Procedural Tectonic Planets

We present a procedural method for authoring synthetic tectonic planets. Instead of relying on computationally demanding physically‐based simulations, we capture the fundamental phenomena into a procedural method that faithfully reproduces large‐scale planetary features generated by the movement and collision of the tectonic plates. We approximate complex phenomena such as plate subduction or collisions to deform the lithosphere, including the continental and oceanic crusts. The user can control the movement of the plates, which dynamically evolve and generate a variety of landforms such as continents, oceanic ridges, large scale mountain ranges or island arcs. Finally, we amplify the large‐scale planet model with either procedurally‐defined or real‐world elevation data to synthesize coherent detailed reliefs. Our method allows the user to control the evolution of an entire planet interactively, and to trigger specific events such as catastrophic plate rifting.     

A Shape Modulus for Fractal Geometry Generation

We present an efficient new method for computing Mandelbrot-like fractals (Julia sets) that approximate a user-defined shape. Our algorithm is orders of magnitude faster than previous methods, as it entirely sidesteps the need for a time-consuming numerical optimization. It is also more robust, succeeding on shapes where previous approaches failed. The key to our approach is a versor-modulus analysis of fractals that allows us to formulate a novel shape modulus function that directly controls the broad shape of a Julia set, while keeping fine-grained fractal details intact. Our formulation contains flexible artistic controls that allow users to seamlessly add fractal detail to desired spatial regions, while transitioning back to the original shape in others. No previous approach allows Mandelbrot-like details to be “painted” onto meshes.     

Environmental Objects for Authoring Procedural Scenes

We propose a novel approach for authoring large scenes with automatic enhancement of objects to create geometric decoration details such as snow cover, icicles, fallen leaves, grass tufts or even trash. We introduce environmental objects that extend an input object geometry with a set of procedural effects that defines how the object reacts to the environment, and by a set of scalar fields that defines the influence of the object over of the environment. The user controls the scene by modifying environmental variables, such as temperature or humidity fields. The scene definition is hierarchical: objects can be grouped and their behaviours can be set at each level of the hierarchy. Our per object definition allows us to optimize and accelerate the effects computation, which also enables us to generate large scenes with many geometric details at a very high level of detail. In our implementation, a complex urban scene of 10 000 m², represented with details of less than 1 cm, can be locally modified and entirely regenerated in a few seconds.     

Combinatorial Construction of Seamless Parameter Domains

The problem of seamless parametrization of surfaces is of interest in the context of structured quadrilateral mesh generation and spline-based surface approximation. It has been tackled by a variety of approaches, commonly relying on continuous numerical optimization to ultimately obtain suitable parameter domains. We present a general combinatorial seamless parameter domain construction, free from the potential numerical issues inherent to continuous optimization techniques in practice. The domains are constructed as abstract polygonal complexes which can be embedded in a discrete planar grid space, as unions of unit squares. We ensure that the domain structure matches any prescribed parametrization singularities (cones) and satisfies seamlessness conditions. Surfaces of arbitrary genus are supported. Once a domain suitable for a given surface is constructed, a seamless and locally injective parametrization over this domain can be obtained using existing planar disk mapping techniques, making recourse to Tutte's classical embedding theorem.     

Procedural Physically based BRDF for Real-Time Rendering of Glints

Physically based rendering of glittering surfaces is a challenging problem in computer graphics. Several methods have proposed off-line solutions, but none is dedicated to high-performance graphics. In this work, we propose a novel physically based BRDF for real-time rendering of glints. Our model can reproduce the appearance of sparkling materials (rocks, rough plastics, glitter fabrics, etc.). Compared to the previous real-time method [ZK16], which is not physically based, our BRDF uses normalized NDFs and converges to the standard microfacet BRDF [CT82] for a large number of microfacets. Our method procedurally computes NDFs with hundreds of sharp lobes. It relies on a dictionary of 1D marginal distributions: at each location two of them are randomly picked and multiplied (to obtain a NDF), rotated (to increase the variety), and scaled (to control standard deviation/roughness). The dictionary is multiscale, does not depend on roughness, and has a low memory footprint (less than 1 MiB).     

Facial Expression Synthesis using a Global-Local Multilinear Framework

We present a practical method to synthesize plausible 3D facial expressions for a particular target subject. The ability to synthesize an entire facial rig from a single neutral expression has a large range of applications both in computer graphics and computer vision, ranging from the efficient and cost-effective creation of CG characters to scalable data generation for machine learning purposes. Unlike previous methods based on multilinear models, the proposed approach is capable to extrapolate well outside the sample pool, which allows it to plausibly predict the identity of the target subject and create artifact free expression shapes while requiring only a small input dataset. We introduce global-local multilinear models that leverage the strengths of expression-specific and identity-specific local models combined with coarse motion estimations from a global model. Experimental results show that we achieve high-quality, plausible facial expression synthesis results for an individual that outperform existing methods both quantitatively and qualitatively.     

