Curvature Aware Fundamental Cycles

We present a graph algorithm to find fundamental cycles aligned with the principal curvature directions of a surface. Specifically, we use the tree‐cotree decomposition of graphs embedded in manifolds, guided with edge weights, in order to produce these cycles. Our algorithm is very quick compared to existing methods, with a worst case running time of O(n log n+gn) where n is the number of faces and g is the surface genus. Further, its flexibility to accommodate different weighting functions and to handle boundaries may be used to produce cycles suitable for a variety of applications and models.     

Smooth Stream Surfaces of Fourth Order Precision

We introduce a novel technique for the construction of smooth stream surfaces of 4th order precision. While common stream surface techniques use linear interpolation for generating seed points for new streamlines in the refinement phase, we use Hermite interpolation. The derivatives needed for Hermite interpolation are obtained by integration along the streamlines. This yields stream surfaces of4th order precision. Additionally, we analyse the accuracy ofthe well known Hultquist approach and our new algorithm and proof that Hultquist's method is exact for linear vector fields. We compare both methods using the well known distance based and a novel error based refinement strategy. Our resulting surface is C¹ -continuous, enabling improved rendering among other benefits.     

Trivial Connections on Discrete Surfaces

This paper presents a straightforward algorithm for constructing connections on discrete surfaces that are as smooth as possible everywhere but on a set of isolated singularities with given index. We compute these connections by solving a single linear system built from standard operators. The solution can be used to design rotationally symmetric direction fields with user‐specified singularities and directional constraints.     

Feature‐Preserving Reconstruction of Singular Surfaces

Reconstructing a surface mesh from a set of discrete point samples is a fundamental problem in geometric modeling. It becomes challenging in presence of ‘singularities’ such as boundaries, sharp features, and non‐manifolds. A few of the current research in reconstruction have addressed handling some of these singularities, but a unified approach to handle them all is missing. In this paper we allow the presence of various singularities by requiring that the sampled object is a collection of smooth surface patches with boundaries that can meet or intersect. Our algorithm first identifies and reconstructs the features where singularities occur. Next, it reconstructs the surface patches containing these feature curves. The identification and reconstruction of feature curves are achieved by a novel combination of the Gaussian weighted graph Laplacian and the Reeb graphs. The global reconstruction is achieved by a method akin to the well known Cocone reconstruction, but with weighted Delaunay triangulation that allows protecting the feature samples with balls. We provide various experimental results to demonstrate the effectiveness of our feature‐preserving singular surface reconstruction algorithm.     

Uncertainty‐Aware Exploration of Continuous Parameter Spaces Using Multivariate Prediction

Systems projecting a continuous n‐dimensional parameter space to a continuous m‐dimensional target space play an important role in science and engineering. If evaluating the system is expensive, however, an analysis is often limited to a small number of sample points. The main contribution of this paper is an interactive approach to enable a continuous analysis of a sampled parameter space with respect to multiple target values. We employ methods from statistical learning to predict results in real‐time at any user‐defined point and its neighborhood. In particular, we describe techniques to guide the user to potentially interesting parameter regions, and we visualize the inherent uncertainty of predictions in 2D scatterplots and parallel coordinates. An evaluation describes a real‐world scenario in the application context of car engine design and reports feedback of domain experts. The results indicate that our approach is suitable to accelerate a local sensitivity analysis of multiple target dimensions, and to determine a sufficient local sampling density for interesting parameter regions.     

Fast Extraction of High‐quality Crease Surfaces for Visual Analysis

We present a novel algorithm for the efficient extraction and visualization of high‐quality ridge and valley surfaces from numerical datasets. Despite their rapidly increasing popularity in visualization, these so‐called crease surfaces remain challenging to compute owing to their strongly nonlinear and non‐orientable nature, and their complex boundaries. In this context, existing meshing techniques require an extremely dense sampling that is computationally prohibitive. Our proposed solution intertwines sampling and meshing steps to yield an accurate approximation of the underlying surfaces while ensuring the geometric quality of the resulting mesh. Using the computation power of the GPU, we propose a fast, parallel method for sampling. Additionally, we present a new front propagation meshing strategy that leverages CPU multiprocessing. Results are shown for synthetic, medical and fluid dynamics datasets.     

Topology Aware Data‐Driven Inverse Kinematics

Creating realistic human movement is a time consuming and labour intensive task. The major difficulty is that the user has to edit individual joints while maintaining an overall realistic and collision free posture. Previous research suggests the use of data‐driven inverse kinematics, such that one can focus on the control of a few joints, while the system automatically composes a natural posture. However, as a common problem of kinematics synthesis, penetration of body parts is difficult to avoid in complex movements. In this paper, we propose a new data‐driven inverse kinematics framework that conserves the topology of the synthesizing postures. Our system monitors and regulates the topology changes using the Gauss Linking Integral (GUI), such that penetration can be efficiently prevented. As a result, complex motions with tight body movements, as well as those involving interaction with external objects, can be simulated with minimal manual intervention. Experimental results show that using our system, the user can create high quality human motion in real‐time by controlling a few joints using a mouse or a multi‐touch screen. The movement generated is both realistic and penetration free. Our system is best applied for interactive motion design in computer animations and games.     

