Volume 38 (2019)
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Item Solid Geometry Processing on Deconstructed Domains(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Sellán, Silvia; Cheng, Herng Yi; Ma, Yuming; Dembowski, Mitchell; Jacobson, Alec; Chen, Min and Benes, BedrichMany tasks in geometry processing are modelled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh. Unfortunately, tetrahedral meshing remains an open challenge and existing methods either struggle to conform to complex boundary surfaces or require manual intervention to prevent failure. Rather than create a single volumetric mesh for the entire shape, we advocate for solid geometry processing on , where a large and complex shape is composed of overlapping solid subdomains. As each smaller and simpler part is now easier to tetrahedralize, the question becomes how to account for overlaps during problem modelling and how to couple solutions on each subdomain together . We explore how and why previous coupling methods fail, and propose a method that couples solid domains only along their boundary surfaces. We demonstrate the superiority of this method through empirical convergence tests and qualitative applications to solid geometry processing on a variety of popular second‐order and fourth‐order partial differential equations.Many tasks in geometry processing are modelled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh. Unfortunately, tetrahedral meshing remains an open challenge and existing methods either struggle to conform to complex boundary surfaces or require manual intervention to prevent failure. Rather than create a single volumetric mesh for the entire shape, we advocate for solid geometry processing on , where a large and complex shape is composed of overlapping solid subdomains. As each smaller and simpler part is now easier to tetrahedralize, the question becomes how to account for overlaps during problem modelling and how to couple solutions on each subdomain together . We explore how and why previous coupling methods fail, and propose a method that couples solid domains only along their boundary surfaces. We demonstrate the superiority of this method through empirical convergence tests and qualitative applications to solid geometry processing on a variety of popular second‐order and fourth‐order partial differential equations.Item Divergence-Free Shape Correspondence by Deformation(The Eurographics Association and John Wiley & Sons Ltd., 2019) Eisenberger, Marvin; Lähner, Zorah; Cremers, Daniel; Bommes, David and Huang, HuiWe present a novel approach for solving the correspondence problem between a given pair of input shapes with non-rigid, nearly isometric pose difference. Our method alternates between calculating a deformation field and a sparse correspondence. The deformation field is constructed with a low rank Fourier basis which allows for a compact representation. Furthermore, we restrict the deformation fields to be divergence-free which makes our morphings volume preserving. This can be used to extract a correspondence between the inputs by deforming one of them along the deformation field using a second order Runge-Kutta method and resulting in an alignment of the inputs. The advantages of using our basis are that there is no need to discretize the embedding space and the deformation is volume preserving. The optimization of the deformation field is done efficiently using only a subsampling of the orginal shapes but the correspondence can be extracted for any mesh resolution with close to linear increase in runtime. We show 3D correspondence results on several known data sets and examples of natural intermediate shape sequences that appear as a by-product of our method.Item MyEvents: A Personal Visual Analytics Approach for Mining Key Events and Knowledge Discovery in Support of Personal Reminiscence(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Parvinzamir, F.; Zhao, Y.; Deng, Z.; Dong, F.; Chen, Min and Benes, BedrichReminiscence is an important aspect in our life. It preserves precious memories, allows us to form our own identities and encourages us to accept the past. Our work takes the advantage of modern sensor technologies to support reminiscence, enabling self‐monitoring of personal activities and individual movement in space and time on a daily basis. This paper presents MyEvents, a web‐based personal visual analytics platform designed for non‐computing experts, that allows for the collection of long‐term location and movement data and the generation of event mementos. Our research is focused on two prominent goals in event reminiscence: (1) selection subjectivity and human involvement in the process of self‐knowledge discovery and memento creation; and (2) the enhancement of event familiarity by presenting target events and their related information for optimal memory recall and reminiscence. A novel multi‐significance event ranking model is proposed to determine significant events in the personal history according to user preferences for event category, frequency and regularity. The evaluation results show that MyEvents effectively fulfils the reminiscence goals and tasks.Reminiscence is an important aspect in our life. It preserves precious memories, allows us to form our own identities and encourages us to accept the past. Our work takes the advantage of modern sensor technologies to support reminiscence, enabling self‐monitoring of personal activities and individual