A survey of Optimal Transport for Computer Graphics and Computer Vision

Optimal transport is a long-standing theory that has been studied in depth from both theoretical and numerical point of views. Starting from the 50s this theory has also found a lot of applications in operational research. Over the last 30 years it has spread to computer vision and computer graphics and is now becoming hard to ignore. Still, its mathematical complexity can make it difficult to comprehend, and as such, computer vision and computer graphics researchers may find it hard to follow recent developments in their field related to optimal transport. This survey first briefly introduces the theory of optimal transport in layman's terms as well as most common numerical techniques to solve it. More importantly, it presents applications of these numerical techniques to solve various computer graphics and vision related problems. This involves applications ranging from image processing, geometry processing, rendering, fluid simulation, to computational optics, and many more. It is aimed at computer graphics researchers desiring to follow optimal transport research in their field as well as optimal transport researchers willing to find applications for their numerical algorithms.     

Procedural Modeling of a Building from a Single Image

Creating a virtual city is demanded for computer games, movies, and urban planning, but it takes a lot of time to create numerous 3D building models. Procedural modeling has become popular in recent years to overcome this issue, but creating a grammar to get a desired output is difficult and time consuming even for expert users. In this paper, we present an interactive tool that allows users to automatically generate such a grammar from a single image of a building. The user selects a photograph and highlights the silhouette of the target building as input to our method. Our pipeline automatically generates the building components, from large‐scale building mass to fine‐scale windows and doors geometry. Each stage of our pipeline combines convolutional neural networks (CNNs) and optimization to select and parameterize procedural grammars that reproduce the building elements of the picture. In the first stage, our method jointly estimates camera parameters and building mass shape. Once known, the building mass enables the rectification of the façades, which are given as input to the second stage that recovers the façade layout. This layout allows us to extract individual windows and doors that are subsequently fed to the last stage of the pipeline that selects procedural grammars for windows and doors. Finally, the grammars are combined to generate a complete procedural building as output. We devise a common methodology to make each stage of this pipeline tractable. This methodology consists in simplifying the input image to match the visual appearance of synthetic training data, and in using optimization to refine the parameters estimated by CNNs. We used our method to generate a variety of procedural models of buildings from existing photographs.     

Greedy Cut Construction for Parameterizations

We present a novel method to construct short cuts for parameterizations with low isometric distortion. The algorithm contains two steps: (i) detect feature points, where the distortion is usually concentrated; and (ii) construct a cut by connecting the detected feature points. Central to each step is a greedy method. After generating a redundant feature point set, a greedy filtering process is performed to identify the feature points required for low isometric distortion parameterizations. This filtering process discards the feature points that are useless for distortion reduction while still enabling us to obtain low isometric distortion. Next, we formulate the process of connecting the detected feature points as a Steiner tree problem. To find an approximate solution, we first successively and greedily produce a collection of auxiliary points. Then, a cut is constructed by connecting the feature points and auxiliary points. In the 26,299 test cases in which an exact solution to the Steiner tree problem is available, the length of the cut obtained by our method is on average 0.17% longer than optimal. Compared to state-of-the-art cut construction methods, our method is one order of magnitude faster and generates shorter cuts while achieving similar isometric distortion.     

Two-stage Resampling for Bidirectional Path Tracing with Multiple Light Sub-paths

Recent advances in bidirectional path tracing (BPT) reveal that the use of multiple light sub-paths and the resampling of a small number of these can improve the efficiency of BPT. By increasing the number of pre-sampled light sub-paths, the possibility of generating light paths that provide large contributions can be better explored and this can alleviate the correlation of light paths due to the reuse of pre-sampled light sub-paths by all eye sub-paths. The increased number of pre-sampled light subpaths, however, also incurs a high computational cost. In this paper, we propose a two-stage resampling method for BPT to efficiently handle a large number of pre-sampled light sub-paths. We also derive a weighting function that can treat the changes in path probability due to the two-stage resampling. Our method can handle a two orders of magnitude larger number of presampled light sub-paths than previous methods in equal-time rendering, resulting in stable and better noise reduction than state-of-the-art methods.     