Fuzzy Geodesics and Consistent Sparse Correspondences For: eformable Shapes

A geodesic is a parameterized curve on a Riemannian manifold governed by a second order partial differential equation. Geodesics are notoriously unstable: small perturbations of the underlying manifold may lead to dramatic changes of the course of a geodesic. Such instability makes it difficult to use geodesics in many applications, in particular in the world of discrete geometry. In this paper, we consider a geodesic as the indicator function of the set of the points on the geodesic. From this perspective, we present a new concept called fuzzy geodesics and show that fuzzy geodesics are stable with respect to the Gromov‐Hausdorff distance. Based on fuzzy geodesics, we propose a new object called the intersection configuration for a set of points on a shape and demonstrate its effectiveness in the application of finding consistent correspondences between sparse sets of points on shapes differing by extreme deformations.     

Image Synthesis for Branching Structures

We present a set of techniques for the synthesis of artificial images that depict branching structures like rivers, cracks, lightning, mountain ranges, or blood vessels. The central idea is to build a statistical model that captures the characteristic bending and branching structure from example images. Then a new skeleton structure is synthesized and the final output image is composed from image fragments of the original input images. The synthesis part of our algorithm runs mostly automatic but it optionally allows the user to control the process in order to achieve a specific result. The combination of the statistical bending and branching model with sophisticated fragment‐based image synthesis corresponds to a multi‐resolution decomposition of the underlying branching structure into the low frequency behavior (captured by the statistical model) and the high frequency detail (captured by the image detail in the fragments). This approach allows for the synthesis of realistic branching structures, while at the same time preserving important textural details from the original image.     

DTI in Context: Illustrating Brain Fiber Tracts In Situ

We present an interactive illustrative visualization method inspired by traditional pen‐and‐ink illustration styles. Specifically, we explore how to provide context around DTI fiber tracts in the form of surfaces of the brain, the skull, or other objects such as tumors. These contextual surfaces are derived from either segmentation data or generated using interactive iso‐surface extraction and are rendered with a flexible, slice‐based hatching technique, controlled with ambient occlusion. This technique allows us to produce a consistent and frame‐coherent appearance with precise control over the lines. In addition, we provide context through cutting planes onto which we render gray matter with stippling. Together, our methods not only facilitate the interactive exploration and illustration of brain fibers within their anatomical context but also allow us to produce high‐quality images for print reproduction. We provide evidence for the success of our approach with an informal evaluation with domain experts.     

Nonrigid Matching of Undersampled Shapes via Medial Diffusion

We introduce medial diffusion for the matching of undersampled shapes undergoing a nonrigid deformation. We construct a diffusion process with respect to the medial axis of a shape, and use the quantity of heat diffusion as a measure which is both tolerant of missing data and approximately invariant to nonrigid deformations. A notable aspect of our approach is that we do not define the diffusion on the shape's medial axis, or similar medial representation. Instead, we construct the diffusion process directly on the shape. This permits the diffusion process to better capture surface features, such as varying spherical and cylindrical parts, as well as combine with other surface‐based diffusion processes. We show how to use medial diffusion to detect intrinsic symmetries, and for computing correspondences between pairs of shapes, wherein shapes contain substantial missing data.     

Optimizing Structure Preserving Embedded Deformation for Resizing Images and Vector Art

Smart deformation and warping tools play an important part in modern day geometric modeling systems. They allow existing content to be stretched or scaled while preserving visually salient information. To date, these techniques have primarily focused on preserving local shape details, not taking into account important global structures such as symmetry and line features. In this work we present a novel framework that can be used to preserve the global structure in images and vector art. Such structures include symmetries and the spatial relations in shapes and line features in an image. Central to our method is a new formulation of preserving structure as an optimization problem. We use novel optimization strategies to achieve the interactive performance required by modern day modeling applications. We demonstrate the effectiveness of our framework by performing structure preservation deformation of images and complex vector art at interactive rates.     

HyperMoVal: Interactive Visual Validation of Regression Models for Real‐Time Simulation

During the development of car engines, regression models that are based on machine learning techniques are increasingly important for tasks which require a prediction of results in real‐time. While the validation of a model is a key part of its identification process, existing computation‐ or visualization‐based techniques do not adequately support all aspects of model validation. The main contribution of this paper is an interactive approach called HyperMoVal that is designed to support multiple tasks related to model validation: 1) comparing known and predicted results, 2) analyzing regions with a bad fit, 3) assessing the physical plausibility of models also outside regions covered by validation data, and 4) comparing multiple models. The key idea is to visually relate one or more n‐dimensional scalar functions to known validation data within a combined visualization. HyperMoVal lays out multiple 2D and 3D sub‐projections of the n‐dimensional function space around a focal point. We describe how linking HyperMoVal to other views further extends the possibilities for model validation. Based on this integration, we discuss steps towards supporting the entire workflow of identifying regression models. An evaluation illustrates a typical workflow in the application context of car‐engine design and reports general feedback of domain experts and users of our approach. These results indicate that our approach significantly accelerates the identification of regression models and increases the confidence in the overall engineering process.     

