Adaptable Anatomical Models for Realistic Bone Motion Reconstruction

We present a system to reconstruct subject‐specific anatomy models while relying only on exterior measurements represented by point clouds. Our model combines geometry, kinematics, and skin deformations (skinning). This joint model can be adapted to different individuals without breaking its functionality, i.e., the bones and the skin remain well‐articulated after the adaptation. We propose an optimization algorithm which learns the subject‐specific (anthropometric) parameters from input point clouds captured using commodity depth cameras. The resulting personalized models can be used to reconstruct motion of human subjects. We validate our approach for upper and lower limbs, using both synthetic data and recordings of three different human subjects. Our reconstructed bone motion is comparable to results obtained by optical motion capture (Vicon) combined with anatomically‐based inverse kinematics (OpenSIM). We demonstrate that our adapted models better preserve the joint structure than previous methods such as OpenSIM or Anatomy Transfer.     

A Key‐Pose Caching System for Rendering an Animated Crowd in Real‐Time

We present a method to accelerate the visualization of large crowds of animated characters. Linear‐blend skinning remains the dominant approach for animating a crowd but its efficiency can be improved by utilizing the temporal and intra‐crowd coherencies that are inherent within a populated scene. Our work adopts a caching system that enables a skinned key‐pose to be re‐used by multi‐pass rendering, between multiple agents and across multiple frames. We investigate two different methods; an intermittent caching scheme (whereby each member of a crowd is animated using only its nearest key‐pose) and an interpolative approach that enables key‐pose blending to be supported. For the latter case, we show that finding the optimal set of key‐poses to store is an NP‐hard problem and present a greedy algorithm suitable for real‐time applications. Both variants deliver a worthwhile performance improvement in comparison to using linear‐blend skinning alone.     

Single-pass Scalable Subsurface Rendering with Lightcuts

This paper presents a new, scalable, single pass algorithm for computing subsurface scattering using the diffusion approximation. Instead of pre‐computing a globally conservative estimate of the surface irradiance like previous two pass methods, the algorithm simultaneously refines hierarchical and adaptive estimates of both the surface irradiance and the subsurface transport. By using an adaptive, top‐down refinement method, the algorithm directs computational effort only to simulating those eye‐surface‐light paths that make significant contributions to the final image. Because the algorithm is driven by image importance, it scales more efficiently than previous methods that have a linear dependence on translucent surface area. We demonstrate that in scenes with many translucent objects and in complex lighting environments, our new algorithm has a significant performance advantage.     

An inclusive Conformal Geometric Algebra GPU animation interpolation and deformation algorithm

In the last years, Geometric Algebra with its Euclidean, Homogeneous and Conformal models attracts the research interest in many areas of Computer Science and Engineering and particularly in Computer Graphics as it is shown that they can produce more efficient and smooth results than other algebras. In this paper, we present an all-inclusive algorithm for real-time animation interpolation and GPU-based geometric skinning of animated, deformable virtual characters using the Conformal model of Geometric Algebra (CGA). We compare our method with standard quaternions, linear algebra matrices and dual-quaternions blending and skinning algorithms and we illustrate how our CGA-GPU inclusive skinning algorithm can provide as smooth and more efficient results as state-of-the-art previous methods. Furthermore, the elements of CGA that handle transformations (CGA motors) can support translation, rotation and dilation(uniform scaling) of joints under a single, GPU-supported mathematical framework and avoid conversion between different mathematical representations in contrast to quaternions and dual-quaternions that support only rotation and rotation–translation, respectively. Hence, our main novelty is the replacement of different types of algebras, and their in-between conversions between CPU and GPU, such as linear algebra matrices, quaternions, dual-quaternions and Euler angles for animation interpolation and skinning with a single mathematical representation, the CGA motors which can optimally handle the composition of translation, rotation and scaling joint transformations and interpolations. Employing latest CGA code generators, we provide a sample implementation of our algorithm running natively in a vertex shader program on modern GPUs for typical deformable virtual character simulations.     

Hyperspectral Inverse Skinning

In example-based inverse linear blend skinning (LBS), a collection of poses (e.g. animation frames) are given, and the goal is finding skinning weights and transformation matrices that closely reproduce the input. These poses may come from physical simulation, direct mesh editing, motion capture or another deformation rig. We provide a re-formulation of inverse skinning as a problem in high-dimensional Euclidean space. The transformation matrices applied to a vertex across all poses can be thought of as a point in high dimensions. We cast the inverse LBS problem as one of finding a tight-fitting simplex around these points (a well-studied problem in hyperspectral imaging). Although we do not observe transformation matrices directly, the 3D position of a vertex across all of its poses defines an affine subspace, or flat. We solve a ‘closest flat’ optimization problem to find points on these flats, and then compute a minimum-volume enclosing simplex whose vertices are the transformation matrices and whose barycentric coordinates are the skinning weights. We are able to create LBS rigs with state-of-the-art reconstruction error and state-of-the-art compression ratios for mesh animation sequences. Our solution does not consider weight sparsity or the rigidity of recovered transformations. We include observations and insights into the closest flat problem. Its ideal solution and optimal LBS reconstruction error remain an open problem.     