State-of-the-art in Automatic 3D Reconstruction of Structured Indoor Environments

Creating high-level structured 3D models of real-world indoor scenes from captured data is a fundamental task which has important applications in many fields. Given the complexity and variability of interior environments and the need to cope with noisy and partial captured data, many open research problems remain, despite the substantial progress made in the past decade. In this survey, we provide an up-to-date integrative view of the field, bridging complementary views coming from computer graphics and computer vision. After providing a characterization of input sources, we define the structure of output models and the priors exploited to bridge the gap between imperfect sources and desired output. We then identify and discuss the main components of a structured reconstruction pipeline, and review how they are combined in scalable solutions working at the building level. We finally point out relevant research issues and analyze research trends.     

Generating Texture for 3D Human Avatar from a Single Image using Sampling and Refinement Networks

There has been significant progress in generating an animatable 3D human avatar from a single image. However, recovering texture for the 3D human avatar from a single image has been relatively less addressed. Because the generated 3D human avatar reveals the occluded texture of the given image as it moves, it is critical to synthesize the occluded texture pattern that is unseen from the source image. To generate a plausible texture map for 3D human avatars, the occluded texture pattern needs to be synthesized with respect to the visible texture from the given image. Moreover, the generated texture should align with the surface of the target 3D mesh. In this paper, we propose a texture synthesis method for a 3D human avatar that incorporates geometry information. The proposed method consists of two convolutional networks for the sampling and refining process. The sampler network fills in the occluded regions of the source image and aligns the texture with the surface of the target 3D mesh using the geometry information. The sampled texture is further refined and adjusted by the refiner network. To maintain the clear details in the given image, both sampled and refined texture is blended to produce the final texture map. To effectively guide the sampler network to achieve its goal, we designed a curriculum learning scheme that starts from a simple sampling task and gradually progresses to the task where the alignment needs to be considered. We conducted experiments to show that our method outperforms previous methods qualitatively and quantitatively.     

Procedural Cloudscapes

We present a phenomenological approach for modeling and animating cloudscapes. We propose a compact procedural model for representing the different types of cloud over a range of altitudes. We define primitive‐based field functions that allow the user to control and author the cloud cover over large distances easily. Our approach allows us to animate cloudscapes by morphing: instead of simulating the evolution of clouds using a physically‐based simulation, we compute the movement of clouds using key‐frame interpolation and tackle the morphing problem as an Optimal Transport problem. The trajectories of the cloud cover primitives are generated by solving an Anisotropic Shortest Path problem with a cost function that takes into account the elevation of the terrain and the parameters of the wind field.     

PowerRTF: Power Diagram based Restricted Tangent Face for Surface Remeshing

Triangular meshes of superior quality are important for geometric processing in practical applications. Existing approximative CVT-based remeshing methodology uses planar polygonal facets to fit the original surface, simplifying the computational complexity. However, they usually do not consider surface curvature. Topological errors and outliers can also occur in the close sheet surface remeshing, resulting in wrong meshes. With this regard, we present a novel method named PowerRTF, an extension of the restricted tangent face (RTF) in conjunction with the power diagram, to better approximate the original surface with curvature adaption. The idea is to introduce a weight property to each sample point and compute the power diagram on the tangent face to produce area-controlled polygonal facets. Based on this, we impose the variable-capacity constraint and centroid constraint to the PowerRTF, providing the trade-off between mesh quality and computational efficiency. Moreover, we apply a normal verification-based inverse side point culling method to address the topological errors and outliers in close sheet surface remeshing. Our method independently computes and optimizes the PowerRTF per sample point, which is efficiently implemented in parallel on the GPU. Experimental results demonstrate the effectiveness, flexibility, and efficiency of our method.     

Sensor‐aware Normal Estimation for Point Clouds from 3D Range Scans

Normal vectors are essential for many point cloud operations, including segmentation, reconstruction and rendering. The robust estimation of normal vectors from 3D range scans is a challenging task due to undersampling and noise, specially when combining points sampled from multiple sensor locations. Our error model assumes a Gaussian distribution of the range error with spatially‐varying variances that depend on sensor distance and reflected intensity, mimicking the features of Lidar equipment. In this paper we study the impact of measurement errors on the covariance matrices of point neighborhoods. We show that covariance matrices of the true surface points can be estimated from those of the acquired points plus sensor‐dependent directional terms. We derive a lower bound on the neighbourhood size to guarantee that estimated matrix coefficients will be within a predefined error with a prescribed probability. This bound is key for achieving an optimal trade‐off between smoothness and fine detail preservation. We also propose and compare different strategies for handling neighborhoods with samples coming from multiple materials and sensors. We show analytically that our method provides better normal estimates than competing approaches in noise conditions similar to those found in Lidar equipment.     

