Complex Transfinite Barycentric Mappings with Similarity Kernels

Transfinite barycentric kernels are the continuous version of traditional barycentric coordinates and are used to define interpolants of values given on a smooth planar contour. When the data is two‐dimensional, i.e. the boundary of a planar map, these kernels may be conveniently expressed using complex number algebra, simplifying much of the notation and results. In this paper we develop some of the basic complex‐valued algebra needed to describe these planar maps, and use it to define similarity kernels, a natural alternative to the usual barycentric kernels. We develop the theory behind similarity kernels, explore their properties, and show that the transfinite versions of the popular three‐point barycentric coordinates (Laplace, mean value and Wachspress) have surprisingly simple similarity kernels. We furthermore show how similarity kernels may be used to invert injective transfinite barycentric mappings using an iterative algorithm which converges quite rapidly. This is useful for rendering images deformed by planar barycentric mappings.     

A Complex View of Barycentric Mappings

Barycentric coordinates are very popular for interpolating data values on polyhedral domains. It has been recently shown that expressing them as complex functions has various advantages when interpolating two‐dimensional data in the plane, and in particular for holomorphic maps. We extend and generalize these results by investigating the complex representation of real‐valued barycentric coordinates, when applied to planar domains. We show how the construction for generating real‐valued barycentric coordinates from a given weight function can be applied to generating complex‐valued coordinates, thus deriving complex expressions for the classical barycentric coordinates: Wachspress, mean value, and discrete harmonic. Furthermore, we show that a complex barycentric map admits the intuitive interpretation as a complex‐weighted combination of edge‐to‐edge similarity transformations, allowing the design of “home‐made” barycentric maps with desirable properties. Thus, using the tools of complex analysis, we provide a methodology for analyzing existing barycentric mappings, as well as designing new ones.     

Enhancing Bounding Volumes using Support Plane Mappings for Collision Detection

In this paper we present a new method for improving the performance of the widely used Bounding Volume Hierarchies for collision detection. The major contribution of our work is a culling algorithm that serves as a generalization of the Separating Axis Theorem for non parallel axes, based on the well‐known concept of support planes. We also provide a rigorous definition of support plane mappings and implementation details regarding the application of the proposed method to commonly used bounding volumes. The paper describes the theoretical foundation and an overall evaluation of the proposed algorithm. It demonstrates its high culling efficiency and in its application, significant improvement of timing performance with different types of bounding volumes and support plane mappings for rigid body simulations.     

BetweenIT: An Interactive Tool for Tight Inbetweening

The generation of inbetween frames that interpolate a given set of key frames is a major component in the production of a 2D feature animation. Our objective is to considerably reduce the cost of the inbetweening phase by offering an intuitive and effective interactive environment that automates inbetweening when possible while allowing the artist to guide, complement, or override the results. Tight inbetweens, which interpolate similar key frames, are particularly time‐consuming and tedious to draw. Therefore, we focus on automating these high‐precision and expensive portions of the process. We have designed a set of user‐guided semi‐automatic techniques that fit well with current practice and minimize the number of required artist‐gestures. We present a novel technique for stroke interpolation from only two keys which combines a stroke motion constructed from logarithmic spiral vertex trajectories with a stroke deformation based on curvature averaging and twisting warps. We discuss our system in the context of a feature animation production environment and evaluate our approach with real production data.     

Matting and Compositing for Fresnel Reflection on Wavy Surfaces

This paper introduces a framework that can extract an alpha matte from a single image with Fresnel reflection, and that can composite other objects with the image such that plausible reflections are included. Our method handles reflections in a plane with small undulations, for example, a water surface with waves or a glossy tabletop. During the matting stage, our method first estimates the transmission color, which is assumed to be uniform, and then calculates a reflection image and alpha matte based on user markups. However, accurate extraction of the matte becomes challenging when a plane has small undulations because these create perturbations in the matte. We therefore propose a filter that can refine the matte effectively. In the compositing stage, the reflection of a composited object is synthesized by ray tracing in real time. We demonstrate the effectiveness of our method through comparisons with ground‐truth data and results using natural images as inputs.     

