32-Issue 6

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https://diglib.eg.org/handle/10.2312/184

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34th EUROGRAPHICS General Assembly
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Holly Rushmeier and Oliver Deussen
Analysis and Visualization of Maps Between Shapes
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Ovsjanikov, M.; Ben-Chen, M.; Chazal, F.; Guibas, L.; Holly Rushmeier and Oliver Deussen
In this paper we propose a method for analysing and visualizing individual maps between shapes, or collections of such maps. Our method is based on isolating and highlighting areas where the maps induce significant distortion of a given measure in a multi‐scale way. Unlike the majority of prior work, which focuses on discovering maps in the context of shape matching, our main focus is on evaluating, analysing and visualizing a given map, and the distortion(s) it introduces, in an efficient and intuitive way. We are motivated primarily by the fact that most existing metrics for map evaluation are quadratic and expensive to compute in practice, and that current map visualization techniques are suitable primarily for global map understanding, and typically do not highlight areas where the map fails to meet certain quality criteria in a multi‐scale way. We propose to address these challenges in a unified way by considering the functional representation of a map, and performing spectral analysis on this representation. In particular, we propose a simple multi‐scale method for map evaluation and visualization, which provides detailed multi‐scale information about the distortion induced by a map, which can be used alongside existing global visualization techniques.In this paper we propose a method for analyzing and visualizing individual maps between shapes, or collections of such maps. Our method is based on isolating and highlighting areas where the maps induce significant distortion of a given measure in a multi‐scale way. Unlike the majority of prior work which focuses on discovering maps in the context of shape matching, our main focus is on evaluating, analyzing and visualizing a given map, and the distortion(s) it introduces, in an efficient and intuitive way. We are motivated primarily by the fact that most existing metrics for map evaluation are quadratic and expensive to compute in practice, and that current map visualization techniques are suitable primarily for global map understanding, and typically do not highlight areas where the map fails to meet certain quality criteria in a multi‐scale way. We propose to address these challenges in a unified way by considering the functional representation of a map, and performing spectral analysis on this representation. In particular, we propose a simple multi‐scale method for map evaluation and visualization, which provides detailed multi‐scale information about the distortion induced by a map, which can be used alongside existing global visualization techniques.
Bilateral Maps for Partial Matching
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Kaick, Oliver van; Zhang, Hao; Hamarneh, Ghassan; Holly Rushmeier and Oliver Deussen
Feature‐driven analysis forms the basis of many shape processing tasks, where detected feature points are characterized by local shape descriptors. Such descriptors have so far been defined to capture regions of interest centred at individual points. Using such regions to compare feature points can be problematic when performing partial shape matching, because the region of interest is typically defined as an isotropic neighbourhood around a point, which does not adapt to the geometry of the shape parts. We introduce the bilateral map, a local shape descriptor whose region of interest is defined by two feature points. Compared to the classical descriptor definition using a single point, the bilateral approach exploits the use of a second point to place more constraints on the selection of the spatial context for feature analysis. This leads to a descriptor where the shape of the region of interest adapts to the context of the two points, making it more refined for shape matching. In particular, we show that our new descriptor is more effective for partial matching, because potentially extraneous regions of the models are selectively ignored owing to the adaptive nature of the bilateral map. This property also renders the bilateral map partially insensitive to topological changes. We demonstrate the effectiveness of the bilateral map for partial matching via several correspondence and retrieval experiments and evaluate the results both qualitatively and quantitatively.Feature‐driven analysis forms the basis of many shape processing tasks, where detected feature points are characterized by local shape descriptors. Such descriptors have so far been defined to capture regions of interest centered at individual points. Using such regions to compare feature points can be problematic when performing partial shape matching, since the region of interest is typically defined as an isotropic neighborhood around a point, which does not adapt to the geometry of the shape parts. We introduce the bilateral map, a local shape descriptor whose region of interest is defined by two feature points. Compared to the classical descriptor definition using a single point, the bilateral approach exploits the use of a second point to place more constraints on the selection of the spatial context for feature analysis.
