Spatio‐temporal geometry fusion for multiple hybrid cameras using moving least squares surfaces

Multi‐view reconstruction aims at computing the geometry of a scene observed by a set of cameras. Accurate 3D reconstruction of dynamic scenes is a key component for a large variety of applications, ranging from special effects to telepresence and medical imaging. In this paper we propose a method based on Moving Least Squares surfaces which robustly and efficiently reconstructs dynamic scenes captured by a calibrated set of hybrid color+depth cameras. Our reconstruction provides spatio‐temporal consistency and seamlessly fuses color and geometric information. We illustrate our approach on a variety of real sequences and demonstrate that it favorably compares to state‐of‐the‐art methods.     

Coded exposure HDR light‐field video recording

Capturing exposure sequences to compute high dynamic range (HDR) images causes motion blur in cases of camera movement. This also applies to light‐field cameras: frames rendered from multiple blurred HDR light‐field perspectives are also blurred. While the recording times of exposure sequences cannot be reduced for a single‐sensor camera, we demonstrate how this can be achieved for a camera array. Thus, we decrease capturing time and reduce motion blur for HDR light‐field video recording. Applying a spatio‐temporal exposure pattern while capturing frames with a camera array reduces the overall recording time and enables the estimation of camera movement within one light‐field video frame. By estimating depth maps and local point spread functions (PSFs) from multiple perspectives with the same exposure, regional motion deblurring can be supported. Missing exposures at various perspectives are then interpolated.     

Sets of Globally Optimal Stream Surfaces for Flow Visualization

Stream surfaces are a well‐studied and widely used tool for the visualization of 3D flow fields. Usually, stream surface seeding is carried out manually in time‐consuming trial and error procedures. Only recently automatic selection methods were proposed. Local methods support the selection of a set of stream surfaces, but, contrary to global selection methods, they evaluate only the quality of the seeding lines but not the quality of the whole stream surfaces. Global methods, on the other hand, only support the selection of a single optimal stream surface until now. However, for certain flow fields a single stream surface is not sufficient to represent all flow features. In our work, we overcome this limitation by introducing a global selection technique for a set of stream surfaces. All selected surfaces optimize global stream surface quality measures and are guaranteed to be mutually distant, such that they can convey different flow features. Our approach is an efficient extension of the most recent global selection method for single stream surfaces. We illustrate its effectiveness on a number of analytical and simulated flow fields and analyze the quality of the results in a user study.     

Towards an Unbiased Comparison of CC,BCC, and FCC Lattices in Terms of Prealiasing

In the literature on optimal regular volume sampling, the Body‐Centered Cubic (BCC) lattice has been proven to be optimal for sampling spherically band‐limited signals above the Nyquist limit. On the other hand, if the sampling frequency is below the Nyquist limit, the Face‐Centered Cubic (FCC) lattice was demonstrated to be optimal in reducing the prealiasing effect. In this paper, we confirm that the FCC lattice is indeed optimal in this sense in a certain interval of the sampling frequency. By theoretically estimating the prealiasing error in a realistic range of the sampling frequency, we show that in other frequency intervals, the BCC lattice and even the traditional Cartesian Cubic (CC) lattice are expected to minimize the prealiasing. The BCC lattice is superior over the FCC lattice if the sampling frequency is not significantly below the Nyquist limit. Interestingly, if the original signal is drastically undersampled, the CC lattice is expected to provide the lowest prealiasing error. Additionally, we give a comprehensible clarification that the sampling efficiency of the FCC lattice is lower than that of the BCC lattice. Although this is a well‐known fact, the exact percentage has been erroneously reported in the literature. Furthermore, for the sake of an unbiased comparison, we propose to rotate the Marschner‐Lobb test signal such that an undue advantage is not given to either lattice.     

Group‐in‐a‐Box Meta‐Layouts for Topological Clusters and Attribute‐Based Groups: Space‐Efficient Visualizations of Network Communities and Their Ties

An important part of network analysis is understanding community structures like topological clusters and attribute‐based groups. Standard approaches for showing communities using colour, shape, rectangular bounding boxes, convex hulls or force‐directed layout algorithms remain valuable, however our Group‐in‐a‐Box meta‐layouts add a fresh strategy for presenting community membership, internal structure and inter‐cluster relationships. This paper extends the basic Group‐in‐a‐Box meta‐layout, which uses a Treemap substrate of rectangular regions whose size is proportional to community size. When there are numerous inter‐community relationships, the proposed extensions help users view them more clearly: (1) the Croissant–Doughnut meta‐layout applies empirically determined rules for box arrangement to improve space utilization while still showing inter‐community relationships, and (2) the Force‐Directed layout arranges community boxes based on their aggregate ties at the cost of additional space. Our free and open source reference implementation in NodeXL includes heuristics to choose what we have found to be the preferable Group‐in‐a‐Box meta‐layout to show networks with varying numbers or sizes of communities. Case study examples, a pilot comparative user preference study (nine participants), and a readability measure‐based evaluation of 309 Twitter networks demonstrate the utility of the proposed meta‐layouts.     