Visual Analysis of Defects in Glass Fiber Reinforced Polymers for 4DCT Interrupted In situ Tests

Material engineers use interrupted in situ tensile testing to investigate the damage mechanisms in composite materials. For each subsequent scan, the load is incrementally increased until the specimen is completely fractured. During the interrupted in situ testing of glass fiber reinforced polymers (GFRPs) defects of four types are expected to appear: matrix fracture, fiber/matrix debonding, fiber pull‐out, and fiber fracture. There is a growing demand for the detection and analysis of these defects among the material engineers. In this paper, we present a novel workflow for the detection, classification, and visual analysis of defects in GFRPs using interrupted in situ tensile tests in combination with X‐ray Computed Tomography. The workflow is based on the automatic extraction of defects and fibers. We introduce the automatic Defect Classifier assigning the most suitable type to each defect based on its geometrical features. We present a visual analysis system that integrates four visualization methods: 1) the Defect Viewer highlights defects with visually encoded type in the context of the original CT image, 2) the Defect Density Maps provide an overview of the defect distributions according to type in 2D and 3D, 3) the Final Fracture Surface estimates the material fracture's location and displays it as a 3D surface, 4) the 3D Magic Lens enables interactive exploration by combining detailed visualizations in the region of interest with overview visualizations as context. In collaboration with material engineers, we evaluate our solution and demonstrate its practical applicability.     

Affective Modelling: Profiling Geometrical Models with Human Emotional Responses

In this paper, a novel concept, Affective Modelling, is introduced to encapsulate the idea of creating 3D models based on the emotional responses that they may invoke. Research on perceptually‐related issues in Computer Graphics focuses mostly on the rendering aspect. Low‐level perceptual criteria taken from established Psychology theories or identified by purposefully‐designed experiments are utilised to reduce rendering effort or derive quality evaluation schemes. For modelling, similar ideas have been applied to optimise the level of geometrical details. High‐level cognitive responses such as emotions/feelings are less addressed in graphics literatures. This paper investigates the possibility of incorporating emotional/affective factors for 3D model creations. Using a glasses frame model as our test case, we demonstrate a methodological framework to build the links between human emotional responses and geometrical features. We design and carry out a factorial experiment to systematically analyse how certain shape factors individually and interactively influence the viewer's impression of the shape of glasses frames. The findings serve as a basis for establishing computational models that facilitate emotionally‐guided 3D modelling.     

Learning 3D Deformation of Animals from 2D Images

Understanding how an animal can deform and articulate is essential for a realistic modification of its 3D model. In this paper, we show that such information can be learned from user‐clicked 2D images and a template 3D model of the target animal. We present a volumetric deformation framework that produces a set of new 3D models by deforming a template 3D model according to a set of user‐clicked images. Our framework is based on a novel locally‐bounded deformation energy, where every local region has its own stiffness value that bounds how much distortion is allowed at that location. We jointly learn the local stiffness bounds as we deform the template 3D mesh to match each user‐clicked image. We show that this seemingly complex task can be solved as a sequence of convex optimization problems. We demonstrate the effectiveness of our approach on cats and horses, which are highly deformable and articulated animals. Our framework produces new 3D models of animals that are significantly more plausible than methods without learned stiffness.     

A Multiscale Metric for 3D Mesh Visual Quality Assessment

Many processing operations are nowadays applied on 3D meshes like compression, watermarking, remeshing and so forth; these processes are mostly driven and/or evaluated using simple distortion measures like the Hausdorff distance and the root mean square error, however these measures do not correlate with the human visual perception while the visual quality of the processed meshes is a crucial issue. In that context we introduce a full‐reference 3D mesh quality metric; this metric can compare two meshes with arbitrary connectivity or sampling density and produces a score that predicts the distortion visibility between them; a visual distortion map is also created. Our metric outperforms its counterparts from the state of the art, in term of correlation with mean opinion scores coming from subjective experiments on three existing databases. Additionally, we present an application of this new metric to the improvement of rate‐distortion evaluation of recent progressive compression algorithms.     

