Möbius Registration

Conformal parameterizations over the sphere provide high‐quality maps between genus zero surfaces, and are essential for applications such as data transfer and comparative shape analysis. However, such maps are not unique: to define correspondence between two surfaces, one must find the Möbius transformation that best aligns two parameterizations—akin to picking a translation and rotation in rigid registration problems. We describe a simple procedure that canonically centers and rotationally aligns two spherical maps. Centering is implemented via elementary operations on triangle meshes in ?³, and minimizes area distortion. Alignment is achieved using the FFT over the group of rotations. We examine this procedure in the context of spherical conformal parameterization, orbifold maps, non‐rigid symmetry detection, and dense point‐to‐point surface correspondence.     

A New Class of Guided C2 Subdivision Surfaces Combining Good Shape with Nested Refinement

Converting quadrilateral meshes to smooth manifolds, guided subdivision offers a way to combine the good highlight line distribution of recent G‐spline constructions with the refinability of subdivision surfaces. This avoids the complex refinement of G‐spline constructions and the poor shape of standard subdivision. Guided subdivision can then be used both to generate the surface and hierarchically compute functions on the surface. Specifically, we present a C² subdivision algorithm of polynomial degree bi‐6 and a curvature bounded algorithm of degree bi‐5. We prove that the common eigenstructure of this class of subdivision algorithms is determined by their guide and demonstrate that their eigenspectrum (speed of contraction) can be adjusted without harming the shape. For practical implementation, a finite number of subdivision steps can be completed by a high‐quality cap. Near irregular points this allows leveraging standard polynomial tools both for rendering of the surface and for approximately integrating functions on the surface.     

Designing Camera Networks by Convex Quadratic Programming

In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera‐to‐camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade‐off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real‐world floorplans (garage, hotel, mall, and airport).     

Visual Assessment of Alleged Plagiarism Cases

We developed a visual analysis tool to support the verification, assessment, and presentation of alleged cases of plagiarism. The analysis of a suspicious document typically results in a compilation of categorized “finding spots”. The categorization reveals the way in which the suspicious text fragment was created from the source, e.g. by obfuscation, translation, or by shake and paste. We provide a three‐level approach for exploring the finding spots in context. The overview shows the relationship of the entire suspicious document to the set of source documents. A glyph‐based view reveals the structural and textual differences and similarities of a set of finding spots and their corresponding source text fragments. For further analysis and editing of the finding spot's assessment, the actual text fragments can be embedded side‐by‐side in the diffline view. The different views are tied together by versatile navigation and selection operations. Our expert reviewers confirm that our tool provides a significant improvement over existing static visualizations for assessing plagiarism cases.     

Persistent Homology for the Evaluation of Dimensionality Reduction Schemes

High‐dimensional data sets are a prevalent occurrence in many application domains. This data is commonly visualized using dimensionality reduction (DR) methods. DR methods provide e.g. a two‐dimensional embedding of the abstract data that retains relevant high‐dimensional characteristics such as local distances between data points. Since the amount of DR algorithms from which users may choose is steadily increasing, assessing their quality becomes more and more important. We present a novel technique to quantify and compare the quality of DR algorithms that is based on persistent homology. An inherent beneficial property of persistent homology is its robustness against noise which makes it well suited for real world data. Our pipeline informs about the best DR technique for a given data set and chosen metric (e.g. preservation of local distances) and provides knowledge about the local quality of an embedding, thereby helping users understand the shortcomings of the selected DR method. The utility of our method is demonstrated using application data from multiple domains and a variety of commonly used DR methods.     

Towards a smooth design process for static communicative node‐link diagrams

Node‐link infographics are visually very rich and can communicate messages effectively, but can be very difficult to create, often involving a painstaking and artisanal process. In this paper we present an investigation of node‐link visualizations for communication and how to better support their creation. We begin by breaking down these images into their basic elements and analyzing how they are created. We then present a set of techniques aimed at improving the creation workflow by bringing more flexibility and power to users, letting them manipulate all aspects of a node‐link diagram (layout, visual attributes, etc.) while taking into account the context in which it will appear. These techniques were implemented in a proof‐of‐concept prototype called GraphCoiffure, which was designed as an intermediary step between graph drawing/editing software and image authoring applications. We describe how GraphCoiffure improves the workflow and illustrate its benefits through practical examples.     

Portal‐Masked Environment Map Sampling

We present a technique to efficiently importance sample distant, all‐frequency illumination in indoor scenes. Standard environment sampling is inefficient in such cases since the distant lighting is typically only visible through small openings (e.g. windows). This visibility is often addressed by manually placing a portal around each window to direct samples towards the openings; however, uniformly sampling the portal (its area or solid angle) disregards the possibly high frequency environment map. We propose a new portal importance sampling technique which takes into account both the environment map and its visibility through the portal, drawing samples proportional to the product of the two. To make this practical, we propose a novel, portal‐rectified reparametrization of the environment map with the key property that the visible region induced by a rectangular portal projects to an axis‐aligned rectangle. This allows us to sample according to the desired product distribution at an arbitrary shading location using a single (precomputed) summed‐area table per portal. Our technique is unbiased, relevant to many renderers, and can also be applied to rectangular light sources with directional emission profiles, enabling efficient rendering of non‐diffuse light sources with soft shadows.     

Mesh Denoising using Extended ROF Model with L1 Fidelity

This paper presents a variational algorithm for feature‐preserved mesh denoising. At the heart of the algorithm is a novel variational model composed of three components: fidelity, regularization and fairness, which are specifically designed to have their intuitive roles. In particular, the fidelity is formulated as an L₁ data term, which makes the regularization process be less dependent on the exact value of outliers and noise. The regularization is formulated as the total absolute edge‐lengthed supplementary angle of the dihedral angle, making the model capable of reconstructing meshes with sharp features. In addition, an augmented Lagrange method is provided to efficiently solve the proposed variational model. Compared to the prior art, the new algorithm has crucial advantages in handling large scale noise, noise along random directions, and different kinds of noise, including random impulsive noise, even in the presence of sharp features. Both visual and quantitative evaluation demonstrates the superiority of the new algorithm.     

Procedural Tree Modeling with Guiding Vectors

We propose guiding vectors to augment graph‐based tree synthesis, in which trees are collections of least‐cost paths in a graph. Each node has an associated guiding vector; edges parallel to the guiding vector are cheap, but edges are more expensive when their orientation differs from the guiding vector. We further propose an incremental method for assigning guiding vectors over the graph, in which a node's guiding vector is an incremental rotation of that of its parent. We present a complete procedural system for tree modeling; our use of guiding vectors enables the graph‐based method to produce high‐quality tree models resembling a variety of real‐world tree species.