Variational Tree Synthesis

Modelling trees according to desired shapes is important for many applications. Despite numerous methods having been proposed in tree modelling, it is still a non‐trivial task and challenging. In this paper, we present a new variational computing approach for generating realistic trees in specific shapes. Instead of directly modelling trees from symbolic rules, we formulate the tree modelling as an optimization process, in which a variational cost function is iteratively minimized. This cost function measures the difference between the guidance shape and the target tree crown. In addition, to faithfully capture the branch structure of trees, several botanical factors, including the minimum total branches volume and spatial branches patterns, are considered in the optimization to guide the tree modelling process. We demonstrate that our approach is applicable to generate trees with different shapes, from interactive design and complex polygonal meshes.     

A Projective Framework for Polyhedral Mesh Modelling

We present a novel framework for polyhedral mesh editing with face‐based projective maps that preserves planarity by definition. Such meshes are essential in the field of architectural design and rationalization. By using homogeneous coordinates to describe vertices, we can parametrize the entire shape space of planar‐preserving deformations with bilinear equations. The generality of this space allows for polyhedral geometric processing methods to be conducted with ease. We demonstrate its usefulness in planar‐quadrilateral mesh subdivision, a resulting multi‐resolution editing algorithm, and novel shape‐space exploration with prescribed transformations. Furthermore, we show that our shape space is a discretization of a continuous space of conjugate‐preserving projective transformation fields on surfaces. Our shape space directly addresses planar‐quad meshes, on which we put a focus, and we further show that our framework naturally extends to meshes with faces of more than four vertices as well.     

Continuous Levels‐of‐Detail and Visual Abstraction for Seamless Molecular Visualization

Molecular visualization is often challenged with rendering of large molecular structures in real time. We introduce a novel approach that enables us to show even large protein complexes. Our method is based on the level‐of‐detail concept, where we exploit three different abstractions combined in one visualization. Firstly, molecular surface abstraction exploits three different surfaces, solvent‐excluded surface (SES), Gaussian kernels and van der Waals spheres, combined as one surface by linear interpolation. Secondly, we introduce three shading abstraction levels and a method for creating seamless transitions between these representations. The SES representation with full shading and added contours stands in focus while on the other side a sphere representation of a cluster of atoms with constant shading and without contours provide the context. Thirdly, we propose a hierarchical abstraction based on a set of clusters formed on molecular atoms. All three abstraction models are driven by one importance function classifying the scene into the near‐, mid‐ and far‐field. Moreover, we introduce a methodology to render the entire molecule directly using the A‐buffer technique, which further improves the performance. The rendering performance is evaluated on series of molecules of varying atom counts.     

Robust Treatment of Degenerate Elements in Interactive Corotational FEM Simulations

We address the problem of robust and efficient treatment of element collapse and inversion in corotational FEM simulations of deformable objects in two and three dimensions, and show that existing degeneration treatment methods have previously unreported flaws that seriously threaten robustness and physical plausibility in interactive applications. We propose a new method that avoids such flaws, yields faster and smoother degeneration recovery and extends the range of well‐behaved degenerate configurations without adding significant complexity or computational cost to standard explicit and quasi‐implicit solvers.     

Visual Analysis of Trajectories in Multi‐Dimensional State Spaces

Multi‐dimensional data originate from many different sources and are relevant for many applications. One specific sub‐type of such data is continuous trajectory data in multi‐dimensional state spaces of complex systems. We adapt the concept of spatially continuous scatterplots and spatially continuous parallel coordinate plots to such trajectory data, leading to continuous‐time scatterplots and continuous‐time parallel coordinates. Together with a temporal heat map representation, we design coordinated views for visual analysis and interactive exploration. We demonstrate the usefulness of our visualization approach for three case studies that cover examples of complex dynamic systems: cyber‐physical systems consisting of heterogeneous sensors and actuators networks (the collection of time‐dependent sensor network data of an exemplary smart home environment), the dynamics of robot arm movement and motion characteristics of humanoids.