An Interactive Visual Analytics System for Bridge Management

Bridges deteriorate over their life cycles and require continuous maintenance to ensure their structural integrity, and in turn, the safety of the public. Maintaining bridges is a multi‐faceted operation that requires both domain knowledge and analytics techniques over large data sources. Although most existing bridge management systems (BMS) are very efficient at data storage, they are not as effective at providing analytical capabilities or as flexible at supporting different inspection technologies. In this paper, we present a visual analytics system that extends the capability of current BMSs. Based on a nation‐wide survey and our interviews with bridge managers, we designed our system to be customizable so that it can provide interactive exploration, information correlation, and domain‐oriented data analysis. When tested by bridge managers of the U.S. Department of Transportation, we validated that our system provides bridge managers with the necessary features for performing in‐depth analysis of bridges from a variety of perspectives that are in accordance to their typical workflow.     

Simulation Guided Hair Dynamics Modeling from Video

In this paper we present a hybrid approach to reconstruct hair dynamics from multi‐view video sequences, captured under uncontrolled lighting conditions. The key of this method is a refinement approach that combines image‐based reconstruction techniques with physically based hair simulation. Given an initially reconstructed sequence of hair fiber models, we develop a hair dynamics refinement system using particle‐based simulation and incompressible fluid simulation. The system allows us to improve reconstructed hair fiber motions and complete missing fibers caused by occlusion or tracking failure. The refined space‐time hair dynamics are consistent with video inputs and can be also used to generate novel hair animations of different hair styles. We validate this method through various real hair examples.     

Pathline: A Tool For Comparative Functional Genomics

Biologists pioneering the new field of comparative functional genomics attempt to infer the mechanisms of gene regulation by looking for similarities and differences of gene activity over time across multiple species. They use three kinds of data: functional data such as gene activity measurements, pathway data that represent a series of reactions within a cellular process, and phylogenetic relationship data that describe the relatedness of species. No existing visualization tool can visually encode the biologically interesting relationships between multiple pathways, multiple genes, and multiple species. We tackle the challenge of visualizing all aspects of this comparative functional genomics dataset with a new interactive tool called Pathline. In addition to the overall characterization of the problem and design of Pathline, our contributions include two new visual encoding techniques. One is a new method for linearizing metabolic pathways that provides appropriate topological information and supports the comparison of quantitative data along the pathway. The second is the curvemap view, a depiction of time series data for comparison of gene activity and metabolite levels across multiple species. Pathline was developed in close collaboration with a team of genomic scientists. We validate our approach with case studies of the biologists’ use of Pathline and report on how they use the tool to confirm existing findings and to discover new scientific insights.     

Efficient opacity specification based on feature visibilities in direct volume rendering

Due to 3D occlusion, the specification of proper opacities in direct volume rendering is a time‐consuming and unintuitive process. The visibility histograms introduced by Correa and Ma reflect the effect of occlusion by measuring the influence of each sample in the histogram to the rendered image. However, the visibility is defined on individual samples, while volume exploration focuses on conveying the spatial relationships between features. Moreover, the high computational cost and large memory requirement limits its application in multi‐dimensional transfer function design. In this paper, we extend visibility histograms to feature visibility, which measures the contribution of each feature in the rendered image. Compared to visibility histograms, it has two distinctive advantages for opacity specification. First, the user can directly specify the visibilities for features and the opacities are automatically generated using an optimization algorithm. Second, its calculation requires only one rendering pass with no additional memory requirement. This feature visibility based opacity specification is fast and compatible with all types of transfer function design. Furthermore, we introduce a two‐step volume exploration scheme, in which an automatic optimization is first performed to provide a clear illustration of the spatial relationship and then the user adjusts the visibilities directly to achieve the desired feature enhancement. The effectiveness of this scheme is demonstrated by experimental results on several volumetric datasets.     

Video Panorama for 2D to 3D Conversion

Accurate depth estimation is a challenging, yet essential step in the conversion of a 2D image sequence to a 3D stereo sequence. We present a novel approach to construct a temporally coherent depth map for each image in a sequence. The quality of the estimated depth is high enough for the purpose of2D to 3D stereo conversion. Our approach first combines the video sequence into a panoramic image. A user can scribble on this single panoramic image to specify depth information. The depth is then propagated to the remainder of the panoramic image. This depth map is then remapped to the original sequence and used as the initial guess for each individual depth map in the sequence. Our approach greatly simplifies the required user interaction during the assignment of the depth and allows for relatively free camera movement during the generation of a panoramic image. We demonstrate the effectiveness of our method by showing stereo converted sequences with various camera motions.