Efficient Monte Carlo rendering with realistic lenses

In this paper we present a novel approach to simulate image formation for a wide range of real world lenses in the Monte Carlo ray tracing framework. Our approach sidesteps the overhead of tracing rays through a system of lenses and requires no tabulation. To this end we first improve the precision of polynomial optics to closely match ground‐truth ray tracing. Second, we show how the Jacobian of the optical system enables efficient importance sampling, which is crucial for difficult paths such as sampling the aperture which is hidden behind lenses on both sides. Our results show that this yields converged images significantly faster than previous methods and accurately renders complex lens systems with negligible overhead compared to simple models, e.g. the thin lens model. We demonstrate the practicality of our method by incorporating it into a bidirectional path tracing framework and show how it can provide information needed for sophisticated light transport algorithms.     

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.     

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.     

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.     

Semi‐Automatic Editing of Graphs with Customized Layouts

Usually visualization is applied to gain insight into data. Yet consuming the data in form of visual representation is not always enough. Instead, users need to edit the data, preferably through the same means used to visualize them. In this work, we present a semi‐automatic approach to visual editing of graphs. The key idea is to use an interactive EditLens that defines where an edit operation affects an already customized and established graph layout. Locally optimal node positions within the lens and edge routes to connected nodes are calculated according to different criteria. This spares the user much manual work, but still provides sufficient freedom to accommodate application‐dependent layout constraints. Our approach utilizes the advantages of multi‐touch gestures, and is also compatible with classic mouse and keyboard interaction. Preliminary user tests have been conducted with researchers from bio‐informatics who need to manually maintain a slowly, but constantly growing molecular network. As the user feedback indicates, our solution significantly improves the editing procedure applied so far.     

Remeshing‐assisted Optimization for Locally Injective Mappings

Constructing locally injective mappings for 2D triangular meshes is vital in applications such as deformations. In such a highly constrained optimization, the prescribed tessellation may impose strong restriction on the solution. As a consequence, the feasible region may be too small to contain an ideal solution, which leads to problems of slow convergence, poor solution, or even that no solution can be found. We propose to integrate adaptive remeshing into interior point method to solve this issue. We update the vertex positions via a parameter‐free relaxation enhanced geometry optimization, and then use edge‐flip operations to reduce the residual and keep a reasonable condition number for better convergence. For more robustness, when the iteration of interior point method terminates but leaves the positional constraints unsatisfied, we estimate the edges in the current tessellation that block vertices moving based on the convergence information of the optimization, and then split neighboring edges to break the restriction. The results show that our method has better performance than the solely geometric optimization approaches, especially for extreme deformations.     

Editing and Synthesizing Two‐Character Motions using a Coupled Inverted Pendulum Model

This study aims to develop a controller for use in the online simulation of two interacting characters. This controller is capable of generalizing two sets of interaction motions of the two characters based on the relationships between the characters. The controller can exhibit similar motions to a captured human motion while reacting in a natural way to the opponent character in real time. To achieve this, we propose a new type of physical model called a coupled inverted pendulum on carts that comprises two inverted pendulum on a cart models, one for each individual, which are coupled by a relationship model. The proposed framework is divided into two steps: motion analysis and motion synthesis. Motion analysis is an offline preprocessing step, which optimizes the control parameters to move the proposed model along a motion capture trajectory of two interacting humans. The optimization procedure generates a coupled pendulum trajectory which represents the relationship between two characters for each frame, and is used as a reference in the synthesis step. In the motion synthesis step, a new coupled pendulum trajectory is planned reflecting the effects of the physical interaction, and the captured reference motions are edited based on the planned trajectory produced by the coupled pendulum trajectory generator. To validate the proposed framework, we used a motion capture data set showing two people performing kickboxing. The proposed controller is able to generalize the behaviors of two humans to different situations such as different speeds and turning speeds in a realistic way in real time.     

Sky Based Light Metering for High Dynamic Range Images

Image calibration requires both linearization of pixel values and scaling so that values in the image correspond to real‐world luminances. In this paper we focus on the latter and rather than rely on camera characterization, we calibrate images by analysing their content and metadata, obviating the need for expensive measuring devices or modeling of lens and camera combinations. Our analysis correlates sky pixel values to luminances that would be expected based on geographical metadata. Combined with high dynamic range (HDR) imaging, which gives us linear pixel data, our algorithm allows us to find absolute luminance values for each pixel—effectively turning digital cameras into absolute light meters. To validate our algorithm we have collected and annotated a calibrated set of HDR images and compared our estimation with several other approaches, showing that our approach is able to more accurately recover absolute luminance. We discuss various applications and demonstrate the utility of our method in the context of calibrated color appearance reproduction and lighting design.     

Sub‐Pixel Anti‐Aliasing Via Triangle‐Based Geometry Reconstruction

Anti‐aliasing has recently been employed as a post‐processing step to adapt to the deferred shading technique in real‐time applications. Some of these existing algorithms store supersampling geometric information as geometric buffer (G‐buffer) to detect and alleviate sub‐pixel‐level aliasing artifacts. However, the anti‐aliasing filter based on sampled sub‐pixel geometries only may introduce unfaithful shading information to the sub‐pixel color in uniform‐geometry regions, and large G‐buffer will increase memory storage and fetch overheads. In this paper, we present a new Triangle‐based Geometry Anti‐Aliasing (TGAA) algorithm, to address these problems. The coverage triangle of each screen pixel is accessed, and then, the coverage information between the triangle and neighboring sub‐pixels is stored in a screen‐resolution bitmask, which allows the geometric information to be stored and accessed in an inexpensive manner. Using triangle‐based geometry, TGAA can exclude irrelevant neighboring shading samples and achieve faithful anti‐aliasing filtering. In addition, a morphological method of estimating the geometric edges in high‐frequency geometry is incorporated into the TGAA's anti‐aliasing filter to complement the algorithm. The implementation results demonstrate that the algorithm is efficient and scalable for generating high‐quality anti‐aliased images.     

Approximate Symmetry Detection in Partial 3D Meshes

Symmetry is a common characteristic in natural and man‐made objects. Its ubiquitous nature can be exploited to facilitate the analysis and processing of computational representations of real objects. In particular, in computer graphics, the detection of symmetries in 3D geometry has enabled a number of applications in modeling and reconstruction. However, the problem of symmetry detection in incomplete geometry remains a challenging task. In this paper, we propose a vote‐based approach to detect symmetry in 3D shapes, with special interest in models with large missing parts. Our algorithm generates a set of candidate symmetries by matching local maxima of a surface function based on the heat diffusion in local domains, which guarantee robustness to missing data. In order to deal with local perturbations, we propose a multi‐scale surface function that is useful to select a set of distinctive points over which the approximate symmetries are defined. In addition, we introduce a vote‐based scheme that is aware of the partiality, and therefore reduces the number of false positive votes for the candidate symmetries. We show the effectiveness of our method in a varied set of 3D shapes and different levels of partiality. Furthermore, we show the applicability of our algorithm in the repair and completion of challenging reassembled objects in the context of cultural heritage.