movement in space and time on a daily basis. This paper presents MyEvents, a web‐based personal visual analytics platform designed for non‐computing experts, that allows for the collection of long‐term location and movement data and the generation of event mementos. Our research is focused on two prominent goals in event reminiscence: (1) selection subjectivity and human involvement in the process of self‐knowledge discovery and memento creation; and (2) the enhancement of event familiarity by presenting target events and their related information for optimal memory recall and reminiscence. A novel multi‐significance event ranking model is proposed to determine significant events in the personal history according to user preferences for event category, frequency and regularity. The evaluation results show that MyEvents effectively fulfils the reminiscence goals and tasks.Item Wavelet Flow: Optical Flow Guided Wavelet Facial Image Fusion(The Eurographics Association and John Wiley & Sons Ltd., 2019) Ding, Hong; Yan, Qingan; Fu, Gang; Xiao, Chunxia; Lee, Jehee and Theobalt, Christian and Wetzstein, GordonEstimating the correspondence between the images using optical flow is the key component for image fusion, however, computing optical flow between a pair of facial images including backgrounds is challenging due to large differences in illumination, texture, color and background in the images. To improve optical flow results for image fusion, we propose a novel flow estimation method, wavelet flow, which can handle both the face and background in the input images. The key idea is that instead of computing flow directly between the input image pair, we estimate the image flow by incorporating multi-scale image transfer and optical flow guided wavelet fusion. Multi-scale image transfer helps to preserve the background and lighting detail of input, while optical flow guided wavelet fusion produces a series of intermediate images for further fusion quality optimizing. Our approach can significantly improve the performance of the optical flow algorithm and provide more natural fusion results for both faces and backgrounds in the images. We evaluate our method on a variety of datasets to show its high outperformance.Item Generic Interactive Pixel-level Image Editing(The Eurographics Association and John Wiley & Sons Ltd., 2019) Liang, Yun; Gan, Yibo; Chen, Mingqin; Gutierrez, Diego; Muñoz Orbañanos, Adolfo; Lee, Jehee and Theobalt, Christian and Wetzstein, GordonSeveral image editing methods have been proposed in the past decades, achieving brilliant results. The most sophisticated of them, however, require additional information per-pixel. For instance, dehazing requires a specific transmittance value per pixel, or depth of field blurring requires depth or disparity values per pixel. This additional per-pixel value is obtained either through elaborated heuristics or through additional control over the capture hardware, which is very often tailored for the specific editing application. In contrast, however, we propose a generic editing paradigm that can become the base of several different applications. This paradigm generates both the needed per-pixel values and the resulting edit at interactive rates, with minimal user input that can be iteratively refined. Our key insight for getting per-pixel values at such speed is to cluster them into superpixels, but, instead of a constant value per superpixel (which yields accuracy problems), we have a mathematical expression for pixel values at each superpixel: in our case, an order two multinomial per superpixel. This leads to a linear leastsquares system, effectively enabling specific per-pixel values at fast speeds. We illustrate this approach in three applications: depth of field blurring (from depth values), dehazing (from transmittance values) and tone mapping (from brightness and contrast local values), and our approach proves both favorably interactive and accurate in all three. Our technique is also evaluated with a common dataset and compared favorably.Item Visualization Support for Developing a Matrix Calculus Algorithm: A Case Study(The Eurographics Association and John Wiley & Sons Ltd., 2019) Giesen, Joachim; Klaus, Julien; Laue, Sören; Schreck, Ferdinand; Gleicher, Michael and Viola, Ivan and Leitte, HeikeThe development of custom interactive visualization tools for specific domains and applications has been made much simpler recently by a surge of visualization tools, libraries and frameworks. Most of these tools are developed for classical data science applications, where a user is supported in analyzing measured or simulated data. But recently, there has also been an increasing interest in visual support for understanding machine learning algorithms and frameworks, especially for deep learning. Many, if not most, of the visualization support for (deep) learning addresses the developer of the learning system and not the end user (data scientist). Here we show on a specific example, namely the development of a matrix calculus algorithm, that supporting visualizations can also greatly benefit the development of algorithms in classical domains like in our case computer algebra. The idea is similar to visually supporting the understanding of learning algorithms, namely provide the developer with an interactive, visual tool that provides insights into the workings and, importantly, also into the failures of the algorithm under development. Developing