A Collaborative Digital Pathology System for Multi‐Touch Mobile and Desktop Computing Platforms
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Jeong, W.; Schneider, J.; Hansen, A.; Lee, M.; Turney, S. G.; Faulkner‐Jones, B. E.; Hecht, J. L.; Najarian, R.; Yee, E.; Lichtman, J. W.; Pfister, H.; Holly Rushmeier and Oliver Deussen
Collaborative slide image viewing systems are becoming increasingly important in pathology applications such as telepathology and E‐learning. Despite rapid advances in computing and imaging technology, current digital pathology systems have limited performance with respect to remote viewing of whole slide images on desktop or mobile computing devices. In this paper we present a novel digital pathology client–server system that supports collaborative viewing of multi‐plane whole slide images over standard networks using multi‐touch‐enabled clients. Our system is built upon a standard HTTP web server and a MySQL database to allow multiple clients to exchange image and metadata concurrently. We introduce a domain‐specific image‐stack compression method that leverages real‐time hardware decoding on mobile devices. It adaptively encodes image stacks in a decorrelated colour space to achieve extremely low bitrates (0.8 bpp) with very low loss of image quality. We evaluate the image quality of our compression method and the performance of our system for diagnosis with an in‐depth user study.Collaborative slide image viewing systems are becoming increasingly important in pathology applications such as telepathology and E‐learning. Despite rapid advances in computing and imaging technology, current digital pathology systems have limited performance with respect to remote viewing of whole slide images on desktop or mobile computing devices. In this paper we present a novel digital pathology client‐server systems that supports collaborative viewing of multi‐plane whole slide images over standard networks using multi‐touch enabled clients. Our system is built upon a standard HTTP web server and a MySQL database to allow multiple clients to exchange image and metadata concurrently.
Concentric Spherical Representation for Omnidirectional Soft Shadow
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Xiao, Yi; Leung, Chi Sing; Ho, Tze Yui; Wan, Liang; Wong, Tien Tsing; Holly Rushmeier and Oliver Deussen
Soft shadows play an important role in photo‐realistic rendering. Although there are many efficient soft shadow algorithms, most of them focus on the one‐side light source situation, where a planar light source is on the outside of the scene. In fact, in many situations, such as games, light sources are omnidirectional. They may be surrounded by a number of 3D objects. This paper proposes a soft shadow algorithm for the omnidirectional situation. We develop a concentric spherical representation to model the behaviour of omnidirectional light sources. To provide better rendering results, a novel summed area table based filtering scheme for spherical functions is proposed. In addition, we utilize unicube mapping, which samples the spherical space more uniformly, to further improve the filtering quality.Soft shadows play an important role in photo‐realistic rendering. Although there are many efficient soft shadow algorithms, most of them focus on the one‐side light source situation, where a planar light source is on the outside of the scene. In fact, in many situations, such as games, light sources are omnidirectional. They may be surrounded by a number of 3D objects. This paper proposes a soft shadow algorithm for the omnidirectional situation.
Curve Style Analysis in a Set of Shapes
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Li, H.; Zhang, H.; Wang, Y.; Cao, J.; Shamir, A.; Cohen‐Or, D.; Holly Rushmeier and Oliver Deussen
The word ‘style’ can be interpreted in so many different ways in so many different contexts. To provide a general analysis and understanding of styles is a highly challenging problem. We pose the open question ‘how to extract styles from geometric shapes?’ and address one instance of the problem. Specifically, we present an unsupervised algorithm for identifying curve styles in a set of shapes. In our setting, a curve style is explicitly represented by a mode of curve features appearing along the 2D silhouettes of the shapes in the set. Unlike previous attempts, we do not rely on any preconceived conceptual characterisations, for example, via specific shape descriptors, to define what is or is not a style. Our definition of styles is data‐dependent; it depends on the input set but we do not require computing a shape correspondence across the set. We provide an operational definition of curve styles which focuses on separating curve features that represent styles from curve features that are content revealing. To this end, we develop a novel formulation and associated algorithm for style‐content separation. The analysis is based on a feature‐shape association matrix (FSM) whose rows correspond to modes of curve features, columns to shapes in the set, and each entry expresses the extent a feature mode is present in a shape. We make several assumptions to drive style‐content separation which only involve properties of, and relations between, rows of the FSM. Computationally, our algorithm only requires row‐wise correlation analysis in the FSM and a heuristic solution of an instance of the set cover problem. Results are demonstrated on several data sets showing the identification of curve styles. We also develop and demonstrate several style‐related applications including style exaggeration, removal, blending, and style transfer for 2D shape synthesis.Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi‐regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this survey we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing.