Feature‐Preserving Surface Reconstruction From Unoriented,Noisy Point Data

We propose a robust method for surface mesh reconstruction from unorganized, unoriented, noisy and outlier‐ridden 3D point data. A kernel‐based scale estimator is introduced to estimate the scale of inliers of the input data. The best tangent planes are computed for all points based on mean shift clustering and adaptive scale sample consensus, followed by detecting and removing outliers. Subsequently, we estimate the normals for the remaining points and smooth the noise using a surface fitting and projection strategy. As a result, the outliers and noise are removed and filtered, while the original sharp features are well preserved. We then adopt an existing method to reconstruct surface meshes from the processed point data. To preserve sharp features of the generated meshes that are often blurred during reconstruction, we describe a two‐step approach to effectively recover original sharp features. A number of examples are presented to demonstrate the effectiveness and robustness of our method.     

FAKIR: An algorithm for revealing the anatomy and pose of statues from raw point sets

3D acquisition of archaeological artefacts has become an essential part of cultural heritage research for preservation or restoration purpose. Statues, in particular, have been at the center of many projects. In this paper, we introduce a way to improve the understanding of acquired statues representing real or imaginary creatures by registering a simple and pliable articulated model to the raw point set data. Our approach performs a Forward And bacKward Iterative Registration (FAKIR) which proceeds joint by joint, needing only a few iterations to converge. We are thus able to detect the pose and elementary anatomy of sculptures, with possibly non realistic body proportions. By adapting our simple skeleton, our method can work on animals and imaginary creatures.     

Exact Constraint Satisfaction for Truly Seamless Parametrization

In the field of global surface parametrization a recent focus has been on so‐called seamless parametrization. This term refers to parametrization approaches which, while using an atlas of charts to enable the handling of surfaces of arbitrary topology, relate the parametrization across the cuts between charts via transition functions from special classes of transformations. This effectively makes the cuts invisible to applications which are invariant to these specific transformations in some sense. In actual implementations of these parametrization approaches, however, these restrictions are obeyed only approximately; errors stem from the tolerances of numerical solvers employed and, ultimately, from the limited accuracy of floating point arithmetic. In practice, robustness issues arise from these flaws in the seamlessness of a parametrization, no matter how small. We present a robust global algorithm that turns a given approximately seamless parametrization into an exactly seamless one ‐ that still is representable by standard floating point numbers. It supports common practically relevant additional constraints regarding boundary and feature curve alignment or isocurve connectivity, and ensures that these are likewise fulfilled exactly. This allows subsequent algorithms to operate robustly on the resulting truly seamless parametrization. We believe that the core of our method will furthermore be of benefit in a broader range of applications involving linearly constrained numerical optimization.     

Sketching in Gestalt Space: Interactive Shape Abstraction through Perceptual Reasoning

We present an interactive method that allows users to easily abstract complex 3D models with only a few strokes. The key idea is to employ well‐known Gestalt principles to help generalizing user inputs into a full model abstraction while accounting for form, perceptual patterns and semantics of the model. Using these principles, we alleviate the user's need to explicitly define shape abstractions. We utilize structural characteristics such as repetitions, regularity and similarity to transform user strokes into full 3D abstractions. As the user sketches over shape elements, we identify Gestalt groups and later abstract them to maintain their structural meaning. Unlike previous approaches, we operate directly on the geometric elements, in a sense applying Gestalt principles in 3D. We demonstrate the effectiveness of our approach with a series of experiments, including a variety of complex models and two extensive user studies to evaluate our framework.     

Subdivision-Specialized Linear Algebra Kernels for Static and Dynamic Mesh Connectivity on the GPU

Subdivision surfaces have become an invaluable asset in production environments. While progress over the last years has allowed the use of graphics hardware to meet performance demands during animation and rendering, high-performance is limited to immutable mesh connectivity scenarios. Motivated by recent progress in mesh data structures, we show how the complete Catmull-Clark subdivision scheme can be abstracted in the language of linear algebra. While this high-level formulation allows for a fully parallel implementation with significant performance gains, the underlying algebraic operations require further specialization for modern parallel hardware. Integrating domain knowledge about the mesh matrix data structure, we replace costly general linear algebra operations like matrix-matrix multiplication by specialized kernels. By further considering innate properties of Catmull-Clark subdivision, like the quad-only structure after refinement, we achieve an additional order of magnitude in performance and significantly reduce memory footprints. Our approach can be adapted seamlessly for different use cases, such as regular subdivision of dynamic meshes, fast evaluation for immutable topology and feature-adaptive subdivision for efficient rendering of animated models. In this way, patchwork solutions are avoided in favor of a streamlined solution with consistent performance gains throughout the production pipeline. The versatility of the sparse matrix linear algebra abstraction underlying our work is further demonstrated by extension to other schemes such as and Loop subdivision.