A Rigging‐Skinning Scheme to Control Fluid Simulation

Inspired by skeletal animation, a novel rigging‐skinning flow control scheme is proposed to animate fluids intuitively and efficiently. The new animation pipeline creates fluid animation via two steps: fluid rigging and fluid skinning. The fluid rig is defined by a point cloud with rigid‐body movement and incompressible deformation, whose time series can be intuitively specified by a rigid body motion and a constrained free‐form deformation, respectively. The fluid skin generates plausible fluid flows by virtually fluidizing the point‐cloud fluid rig with adjustable zero‐ and first‐order flow features and at fixed computational cost. Fluid rigging allows the animator to conveniently specify the desired low‐frequency flow motion through intuitive manipulations of a point cloud, while fluid skinning truthfully and efficiently converts the motion specified on the fluid rig into plausible flows of the animation fluid, with adjustable fine‐scale effects. Besides being intuitive, the rigging‐skinning scheme for fluid animation is robust and highly efficient, avoiding completely iterative trials or time‐consuming nonlinear optimization. It is also versatile, supporting both particle‐ and grid‐ based fluid solvers. A series of examples including liquid, gas and mixed scenes are presented to demonstrate the performance of the new animation pipeline.     

Distributed iterative command governor schemes for interconnected linear systems

A novel distributed command governor (CG) supervision strategy relying on iterative optimization procedure is presented for multi‐agent interconnected linear systems subject to pointwise‐in‐time set‐membership coordination constraints. Unlike non‐iterative distributed CG schemes, here all agents undertake several optimization iterations and data exchange before arriving to the optimal solution. As a result, these methods are able to achieve Pareto‐optimal solutions not only in steady‐state conditions as the ones based on non‐iterative optimization procedures but also during transients and are not hampered by the presence of undesirable Nash‐equilibria or deadlock situations. The main properties of the method are fully investigated and in particular its optimality, stability, and feasibility properties rigorously proved. A final example is presented where the proposed distributed solution is contrasted with existing centralized and distributed non‐iterative CG solutions. Copyright © 2017 John Wiley & Sons, Ltd.     

Isotropic Surface Remeshing Using Constrained Centroidal Delaunay Mesh

We develop a novel isotropic remeshing method based on constrained centroidal Delaunay mesh (CCDM), a generalization of centroidal patch triangulation from 2D to mesh surface. Our method starts with resampling an input mesh with a vertex distribution according to a user‐defined density function. The initial remeshing result is then progressively optimized by alternatively recovering the Delaunay mesh and moving each vertex to the centroid of its 1‐ring neighborhood. The key to making such simple iterations work is an efficient optimization framework that combines both local and global optimization methods. Our method is parameterization‐free, thus avoiding the metric distortion introduced by parameterization, and generating more well‐shaped triangles. Our method guarantees that the topology of surface is preserved without requiring geodesic information. We conduct various experiments to demonstrate the simplicity, efficacy, and robustness of the presented method.     

Fast Isosurface Rendering on a GPU by Cell Rasterization

This paper presents a fast, high‐quality, GPU‐based isosurface rendering pipeline for implicit surfaces defined by a regular volumetric grid. GPUs are designed primarily for use with polygonal primitives, rather than volume primitives, but here we directly treat each volume cell as a single rendering primitive by designing a vertex program and fragment program on a commodity GPU. Compared with previous raycasting methods, ours has a more effective memory footprint (cache locality) and better coherence between multiple parallel SIMD processors. Furthermore, we extend and speed up our approach by introducing a new view‐dependent sorting algorithm to take advantage of the early‐z‐culling feature of the GPU to gain significant performance speed‐up. As another advantage, this sorting algorithm makes multiple transparent isosurfaces rendering available almost for free. Finally, we demonstrate the effectiveness and quality of our techniques in several real‐time rendering scenarios and include analysis and comparisons with previous work.     

