The Grassmannian Atlas: A General Framework for Exploring Linear Projections of High‐Dimensional Data

Linear projections are one of the most common approaches to visualize high‐dimensional data. Since the space of possible projections is large, existing systems usually select a small set of interesting projections by ranking a large set of candidate projections based on a chosen quality measure. However, while highly ranked projections can be informative, some lower ranked ones could offer important complementary information. Therefore, selection based on ranking may miss projections that are important to provide a global picture of the data. The proposed work fills this gap by presenting the Grassmannian Atlas, a framework that captures the global structures of quality measures in the space of all projections, which enables a systematic exploration of many complementary projections and provides new insights into the properties of existing quality measures.     

Visual Exploration of High‐Dimensional Data through Subspace Analysis and Dynamic Projections

We introduce a novel interactive framework for visualizing and exploring high‐dimensional datasets based on subspace analysis and dynamic projections. We assume the high‐dimensional dataset can be represented by a mixture of low‐dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that create smooth animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real‐world examples to demonstrate the novelty and usability of our proposed framework.     

Real‐time Texture Synthesis and Concurrent Random‐access Rendering for Low‐cost GPU Chip Design

Numerous algorithms have been researched in the area of texture synthesis. However, it remains difficult to design a low‐cost synthesis scheme capable of generating high quality results while simultaneously achieving real‐time performance. Additional challenges include making a scheme parallel and being able to partially render/synthesize high‐resolution textures. Furthermore, it would be beneficial for a synthesis scheme to be able to incorporate Texture Compression and minimize the bandwidth usage, especially on mobile devices. In this paper, we propose a practical method which has low computational complexity and produces textures with small storage requirements. Through use of an index table, random access of the texture is another essential advantage, with which parallel rendering becomes feasible including generation of mip‐map sequences. Integrating the index table with existing compression algorithms, for example ETC or PVRTC, the bandwidth is further reduced and avoids the need for a separate, computationally expensive pass to compress the synthesized output. It should be noted that our texture synthesis achieves real‐time performance and low power consumption even on mobile devices, for which texture synthesis has been traditionally considered too expensive.     

Line Integral Convolution for Real‐Time Illustration of Molecular Surface Shape and Salient Regions

We present a novel line drawing algorithm that illustrates surfaces in real‐time to convey their shape. We use line integral convolution (LIC) and employ ambient occlusion for illustrative surface rendering. Furthermore, our method depicts salient regions based on the illumination gradient. Our method works on animated surfaces in a frame‐coherent manner. Therefore, it yields an illustrative representation of time‐dependent surfaces as no preprocessing step is needed. In this paper, the method is used to highlight the structure of molecular surfaces and to illustrate important surface features like cavities, channels, and pockets. The benefit of our method was evaluated with domain experts. We also demonstrate the applicability of our method to medical visualization.     

Adaptive multi‐scale analysis for point‐based surface editing

This paper presents a tool that enables the direct editing of surface features in large point‐clouds or meshes. This is made possible by a novel multi‐scale analysis of unstructured point‐clouds that automatically extracts the number of relevant features together with their respective scale all over the surface. Then, combining this ingredient with an adequate multi‐scale decomposition allows us to directly enhance or reduce each feature in an independent manner. Our feature extraction is based on the analysis of the scale‐variations of locally fitted surface primitives combined with unsupervised learning techniques. Our tool may be applied either globally or locally, and millions of points are handled in real‐time. The resulting system enables users to accurately edit complex geometries with minimal interaction.     

Minimum‐Displacement Overlap Removal for Geo‐referenced Data Visualization

Given a set of rectangles embedded in the plane, we consider the problem of adjusting the layout to remove all overlap while preserving the orthogonal order of the rectangles. The objective is to minimize the displacement of the rectangles. We call this problem Minimum -Displacement Overlap Removal (mdor ). Our interest in this problem is motivated by the application of displaying metadata of archaeological sites. Because most existing overlap removal algorithms are not designed to minimize displacement while preserving orthogonal order, we present and compare several approaches which are tailored to our particular usecase. We introduce a new overlap removal heuristic which we call re Arrange . Although conceptually simple, it is very effective in removing the overlap while keeping the displacement small. Furthermore, we propose an additional procedure to repair the orthogonal order after every iteration, with which we extend both our new heuristic and PRISM, a widely used overlap removal algorithm. We compare the performance of both approaches with and without this order repair method. The experimental results indicate that re Arrange is very effective for heterogeneous input data where the overlap is concentrated in few dense regions.     