Manifold‐Based 3D Face Caricature Generation with Individualized Facial Feature Extraction

Caricature is an interesting art to express exaggerated views of different persons and things through drawing. The face caricature is popular and widely used for different applications. To do this, we have to properly extract unique/specialized features of a person's face. A person's facial feature not only depends on his/her natural appearance, but also the associated expression style. Therefore, we would like to extract the neutural facial features and personal expression style for different applicaions. In this paper, we represent the 3D neutral face models in BU–3DFE database by sparse signal decomposition in the training phase. With this decomposition, the sparse training data can be used for robust linear subspace modeling of public faces. For an input 3D face model, we fit the model and decompose the 3D model geometry into a neutral face and the expression deformation separately. The neutral geomertry can be further decomposed into public face and individualized facial feature. We exaggerate the facial features and the expressions by estimating the probability on the corresponding manifold. The public face, the exaggerated facial features and the exaggerated expression are combined to synthesize a 3D caricature for a 3D face model. The proposed algorithm is automatic and can effectively extract the individualized facial features from an input 3D face model to create 3D face caricature.     

Fast Planar Harmonic Deformations with Alternating Tangential Projections

We present a planar harmonic cage‐based deformation method with local injectivity and bounded distortion guarantees, that is significantly faster than state‐of‐the‐art methods with similar guarantees, and allows for real‐time interaction. With a convex proxy for a near‐convex characterization of the bounded distortion harmonic mapping space from [ LW16 ], we utilize a modified alternating projection method (referred to as ATP) to project to this proxy. ATP draws inspiration from [ KABL15 ] and restricts every other projection to lie in a tangential hyperplane. In contrast to [ KABL15 ], our convex setting allows us to show that ATP is provably convergent (and is locally injective). Compared to the standard alternating projection method, it demonstrates superior convergence in fewer iterations, and it is also embarrassingly parallel, allowing for straightforward GPU implementation. Both of these factors combine to result in unprecedented speed. The convergence proof generalizes to arbitrary pairs of intersecting convex sets, suggesting potential use in other applications. Additional theoretical results sharpen the near‐convex characterization that we use and demonstrate that it is homeomorphic to the bounded distortion harmonic mapping space (instead of merely being bijective).     

Flow Curves: an Intuitive Interface for Coherent Scene Deformation

Effective composition in visual arts relies on the principle of movement, where the viewer's eye is directed along subjective curves to a center of interest. We call these curves subjective because they may span the edges and/or center‐lines of multiple objects, as well as contain missing portions which are automatically filled by our visual system. By carefully coordinating the shape of objects in a scene, skilled artists direct the viewer's attention via strong subjective curves. While traditional 2D sketching is a natural fit for this task, current 3D tools are object‐centric and do not accommodate coherent deformation of multiple shapes into smooth flows. We address this shortcoming with a new sketch‐based interface called Flow Curves which allows coordinating deformation across multiple objects. Core components of our method include an understanding of the principle of flow, algorithms to automatically identify subjective curve elements that may span multiple disconnected objects, and a deformation representation tailored to the view‐dependent nature of scene movement. As demonstrated in our video, sketching flow curves requires significantly less time than using traditional 3D editing workflows.     

Learning Style Compatibility Between Objects in a Real‐World 3D Asset Database

Large 3D asset databases are critical for designing virtual worlds, and using them effectively requires techniques for efficient querying and navigation. One important form of query is search by style compatibility: given a query object, find others that would be visually compatible if used in the same scene. In this paper, we present a scalable, learning‐based approach for solving this problem which is designed for use with real‐world 3D asset databases; we conduct experiments on 121 3D asset packages containing around 4000 3D objects from the Unity Asset Store. By leveraging the structure of the object packages, we introduce a technique to synthesize training labels for metric learning that work as well as human labels. These labels can grow exponentially with the number of objects, allowing our approach to scale to large real‐world 3D asset databases without the need for expensive human training labels. We use these synthetic training labels in a metric learning model that analyzes the in‐engine rendered appearance of an object—combining geometry, material, and texture—whereas prior work considers only object geometry, or disjoint geometry and texture features. Through an ablation experiment, we find that using this representation yields better results than using renders which lack texture, materiality, or both.     