Efficient Gradient‐Domain Compositing Using an Approximate Curl‐free Wavelet Projection

Gradient‐domain compositing has been widely used to create a seamless composite with gradient close to a composite gradient field generated from one or more registered images. The key to this problem is to solve a Poisson equation, whose unknown variables can reach the size of the composite if no region of interest is drawn explicitly, thus making both the time and memory cost expensive in processing multi‐megapixel images. In this paper, we propose an approximate projection method based on biorthogonal Multiresolution Analyses (MRA) to solve the Poisson equation. Unlike previous Poisson equation solvers which try to converge to the accurate solution with iterative algorithms, we use biorthogonal compactly supported curl‐free wavelets as the fundamental bases to approximately project the composite gradient field onto a curl‐free vector space. Then, the composite can be efficiently recovered by applying a fast inverse wavelet transform. Considering an n‐pixel composite, our method only requires 2n of memory for all vector fields and is more efficient than state‐of‐the‐art methods while achieving almost identical results. Specifically, experiments show that our method gains a 5× speedup over the streaming multigrid in certain cases.     

Uniformization and Density Adaptation for Point Cloud Data Via Graph Laplacian

Point cloud data is one of the most common types of input for geometric processing applications. In this paper, we study the point cloud density adaptation problem that underlies many pre‐processing tasks of points data. Specifically, given a (sparse) set of points Q sampling an unknown surface and a target density function, the goal is to adapt Q to match the target distribution. We propose a simple and robust framework that is effective at achieving both local uniformity and precise global density distribution control. Our approach relies on the Gaussian‐weighted graph Laplacian and works purely in the points setting. While it is well known that graph Laplacian is related to mean‐curvature flow and thus has denoising ability, our algorithm uses certain information encoded in the graph Laplacian that is orthogonal to the mean‐curvature flow. Furthermore, by leveraging the natural scale parameter contained in the Gaussian kernel and combining it with a simulated annealing idea, our algorithm moves points in a multi‐scale manner. The resulting algorithm relies much less on the input points to have a good initial distribution (neither uniform nor close to the target density distribution) than many previous refinement‐based methods. We demonstrate the simplicity and effectiveness of our algorithm with point clouds sampled from different underlying surfaces with various geometric and topological properties.     

Non‐Linear Beam Tracing on a GPU

Beam tracing combines the flexibility of ray tracing and the speed of polygon rasterization. However, beam tracing so far only handles linear transformations; thus, it is only applicable to linear effects such as planar mirror reflections but not to non‐linear effects such as curved mirror reflection, refraction, caustics and shadows. In this paper, we introduce non‐linear beam tracing to render these non‐linear effects. Non‐linear beam tracing is highly challenging because commodity graphics hardware supports only linear vertex transformation and triangle rasterization. We overcome this difficulty by designing a non‐linear graphics pipeline and implementing it on top of a commodity GPU. This allows beams to be non‐linear where rays within the same beam do not have to be parallel or intersect at a single point. Using these non‐linear beams, real‐time GPU applications can render secondary rays via polygon streaming similar to how they render primary rays. A major strength of this methodology is that it naturally supports fully dynamic scenes without the need to pre‐store a scene database. Utilizing our approach, non‐linear ray tracing effects can be rendered in real‐time on a commodity GPU under a unified framework.     

SIMD Optimization of Linear Expressions for Programmable Graphics Hardware

The increased programmability of graphics hardware allows efficient graphical processing unit (GPU) implementations of a wide range of general computations on commodity PCs. An important factor in such implementations is how to fully exploit the SIMD computing capacities offered by modern graphics processors. Linear expressions in the form of , where A is a matrix, and and are vectors, constitute one of the most basic operations in many scientific computations. In this paper, we propose a SIMD code optimization technique that enables efficient shader codes to be generated for evaluating linear expressions. It is shown that performance can be improved considerably by efficiently packing arithmetic operations into four‐wide SIMD instructions through reordering of the operations in linear expressions. We demonstrate that the presented technique can be used effectively for programming both vertex and pixel shaders for a variety of mathematical applications, including integrating differential equations and solving a sparse linear system of equations using iterative methods.     

Deformable 3D Shape Registration Based on Local Similarity Transforms

In this paper, a new method for deformable 3D shape registration is proposed. The algorithm computes shape transitions based on local similarity transforms which allows to model not only as‐rigid‐as‐possible deformations but also local and global scale. We formulate an ordinary differential equation (ODE) which describes the transition of a source shape towards a target shape. We assume that both shapes are roughly pre‐aligned (e.g., frames of a motion sequence). The ODE consists of two terms. The first one causes the deformation by pulling the source shape points towards corresponding points on the target shape. Initial correspondences are estimated by closest‐point search and then refined by an efficient smoothing scheme. The second term regularizes the deformation by drawing the points towards locally defined rest positions. These are given by the optimal similarity transform which matches the initial (undeformed) neighborhood of a source point to its current (deformed) neighborhood. The proposed ODE allows for a very efficient explicit numerical integration. This avoids the repeated solution of large linear systems usually done when solving the registration problem within general‐purpose non‐linear optimization frameworks. We experimentally validate the proposed method on a variety of real data and perform a comparison with several state‐of‐the‐art approaches.     