Time‐Series Plots Integrated in Parallel‐Coordinates Displays

We present a natural extension of two‐dimensional parallel‐coordinates plots for revealing relationships in time‐dependent multi‐attribute data by building on the idea that time can be considered as the third dimension. A time slice through the visualization represents a certain point in time and can be viewed as a regular parallel‐coordinates display. A vertical slice through one of the axes of the parallel‐coordinates display would show a time‐series plot. For a focus‐and‐context Integration of both views, we embed time‐series plots between two adjacent axes of the parallel‐coordinates plot. Both time‐series plots are drawn using a pseudo three‐dimensional perspective with a single vanishing point. An independent parallel‐coordinates panel that connects the two perspectively displayed time‐series plots can move forward and backward in time to reveal changes in the relationship between the time‐dependent attributes. The visualization of time‐series plots in the context of the parallel‐coordinates plot facilitates the exploration of time‐related aspects of the data without the need to switch to a separate display. We provide a consistent set of tools for selecting and contrasting subsets of the data, which are important for various application domains.     

Selective Degree Elevation for Multi‐Sided Bézier Patches

This paper presents a method to selectively elevate the degree of an S‐Patch of arbitrary dimension. We consider not only S‐Patches with 2D domains but 3D and higher‐dimensional domains as well, of which volumetric cage deformations are a subset. We show how to selectively insert control points of a higher degree patch into a lower degree patch while maintaining the polynomial reproduction order of the original patch. This process allows the user to elevate the degree of only one portion of the patch to add new degrees of freedom or maintain continuity with adjacent patches without elevating the degree of the entire patch, which could create far more degrees of freedom than necessary. Finally we show an application to cage‐based deformations where we increase the number of control points by elevating the degree of a subset of cage faces. The result is a cage deformation with higher degree triangular Bézier functions on a subset of cage faces but no interior control points.     

Physically Based Video Editing

Convincing manipulation of objects in live action videos is a difficult and often tedious task. Skilled video editors achieve this with the help of modern professional tools, but complex motions might still lack physical realism since existing tools do not consider the laws of physics. On the other hand, physically based simulation promises a high degree of realism, but typically creates a virtual 3D scene animation rather than returning an edited version of an input live action video. We propose a framework that combines video editing and physics‐based simulation. Our tool assists unskilled users in editing an input image or video while respecting the laws of physics and also leveraging the image content. We first fit a physically based simulation that approximates the object's motion in the input video. We then allow the user to edit the physical parameters of the object, generating a new physical behavior for it. The core of our work is the formulation of an image‐aware constraint within physics simulations. This constraint manifests as external control forces to guide the object in a way that encourages proper texturing at every frame, yet producing physically plausible motions. We demonstrate the generality of our method on a variety of physical interactions: rigid motion, multi‐body collisions, clothes and elastic bodies.     

Re‐Compositable Panoramic Selfie with Robust Multi‐Frame Segmentation and Stitching

It is a challenging task for ordinary users to capture selfies with a good scene composition, given the limited freedom to position the camera. Creative hardware (e.g., selfie sticks) and software (e.g., panoramic selfie apps) solutions have been proposed to extend the background coverage of a selife, but to achieve a perfect composition on the spot when the selfie is captured remains to be difficult. In this paper, we propose a system that allows the user to shoot a selfie video by rotating the body first, then produce a final panoramic selfie image with user‐guided scene composition as postprocessing. Our key technical contribution is a fully Automatic, robust multi‐frame segmentation and stitching framework that is tailored towards the special characteristics of selfie images. We analyze the sparse feature points and employ a spatial‐temporal optimization for bilayer feature segmentation, which leads to more reliable background alignment than previous image stitching techniques. The sparse classification is then propagated to all pixels to create dense foreground masks for person‐background composition. Finally, based on a user‐selected foreground position, our system uses content‐preserving warping to produce a panoramic seflie with minimal distortion to the face region. Experimental results show that our approach can reliably generate high quality panoramic selfies, while a simple combination of previous image stitching and segmentation approaches often fails.     