Efficient Non‐linear Optimization via Multi‐scale Gradient Filtering
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Martin, Tobias; Joshi, Pushkar; Bergou, Miklós; Carr, Nathan; Holly Rushmeier and Oliver Deussen
We present a method for accelerating the convergence of continuous non‐linear shape optimization algorithms. We start with a general method for constructing gradient vector fields on a manifold, and we analyse this method from a signal processing viewpoint. This analysis reveals that we can construct various filters using the Laplace–Beltrami operator of the shape that can effectively separate the components of the gradient at different scales. We use this idea to adaptively change the scale of features being optimized to arrive at a solution that is optimal across multiple scales. This is in contrast to traditional descent‐based methods, for which the rate of convergence often stalls early once the high frequency components have been optimized. We demonstrate how our method can be easily integrated into existing non‐linear optimization frameworks such as gradient descent, Broyden–Fletcher–Goldfarb–Shanno (BFGS) and the non‐linear conjugate gradient method. We show significant performance improvement for shape optimization in variational shape modelling and parameterization, and we also demonstrate the use of our method for efficient physical simulation.We present a method for accelerating the convergence of continuous nonlinear shape optimization algorithms. We start with a general method for constructing gradient vector fields on a manifold, and we analyze this method from a signal processing viewpoint. This analysis reveals that we can construct various filters using the Laplace‐Beltrami operator of the shape that can effectively separate the components of the gradient at different scales. We use this idea to adaptively change the scale of features being optimized in order to arrive at a solution that is optimal across multiple scales.
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 Deussen
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 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.
Erratum
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Holly Rushmeier and Oliver Deussen
Full Wave Modelling of Light Propagation and Reflection
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Musbach, A.; Meyer, G. W.; Reitich, F.; Oh, S. H.; Holly Rushmeier and Oliver Deussen
The propagation and reflection of electromagnetic waves in a three‐dimensional environment is simulated, and realistic images are produced using the resulting light distributions and reflectance functions. A finite difference time domain method is employed to advance the electric and magnetic fields in a scene. Surfaces containing wavelength scaled structures are created, the interaction of the electromagnetic waves with these nano‐structured materials is calculated, and the sub‐surface interference and diffraction effects are modelled. The result is a reflectance function with wavelength composition and spatial distribution properties that could not have been predicted using classic computer graphic ray tracing approaches. The techniques are employed to reproduce demonstrations of simple interference and diffraction effects, and to create computer‐generated pictures of a Morpho butterfly.The propagation and reflection of electromagnetic waves in a three‐dimensional environment is simulated, and realistic images are produced using the resulting light distributions and reflectance functions. A finite difference time domain method is employed to advance the electric and magnetic fields in a scene. Surfaces containing wavelength scaled structures are created, the interaction of the electromagnetic waves with these nano‐structured materials is calculated, and the sub‐surface interference and diffraction effects are modeled. The result is a reflectance function with wavelength composition and spatial distribution properties that could not have been predicted using classic computer graphic ray tracing approaches.
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 Deussen
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. 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.
Issue Information
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Holly Rushmeier and Oliver Deussen
Mesh‐Free Discrete Laplace–Beltrami Operator
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Petronetto, F.; Paiva, A.; Helou, E. S.; Stewart, D. E.; Nonato, L. G.; Holly Rushmeier and Oliver Deussen
In this work we propose a new discretization method for the Laplace–Beltrami operator defined on point‐based surfaces. In contrast to the existing point‐based discretization techniques, our approach does not rely on any triangle mesh structure, turning out truly mesh‐free. Based on a combination of Smoothed Particle Hydrodynamics and an optimization procedure to estimate area elements, our discretization method results in accurate solutions while still being robust when facing abrupt changes in the density of points. Moreover, the proposed scheme results in numerically stable discrete operators. The effectiveness of the proposed technique is brought to bear in many practical applications. In particular, we use the eigenstructure of the discrete operator for filtering and shape segmentation. Point‐based surface deformation is another application that can be easily carried out from the proposed discretization method.In this work we propose a new discretization method for the Laplace–Beltrami operator defined on point‐based surfaces. In contrast to the existing point‐based discretization techniques, our approach does not rely on any triangle mesh structure, turning out truly meshfree. Based on a combination of Smoothed Particle Hydrodynamics and an optimization procedure to estimate area elements, our discretization method results in accurate solutions while still being robust when facing abrupt changes in the density of points. Moreover, the proposed scheme results in numerically stable discrete operators. The effectiveness of the proposed technique is brought to bear in many practical applications.
New EUROGRAPHICS Fellows
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Deussen, Oliver; Rushmeier, Holly; Holly Rushmeier and Oliver Deussen
Quad‐Mesh Generation and Processing: A Survey
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Bommes, David; Lévy, Bruno; Pietroni, Nico; Puppo, Enrico; Silva, Claudio; Tarini, Marco; Zorin, Denis; Holly Rushmeier and Oliver Deussen
Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi‐regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this survey we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrisation and remeshing.Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi‐regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this survey we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing.