visualization support for matrix calculus development went similar as the development of more traditional visual support systems for data analysts. First, we had to acquaint ourselves with the problem, its language and challenges by talking to the core developer of the matrix calculus algorithm. Once we understood the challenge, it was fairly easy to develop visual support that streamlined the development of the matrix calculus algorithm significantly.Item Augmenting Tactile 3D Data Navigation With Pressure Sensing(The Eurographics Association and John Wiley & Sons Ltd., 2019) Wang, Xiyao; Besançon, Lonni; Ammi, Mehdi; Isenberg, Tobias; Gleicher, Michael and Viola, Ivan and Leitte, HeikeWe present a pressure-augmented tactile 3D data navigation technique, specifically designed for small devices, motivated by the need to support the interactive visualization beyond traditional workstations. While touch input has been studied extensively on large screens, current techniques do not scale to small and portable devices. We use phone-based pressure sensing with a binary mapping to separate interaction degrees of freedom (DOF) and thus allow users to easily select different manipulation schemes (e. g., users first perform only rotation and then with a simple pressure input to switch to translation). We compare our technique to traditional 3D-RST (rotation, scaling, translation) using a docking task in a controlled experiment. The results show that our technique increases the accuracy of interaction, with limited impact on speed. We discuss the implications for 3D interaction design and verify that our results extend to older devices with pseudo pressure and are valid in realistic phone usage scenarios.Item High Quality Refinable G-splines for Locally Quad-dominant Meshes With T-gons(The Eurographics Association and John Wiley & Sons Ltd., 2019) Karciauskas, Kestutis; Peters, Jorg; Bommes, David and Huang, HuiPolyhedral modeling and re-meshing algorithms use T-junctions to add or remove feature lines in a quadrilateral mesh. In many ways this is akin to adaptive knot insertion in a tensor-product spline, but differs in that the designer or meshing algorithm does not necessarily protect the consistent combinatorial structure that is required to interpret the resulting quad-dominant mesh as the control net of a hierarchical spline - and so associate a smooth surface with the mesh as in the popular tensor-product spline paradigm. While G-splines for multi-sided holes or generalized subdivision can, in principle, convert quad-dominant meshes with T-junctions into smooth surfaces, they do not preserve the two preferred directions and so cause visible shape artifacts. Only recently have n-gons with T-junctions (T-gons) in unstructured quad-dominant meshes been recognized as a distinct challenge for generalized splines. This paper makes precise the notion of locally quad-dominant mesh as quad-meshes including t-nets, i.e. T-gons surrounded by quads; and presents the first high-quality G-spline construction that can use t-nets as control nets for spline surfaces suitable, e.g., for automobile outer surfaces. Remarkably, T-gons can be neighbors, separated by only one quad, both of T-gons and of points where many quads meet. A t-net surface cap consists of 16 polynomial pieces of degree (3,5) and is refinable in a way that is consistent with the surrounding surface. An alternative, everywhere bi-3 cap is not formally smooth, but achieves the same high-quality highlight line distribution.Item Subdivision Schemes for Quadrilateral Meshes with the Least Polar Artifact in Extraordinary Regions(The Eurographics Association and John Wiley & Sons Ltd., 2019) Ma, Yue; Ma, Weiyin; Lee, Jehee and Theobalt, Christian and Wetzstein, GordonThis paper presents subdivision schemes with subdivision stencils near an extraordinary vertex that are free from or with substantially reduced polar artifact in extraordinary regions while maintaining the best possible bounded curvature at extraordinary positions. The subdivision stencils are firstly constructed to meet tangent plane continuity with bounded curvature at extraordinary positions. They are further optimized towards curvature continuity at an extraordinary position with additional measures for removing or for minimizing the polar artifact in extraordinary regions. The polar artifact for subdivision stencils of lower valences is removed by applying an additional constraint to the subdominant eigenvalue to be the same as that of subdivision at regular vertices, while the polar artifact for subdivision stencils of higher valances is substantially reduced by introducing an additional thin-plate energy function and a penalty function for maintaining the uniformity and regularity of the characteristic map. A new tuned subdivision scheme is introduced by replacing subdivision stencils of Catmull-Clark subdivision with that from this paper for extraordinary vertices of valences up to nine. We also compare the refined meshes and limit surface quality of the resulting subdivision scheme with that of Catmull-Clark subdivision and other tuned subdivision schemes. The results show that subdivision stencils from our method produce well behaved subdivision meshes with the least polar artifact while maintaining satisfactory limit surface quality.Item Inertia-based Fast Vectorization of Line Drawings(The Eurographics Association and John Wiley & Sons Ltd., 2019) Najgebauer, Patryk; Scherer, Rafal; Lee, Jehee