Rule‐Enhanced Transfer Function Generation for Medical Volume Visualization

In volume visualization, transfer functions are used to classify the volumetric data and assign optical properties to the voxels. In general, transfer functions are generated in a transfer function space, which is the feature space constructed by data values and properties derived from the data. If volumetric objects have the same or overlapping data values, it would be difficult to separate them in the transfer function space. In this paper, we present a rule‐enhanced transfer function design method that allows important structures of the volume to be more effectively separated and highlighted. We define a set of rules based on the local frequency distribution of volume attributes. A rule‐selection method based on a genetic algorithm is proposed to learn the set of rules that can distinguish the user‐specified target tissue from other tissues. In the rendering stage, voxels satisfying these rules are rendered with higher opacities in order to highlight the target tissue. The proposed method was tested on various volumetric datasets to enhance the visualization of important structures that are difficult to be visualized by traditional transfer function design methods. The results demonstrate the effectiveness of the proposed method.     

Finite‐Time Mass Separation for Comparative Visualizations of Inertial Particles

The visual analysis of flows with inertial particle trajectories is a challenging problem because time‐dependent particle trajectories additionally depend on mass, which gives rise to an infinite number of possible trajectories passing through every point in space‐time. This paper presents an approach to a comparative visualization of the inertial particles’ separation behavior. For this, we define the Finite‐Time Mass Separation (FTMS), a scalar field that measures at each point in the domain how quickly inertial particles separate that were released from the same location but with slightly different mass. Extracting and visualizing the mass that induces the largest separation provides a simplified view on the critical masses. By using complementary coordinated views, we additionally visualize corresponding inertial particle trajectories in space‐time by integral curves and surfaces. For a quantitative analysis, we plot Euclidean and arc length‐based distances to a reference particle over time, which allows to observe the temporal evolution of separation events. We demonstrate our approach on a number of analytic and one real‐world unsteady 2D field.     

Sliceplorer: 1D slices for multi‐dimensional continuous functions

Multi‐dimensional continuous functions are commonly visualized with 2D slices or topological views. Here, we explore 1D slices as an alternative approach to show such functions. Our goal with 1D slices is to combine the benefits of topological views, that is, screen space efficiency, with those of slices, that is a close resemblance of the underlying function. We compare 1D slices to 2D slices and topological views, first, by looking at their performance with respect to common function analysis tasks. We also demonstrate 3 usage scenarios: the 2D sinc function, neural network regression, and optimization traces. Based on this evaluation, we characterize the advantages and drawbacks of each of these approaches, and show how interaction can be used to overcome some of the shortcomings.     

Perception‐driven Accelerated Rendering

Advances in computer graphics enable us to create digital images of astonishing complexity and realism. However, processing resources are still a limiting factor. Hence, many costly but desirable aspects of realism are often not accounted for, including global illumination, accurate depth of field and motion blur, spectral effects, etc. especially in real‐time rendering. At the same time, there is a strong trend towards more pixels per display due to larger displays, higher pixel densities or larger fields of view. Further observable trends in current display technology include more bits per pixel (high dynamic range, wider color gamut/fidelity), increasing refresh rates (better motion depiction), and an increasing number of displayed views per pixel (stereo, multi‐view, all the way to holographic or lightfield displays). These developments cause significant unsolved technical challenges due to aspects such as limited compute power and bandwidth. Fortunately, the human visual system has certain limitations, which mean that providing the highest possible visual quality is not always necessary. In this report, we present the key research and models that exploit the limitations of perception to tackle visual quality and workload alike. Moreover, we present the open problems and promising future research targeting the question of how we can minimize the effort to compute and display only the necessary pixels while still offering a user full visual experience.     

Towards User‐Centered Active Learning Algorithms

The labeling of data sets is a time‐consuming task, which is, however, an important prerequisite for machine learning and visual analytics. Visual‐interactive labeling (VIAL) provides users an active role in the process of labeling, with the goal to combine the potentials of humans and machines to make labeling more efficient. Recent experiments showed that users apply different strategies when selecting instances for labeling with visual‐interactive interfaces. In this paper, we contribute a systematic quantitative analysis of such user strategies. We identify computational building blocks of user strategies, formalize them, and investigate their potentials for different machine learning tasks in systematic experiments. The core insights of our experiments are as follows. First, we identified that particular user strategies can be used to considerably mitigate the bootstrap (cold start) problem in early labeling phases. Second, we observed that they have the potential to outperform existing active learning strategies in later phases. Third, we analyzed the identified core building blocks, which can serve as the basis for novel selection strategies. Overall, we observed that data‐based user strategies (clusters, dense areas) work considerably well in early phases, while model‐based user strategies (e.g., class separation) perform better during later phases. The insights gained from this work can be applied to develop novel active learning approaches as well as to better guide users in visual interactive labeling.     

