, and surface voxelization in computer graphics and visualization. We present a novel In‐Kernel stream compaction method, where compaction is completed before leaving an operating kernel. This contrasts with conventional parallel compaction methods that require leaving the kernel and running a prefix sum kernel followed by a scatter kernel.