and Theobalt, Christian and Wetzstein, GordonImage vectorisation is a fundamental method in graphic design and is one of the tools allowing to transfer artist work into computer graphics. The existing methods are based mainly on segmentation, or they analyse every image pixel; thus, they are relatively slow. We introduce a novel method for fast line drawing image vectorisation, based on a multi-scale second derivative detector accelerated by the summed-area table and an auxiliary grid. Image is scanned initially along the grid lines, and nodes are added to improve accuracy. Applying inertia in the line tracing allows for better junction mapping in a single pass. Our method is dedicated to grey-scale sketches and line drawings. It works efficiently regardless of the thickness of the line or its shading. Experiments show it is more than two orders of magnitude faster than the existing methods, not sacrificing accuracy.Item Offline Deep Importance Sampling for Monte Carlo Path Tracing(The Eurographics Association and John Wiley & Sons Ltd., 2019) Bako, Steve; Meyer, Mark; DeRose, Tony; Sen, Pradeep; Lee, Jehee and Theobalt, Christian and Wetzstein, GordonAlthough modern path tracers are successfully being applied to many rendering applications, there is considerable interest to push them towards ever-decreasing sampling rates. As the sampling rate is substantially reduced, however, even Monte Carlo (MC) denoisers-which have been very successful at removing large amounts of noise-typically do not produce acceptable final results. As an orthogonal approach to this, we believe that good importance sampling of paths is critical for producing betterconverged, path-traced images at low sample counts that can then, for example, be more effectively denoised. However, most recent importance-sampling techniques for guiding path tracing (an area known as ''path guiding'') involve expensive online (per-scene) training and offer benefits only at high sample counts. In this paper, we propose an offline, scene-independent deeplearning approach that can importance sample first-bounce light paths for general scenes without the need of the costly online training, and can start guiding path sampling with as little as 1 sample per pixel. Instead of learning to ''overfit'' to the sampling distribution of a specific scene like most previous work, our data-driven approach is trained a priori on a set of training scenes on how to use a local neighborhood of samples with additional feature information to reconstruct the full incident radiance at a point in the scene, which enables first-bounce importance sampling for new test scenes. Our solution is easy to integrate into existing rendering pipelines without the need for retraining, as we demonstrate by incorporating it into both the Blender/Cycles and Mitsuba path tracers. Finally, we show how our offline, deep importance sampler (ODIS) increases convergence at low sample counts and improves the results of an off-the-shelf denoiser relative to other state-of-the-art sampling techniques.Item An Analysis of Region Clustered BVH Volume Rendering on GPU(The Eurographics Association and John Wiley & Sons Ltd., 2019) Ganter, David; Manzke, Michael; Steinberger, Markus and Foley, TimWe present a Direct Volume Rendering method that makes use of newly available Nvidia graphics hardware for Bounding Volume Hierarchies. Using BVHs for DVR has been overlooked in recent research due to build times potentially impeding interactive rates. We indicate that this is not necessarily the case, especially when a clustering algorithm is applied before the BVH build to reduce leaf-node complexity. Our results show substantial render time improvements for full-resolution DVR on GPU in comparison to a recent state-of-the-art approach for empty-space-skipping. Furthermore, the use of a BVH for DVR allows seamless integration into popular surface-based path-tracing technologies like Nvidia's OptiX.Item A Unified Neural Network for Panoptic Segmentation(The Eurographics Association and John Wiley & Sons Ltd., 2019) Yao, Li; Chyau, Ang; Lee, Jehee and Theobalt, Christian and Wetzstein, GordonIn this paper, we propose a unified neural network for panoptic segmentation, a task aiming to achieve more fine-grained segmentation. Following existing methods combining semantic and instance segmentation, our method relies on a triple-branch neural network for tackling the unifying work. In the first stage, we adopt a ResNet50 with a feature pyramid network (FPN) as shared backbone to extract features. Then each branch leverages the shared feature maps and serves as the stuff, things, or mask branch. Lastly, the outputs are fused following a well-designed strategy. Extensive experimental results on MS-COCO dataset demonstrate that our approach achieves a competitive Panoptic Quality (PQ) metric score with the state of the art.Item Feature Preserving Octree-Based Hexahedral Meshing(The Eurographics Association and John Wiley & Sons Ltd., 2019) Gao, Xifeng; Shen, Hanxiao; Panozzo, Daniele; Bommes, David and Huang, HuiWe propose an octree-based algorithm to tessellate the interior of a closed surface with hexahedral cells. The generated hexahedral mesh (1) explicitly preserves sharp features of the original input, (2) has a maximal, user-controlled distance deviation from the input surface, (3) is composed of elements with only positive scaled jacobians (measured by the eight corners of a hex [SEK*07]), and (4) does