As‐Killing‐As‐Possible Vector Fields for Planar Deformation

Cartoon animation, image warping, and several other tasks in two‐dimensional computer graphics reduce to the formulation of a reasonable model for planar deformation. A deformation is a map from a given shape to a new one, and its quality is determined by the type of distortion it introduces. In many applications, a desirable map is as isometric as possible. Finding such deformations, however, is a nonlinear problem, and most of the existing solutions approach it by minimizing a nonlinear energy. Such methods are not guaranteed to converge to a global optimum and often suffer from robustness issues. We propose a new approach based on approximate Killing vector fields (AKVFs), first introduced in shape processing. AKVFs generate near‐isometric deformations, which can be motivated as direction fields minimizing an “as‐rigid‐as‐possible” (ARAP) energy to first order. We first solve for an AKVF on the domain given user constraints via a linear optimization problem and then use this AKVF as the initial velocity field of the deformation. In this way, we transfer the inherent nonlinearity of the deformation problem to finding trajectories for each point of the domain having the given initial velocities. We show that a specific class of trajectories — the set of logarithmic spirals — is especially suited for this task both in practice and through its relationship to linear holomorphic vector fields. We demonstrate the effectiveness of our method for planar deformation by comparing it with existing state‐of‐the‐art deformation methods.     

Deformation Transfer to Multi‐Component Objects

We present a simple and effective algorithm to transfer deformation between surface meshes with multiple components. The algorithm automatically computes spatial relationships between components of the target object, builds correspondences between source and target, and finally transfers deformation of the source onto the target while preserving cohesion between the target's components. We demonstrate the versatility of our approach on various complex models.     

Semantizing Complex 3D Scenes using Constrained Attribute Grammars

We propose a new approach to automatically semantize complex objects in a 3D scene. For this, we define an expressive formalism combining the power of both attribute grammars and constraint. It offers a practical conceptual interface, which is crucial to write large maintainable specifications. As recursion is inadequate to express large collections of items, we introduce maximal operators, that are essential to reduce the parsing search space. Given a grammar in this formalism and a 3D scene, we show how to automatically compute a shared parse forest of all interpretations — in practice, only a few, thanks to relevant constraints. We evaluate this technique for building model semantization using CAD model examples as well as photogrammetric and simulated LiDAR data.     

Still‐Frame Simulation for Fire Effects of Images

We propose various simulation strategies to generate single‐frame fire effects for images, as opposed to multi‐frame fire effects for animations. To accelerate 3D simulation and to provide a user with early hints on the final effect, we propose a 2D‐guided 3D simulation approach, which runs a faster 2D simulation first, and then guides 3D simulation using the 2D simulation result. To achieve this, we explore various boundary conditions and develop a constrained projection method. Since only the final frame will be used while intermediate frames are abandoned, earlier intermediate frames can take larger time steps and have large noise applied, quickly generating turbulent flow structures. As the final frame approaches, we increase the flow quality by reducing the time step and not adding any noise. This adaptive time stepping allows us to use more computational resource near or at the final frame. We also develop divergence and buoyancy modification methods to guide flames along arbitrary, even physically implausible, directions. Our simulation methods can effectively and efficiently generate a variety of fire effects useful for image decoration.     

Expression Synthesis and Transfer in Parameter Spaces

In this paper, we introduce a novel framework that allows users to synthesize the expression of a 3D character by providing a intuitive set of parametric controls. Assuming that human face movements are formed by a set of basis actuation, we analyze a set of real expressions to extract this set together with skin deformation due to the actuation of face. To do this, we first decompose the movement of each marker into a set of distinctive movements. Independent component analysis technique is then adopted to find a independent set of actuations. Our simple and efficient skin deformation model are learned to reproduce the realistic movements of facial parts due to the actuations. In this framework, users can animate characters' faces by controlling the amount actuation or by directly manipulating the face geometry. In addition, the proposed method can be applied to expression transfer which reproduces one character's expression in another character's face. Experimental results demonstrate that our method can produce realistic expression efficiently.     

Retrieval and Visualization of Human Motion Data via Stick Figures

We propose 2D stick figures as a unified medium for visualizing and searching for human motion data. The stick figures can express a wide range or human motion, and they are easy to be drawn by people without any professional training. In our interface, the user can browse overall motion by viewing the stick figure images generated from the database and retrieve them directly by using sketched stick figures as an input query. We started with a preliminary survey to observe how people draw stick figures. Based on the rules observed from the user study, we developed an algorithm converting motion data to a sequence of stick figures. The feature‐based comparison method between the stick figures provides an interactive and progressive search for the users. They assist the user's sketching by showing the current retrieval result at each stroke. We demonstrate the utility of the system with a user study, in which the participants retrieved example motion segments from the database with 102 motion files by using our interface.