Real‐Time Defocus Rendering With Level of Detail and Sub‐Sample Blur
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Jeong, Yuna; Kim, Kangtae; Lee, Sungkil; Holly Rushmeier and Oliver Deussen
This paper presents a GPU‐based rendering algorithm for real‐time defocus blur effects, which significantly improves the accumulation buffering. The algorithm combines three distinctive techniques: (1) adaptive discrete geometric level of detail (LOD), made popping‐free by blending visibility samples across the two adjacent geometric levels; (2) adaptive visibility/shading sampling via sample reuse; (3) visibility supersampling via height‐field ray casting. All the three techniques are seamlessly integrated to lower the rendering cost of smooth defocus blur with high visibility sampling rates, while maintaining most of the quality of brute‐force accumulation buffering.This paper presents a GPU‐based rendering algorithm for real‐time defocus blur effects, which significantly improves the accumulation buffering. The algorithm combines three distinctive techniques: (1) adaptive discrete geometric level of detail (LOD), made popping‐free by blending visibility samples across the two adjacent geometric levels; (2) adaptive visibility/shading sampling via sample reuse; (3) visibility supersampling via height‐field ray casting. All the three techniques are seamlessly integrated to lower the rendering cost of smooth defocus blur with high visibility sampling rates, while maintaining most of the quality of brute‐force accumulation buffering.
REPORT OF THE STATUTORY AUDITORS TO THE GENERAL MEETING OF THE MEMBERS OF EUROGRAPHICS ASSOCIATION GENEVA
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Holly Rushmeier and Oliver Deussen
Robust Fitting on Poorly Sampled Data for Surface Light Field Rendering and Image Relighting
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Vanhoey, K.; Sauvage, B.; Génevaux, O.; Larue, F.; Dischler, J.‐M.; Holly Rushmeier and Oliver Deussen
Two‐dimensional (2D) parametric colour functions are widely used in Image‐Based Rendering and Image Relighting. They make it possible to express the colour of a point depending on a continuous directional parameter: the viewing or the incident light direction. Producing such functions from acquired data is promising but difficult. Indeed, an intensive acquisition process resulting in dense and uniform sampling is not always possible. Conversely, a simpler acquisition process results in sparse, scattered and noisy data on which parametric functions can hardly be fitted without introducing artefacts. Within this context, we present two contributions. The first one is a robust least‐squares‐based method for fitting 2D parametric colour functions on sparse and scattered data. Our method works for any amount and distribution of acquired data, as well as for any function expressed as a linear combination of basis functions. We tested our fitting for both image‐based rendering (surface light fields) and image relighting using polynomials and spherical harmonics. The second one is a statistical analysis to measure the robustness of any fitting method. This measure assesses a trade‐off between precision of the fitting and stability with respect to input sampling conditions. This analysis along with visual results confirm that our fitting method is robust and reduces reconstruction artefacts for poorly sampled data while preserving the precision for a dense and uniform sampling.Generating surface light fields from real acquisition campaigns' data often leads to robustness issues that are due to irregular distribution and sparsity of the photographic sampling. Within this context, we present a robust least‐squares‐based method for fitting 2D parametric colour functions on sparse and scattered data. Moreover, we provide a statistical analysis to measure the robustness of such fitting approaches. The proposed method allows, on one hand, for high‐quality reconstructions in good sampling conditions and, on the other hand, for robust and predictable reconstructions in poor sampling conditions.
A Survey of Urban Reconstruction
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Musialski, P.; Wonka, P.; Aliaga, D. G.; Wimmer, M.; Gool, L.; Purgathofer, W.; Holly Rushmeier and Oliver Deussen
This paper provides a comprehensive overview of urban reconstruction. While there exists a considerable body of literature, this topic is still under active research. The work reviewed in this survey stems from the following three research communities: computer graphics, computer vision and photogrammetry and remote sensing. Our goal is to provide a survey that will help researchers to better position their own work in the context of existing solutions, and to help newcomers and practitioners in computer graphics to quickly gain an overview of this vast field. Further, we would like to bring the mentioned research communities to even more interdisciplinary work, since the reconstruction problem itself is by far not solved.This paper provides a comprehensive overview of urban reconstruction. While there exists a considerable body of literature, this topic is still under active research. The work reviewed in this survey stems from the following three research communities: computer graphics, computer vision and photogrammetry and remote sensing. Our goal is to provide a survey that will help researchers to better position their own work in the context of existing solutions, and to help newcomers and practitioners in computer graphics to quickly gain an overview of this vast field. Further, we would like to bring the mentioned research communities to even more interdisciplinary work, since the reconstruction problem itself is by far not solved.
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 Deussen
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. 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.

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