not have self-intersections. We attempt to achieve these goals by proposing a novel pipeline to create an initial pure hexahedral mesh from an octree structure, taking advantage of recent developments in the generation of locally injective 3D parametrizations to warp the octree boundary to conform to the input surface. Sharp features in the input are bijectively mapped to poly-lines in the output and preserved by the deformation, which takes advantage of a scaffold mesh to prevent local and global intersections. The robustness of our technique is experimentally validated by batch processing a large collection of organic and CAD models, without any manual cleanup or parameter tuning. All results including mesh data and statistics in the paper are provided in the additional material. The open-source implementation will be made available online to foster further research in this direction.Item Shading‐Based Surface Recovery Using Subdivision‐Based Representation(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Deng, Teng; Zheng, Jianmin; Cai, Jianfei; Cham, Tat‐Jen; Chen, Min and Benes, BedrichThis paper presents subdivision‐based representations for both lighting and geometry in shape‐from‐shading. A very recent shading‐based method introduced a per‐vertex overall illumination model for surface reconstruction, which has advantage of conveniently handling complicated lighting condition and avoiding explicit estimation of visibility and varied albedo. However, due to its discrete nature, the per‐vertex overall illumination requires a large amount of memory and lacks intrinsic coherence. To overcome these problems, in this paper we propose to use classic subdivision to define the basic smooth lighting function and surface, and introduce additional independent variables into the subdivision to adaptively model sharp changes of illumination and geometry. Compared to previous works, the new model not only preserves the merits of the per‐vertex illumination model, but also greatly reduces the number of variables required in surface recovery and intrinsically regularizes the illumination vectors and the surface. These features make the new model very suitable for multi‐view stereo surface reconstruction under general, unknown illumination condition. Particularly, a variational surface reconstruction method built upon the subdivision representations for lighting and geometry is developed. The experiments on both synthetic and real‐world data sets have demonstrated that the proposed method can achieve memory efficiency and improve surface detail recovery.This paper presents subdivision‐based representations for both lighting and geometry in shape‐from‐shading. A very recent shading‐based method introduced a per‐vertex overall illumination model for surface reconstruction, which has advantage of conveniently handling complicated lighting condition and avoiding explicit estimation of visibility and varied albedo. However, due to its discrete nature, the per‐vertex overall illumination requires a large amount of memory and lacks intrinsic coherence. To overcome these problems, in this paper we propose to use classic subdivision to define the basic smooth lighting function and surface, and introduce additional independent variables into the subdivision to adaptively model sharp changes of illumination and geometry. Compared to previous works, the new model not only preserves the merits of the per‐vertex illumination model, but also greatly reduces the number of variables required in surface recovery and intrinsically regularizes the illumination vectors and the surface. These features make the new model very suitable for multi‐view stereo surface reconstruction under general, unknown illumination condition. Particularly, a variational surface reconstruction method built upon the subdivision representations for lighting and geometry is developed. The experiments on both synthetic and real‐world data sets have demonstrated that the proposed method can achieve memory efficiency and improve surface detail recovery.Item Learning to Importance Sample in Primary Sample Space(The Eurographics Association and John Wiley & Sons Ltd., 2019) Zheng, Quan; Zwicker, Matthias; Alliez, Pierre and Pellacini, FabioImportance sampling is one of the most widely used variance reduction strategies in Monte Carlo rendering. We propose a novel importance sampling technique that uses a neural network to learn how to sample from a desired density represented by a set of samples. Our approach considers an existing Monte Carlo rendering algorithm as a black box. During a scene-dependent training phase, we learn to generate samples with a desired density in the primary sample space of the renderer using maximum likelihood estimation. We leverage a recent neural network architecture that was designed to represent real-valued non-volume preserving (''Real NVP'') transformations in high dimensional spaces. We use Real NVP to non-linearly warp primary sample space and obtain desired densities. In addition, Real NVP efficiently computes the determinant of the Jacobian of the warp, which is required to implement the change of integration variables implied by the warp. A main advantage of our approach is that it is agnostic of underlying light transport effects, and can be combined with an existing rendering technique by treating it as a black box. We show that our approach leads to effective variance reduction in several practical scenarios.Item Dual