Tracing Field‐Coherent Quad Layouts

Given a cross field over a triangulated surface we present a practical and robust method to compute a field aligned coarse quad layout over the surface. The method works directly on a triangle mesh without requiring any parametrization and it is based on a new technique for tracing field‐coherent geodesic paths directly on a triangle mesh, and on a new relaxed formulation of a binary LP problem, which allows us to extract both conforming quad layouts and coarser layouts containing t‐junctions. Our method is easy to implement, very robust, and, being directly based on the input cross field, it is able to generate better aligned layouts, even with complicated fields containing many singularities. We show results on a number of datasets and comparisons with state‐of‐the‐art methods.     

Generalized Diffusion Curves: An Improved Vector Representation for Smooth‐Shaded Images

This paper generalizes the well‐known Diffusion Curves Images (DCI), which are composed of a set of Bezier curves with colors specified on either side. These colors are diffused as Laplace functions over the image domain, which results in smooth color gradients interrupted by the Bezier curves. Our new formulation allows for more color control away from the boundary, providing a similar expressive power as recent Bilaplace image models without introducing associated issues and computational costs. The new model is based on a special Laplace function blending and a new edge blur formulation. We demonstrate that given some user‐defined boundary curves over an input raster image, fitting colors and edge blur from the image to the new model and subsequent editing and animation is equally convenient as with DCIs. Numerous examples and comparisons to DCIs are presented.     

Contrast‐Enhanced Black and White Images

This paper investigates contrast enhancement as an approach to tone reduction, aiming to convert a photograph to black and white. Using a filter‐based approach to strengthen contrast, we avoid making a hard decision about how to assign tones to segmented regions. Our method is inspired by sticks filtering, used to enhance medical images but not previously used in non‐photorealistic rendering. We amplify contrast of pixels along the direction of greatest local difference from the mean, strengthening even weak features if they are most prominent. A final thresholding step converts the contrast‐enhanced image to black and white. Local smoothing and contrast enhancement balances abstraction and structure preservation; the main advantage of our method is its faithful depiction of image detail. Our method can create a set of effects: line drawing, hatching, and black and white, all having superior details to previous black and white methods.     

Flow‐Induced Inertial Steady Vector Field Topology

Traditionally, vector field visualization is concerned with 2D and 3D flows. Yet, many concepts can be extended to general dynamical systems, including the higher‐dimensional problem of modeling the motion of finite‐sized objects in fluids. In the steady case, the trajectories of these so‐called inertial particles appear as tangent curves of a 4D or 6D vector field. These higher‐dimensional flows are difficult to map to lower‐dimensional spaces, which makes their visualization a challenging problem. We focus on vector field topology, which allows scientists to study asymptotic particle behavior. As recent work on the 2D case has shown, both extraction and classification of isolated critical points depend on the underlying particle model. In this paper, we aim for a model‐independent classification technique, which we apply to two different particle models in not only 2D, but also 3D cases. We show that the classification can be done by performing an eigenanalysis of the spatial derivatives' velocity subspace of the higher‐dimensional 4D or 6D flow. We construct glyphs that depict not only the types of critical points, but also encode the directional information given by the eigenvectors. We show that the eigenvalues and eigenvectors of the inertial phase space have sufficient symmetries and structure so that they can be depicted in 2D or 3D, instead of 4D or 6D.     

Visualnostics: Visual Guidance Pictograms for Analyzing Projections of High‐dimensional Data

The visual analysis of multivariate projections is a challenging task, because complex visual structures occur. This causes fatigue or misinterpretations, which distorts the analysis. In fact, the same projection can lead to different analysis results. We provide visual guidance pictograms to improve objectivity of the visual search. A visual guidance pictogram is an iconic visual density map encoding the visual structure of certain data properties. By using them to guide the analysis, structures in the projection can be better understood and mentally linked to properties in the data. We introduce a systematic scheme for designing such pictograms and provide a set of pictograms for standard visual tasks, such as correlation and distribution analysis, for standard projections like scatterplots, RadVis, and Star Coordinates. We conduct a study that compares the visual analysis of real data with and without the support of guidance pictograms. Our tests show that the training effort for a visual search can be decreased and the analysis bias can be reduced by supporting the user's visual search with guidance pictograms.