Sheet Meshing: An Interactive Approach to Robust Hexahedralization(The Eurographics Association and John Wiley & Sons Ltd., 2019) Takayama, Kenshi; Alliez, Pierre and Pellacini, FabioThe combinatorial dual of a hex mesh induces a collection of mutually intersecting surfaces (dual sheets). Inspired by Campen et al.'s work on quad meshing [CBK12,CK14], we propose to directly generate such dual sheets so that, as long as the volume is properly partitioned by the dual sheets, we are guaranteed to arrive at a valid all-hex mesh topology. Since automatically generating dual sheets seems much harder than the 2D counterpart, we chose to leave the task to the user; our system is equipped with a few simple 3D modeling tools for interactively designing dual sheets. Dual sheets are represented as implicit surfaces in our approach, greatly simplifying many of the computational steps such as finding intersections and analyzing topology. We also propose a simple algorithm for primalizing the dual graph where each dual cell, often enclosing singular edges, gets mapped onto a reference polyhedron via harmonic parameterization. Preservation of sharp features is simply achieved by modifying the boundary conditions. We demonstrate the feasibility of our approach through various modeling examples.Item Toward Understanding Representation Methods in Visualization Recommendations through Scatterplot Construction Tasks(The Eurographics Association and John Wiley & Sons Ltd., 2019) L'Yi, Sehi; Chang, Youli; Shin, DongHwa; Seo, Jinwook; Gleicher, Michael and Viola, Ivan and Leitte, HeikeMost visualization recommendation systems predominantly rely on graphical previews to describe alternative visual encodings. However, since InfoVis novices are not familiar with visual representations (e.g., interpretation barriers [GTS10]), novices might have difficulty understanding and choosing recommended visual encodings. As an initial step toward understanding effective representation methods for visualization recommendations, we investigate the effectiveness of three representation methods (i.e., previews, animated transitions, and textual descriptions) under scatterplot construction tasks. Our results show how different representations individually and cooperatively help users understand and choose recommended visualizations, for example, by supporting their expect-and-confirm process. Based on our study results, we discuss design implications for visualization recommendation interfaces.Item FontRNN: Generating Large-scale Chinese Fonts via Recurrent Neural Network(The Eurographics Association and John Wiley & Sons Ltd., 2019) Tang, Shusen; Xia, Zeqing; Lian, Zhouhui; Tang, Yingmin; Xiao, Jianguo; Lee, Jehee and Theobalt, Christian and Wetzstein, GordonDespite the recent impressive development of deep neural networks, using deep learning based methods to generate largescale Chinese fonts is still a rather challenging task due to the huge number of intricate Chinese glyphs, e.g., the official standard Chinese charset GB18030-2000 consists of 27,533 Chinese characters. Until now, most existing models for this task adopt Convolutional Neural Networks (CNNs) to generate bitmap images of Chinese characters due to CNN based models' remarkable success in various applications. However, CNN based models focus more on image-level features while usually ignore stroke order information when writing characters. Instead, we treat Chinese characters as sequences of points (i.e., writing trajectories) and propose to handle this task via an effective Recurrent Neural Network (RNN) model with monotonic attention mechanism, which can learn from as few as hundreds of training samples and then synthesize glyphs for remaining thousands of characters in the same style. Experimental results show that our proposed FontRNN can be used for synthesizing large-scale Chinese fonts as well as generating realistic Chinese handwritings efficiently.Item Towards Glyphs for Uncertain Symmetric Second-Order Tensors(The Eurographics Association and John Wiley & Sons Ltd., 2019) Gerrits, Tim; Rössl, Christian; Theisel, Holger; Gleicher, Michael and Viola, Ivan and Leitte, HeikeMeasured data often incorporates some amount of uncertainty, which is generally modeled as a distribution of possible samples. In this paper, we consider second-order symmetric tensors with uncertainty. In the 3D case, this means the tensor data consists of 6 coefficients - uncertainty, however, is encoded by 21 coefficients assuming a multivariate Gaussian distribution as model. The high dimension makes the direct visualization of tensor data with uncertainty a difficult problem, which was until now unsolved. The contribution of this paper consists in the design of glyphs for uncertain second-order symmetric tensors in 2D and 3D. The construction consists of a standard glyph for the mean tensor that is augmented by a scalar field that represents uncertainty. We show that this scalar field and therefore the displayed glyph encode the uncertainty comprehensively, i.e., there exists a bijective map between the glyph and the parameters of the distribution. Our approach can extend several classes of existing glyphs for symmetric tensors to additionally encode uncertainty and therefore provides a possible foundation for further uncertain tensor glyph design. For demonstration, we choose the well-known superquadric glyphs, and we show that the uncertainty visualization satisfies all their design constraints.