Efficient Interpolation of Articulated Shapes Using Mixed Shape Spaces

Interpolation between compatible triangle meshes that represent different poses of some object is a fundamental operation in geometry processing. A common approach is to consider the static input shapes as points in a suitable shape space and then use simple linear interpolation in this space to find an interpolated shape. In this paper, we present a new interpolation technique that is particularly tailored for meshes that represent articulated shapes. It is up to an order of magnitude faster than state‐of‐the‐art methods and gives very similar results. To achieve this, our approach introduces a novel shape space that takes advantage of the underlying structure of articulated shapes and distinguishes between rigid parts and non‐rigid joints. This allows us to use fast vertex interpolation on the rigid parts and resort to comparatively slow edge‐based interpolation only for the joints.     

A Subspace Method for Fast Locally Injective Harmonic Mapping

We present a fast algorithm for low‐distortion locally injective harmonic mappings of genus 0 triangle meshes with and without cone singularities. The algorithm consists of two portions, a linear subspace analysis and construction, and a nonlinear non‐convex optimization for determination of a mapping within the reduced subspace. The subspace is the space of solutions to the Harmonic Global Parametrization (HGP) linear system [BCW17], and only vertex positions near cones are utilized, decoupling the variable count from the mesh density. A key insight shows how to construct the linear subspace at a cost comparable to that of a linear solve, extracting a very small set of elements from the inverse of the matrix without explicitly calculating it. With a variable count on the order of the number of cones, a tangential alternating projection method [HCW17] and a subsequent Newton optimization [CW17] are used to quickly find a low‐distortion locally injective mapping. This mapping determination is typically much faster than the subspace construction. Experiments demonstrating its speed and efficacy are shown, and we find it to be an order of magnitude faster than HGP and other alternatives.     

Efficient GPU Data Structures and Methods to Solve Sparse Linear Systems in Dynamics Applications

We present graphics processing unit (GPU) data structures and algorithms to efficiently solve sparse linear systems that are typically required in simulations of multi‐body systems and deformable bodies. Thereby, we introduce an efficient sparse matrix data structure that can handle arbitrary sparsity patterns and outperforms current state‐of‐the‐art implementations for sparse matrix vector multiplication. Moreover, an efficient method to construct global matrices on the GPU is presented where hundreds of thousands of individual element contributions are assembled in a few milliseconds. A finite‐element‐based method for the simulation of deformable solids as well as an impulse‐based method for rigid bodies are introduced in order to demonstrate the advantages of the novel data structures and algorithms. These applications share the characteristic that a major computational effort consists of building and solving systems of linear equations in every time step. Our solving method results in a speed‐up factor of up to 13 in comparison to other GPU methods.     

Classification of Illumination Methods for Mixed Reality

A mixed reality (MR) represents an environment composed both by real and virtual objects. MR applications are used more and more, for instance in surgery, architecture, cultural heritage, entertainment, etc. For some of these applications it is important to merge the real and virtual elements using consistent illumination. This paper proposes a classification of illumination methods for MR applications that aim at generating a merged environment in which illumination and shadows are consistent. Three different illumination methods can be identified: common illumination, relighting and methods based on inverse illumination. In this paper a classification of the illumination methods for MR is given based on their input requirements: the amount of geometry and radiance known of the real environment. This led us to define four categories of methods that vary depending on the type of geometric model used for representing the real scene, and the sdifferent radiance information available for each point of the real scene. Various methods are described within their category. The classification points out that in general the quality of the illumination interactions increases with the amount of input information available. On the other hand, the accessibility of the method decreases since its pre‐processing time increases to gather the extra information. Recent developed techniques managed to compensate unknown data with clever techniques using an iterative algorithm, hardware illumination or recent progress in stereovision. Finally, a review of illumination techniques for MR is given with a discussion on important properties such as the possibility of interactivity or the amount of complexity in the simulated illumination.     

Feature Oriented Progressive Lossless Mesh Coding

A feature‐oriented generic progressive lossless mesh coder (FOLProM) is proposed to encode triangular meshes with arbitrarily complex geometry and topology. In this work, a sequence of levels of detail (LODs) are generated through iterative vertex set split and bounding volume subdivision. The incremental geometry and connectivity updates associated with each vertex set split and/or bounding volume subdivision are entropy coded. Due to the visual importance of sharp geometric features, the whole geometry coding process is optimized for a better presentation of geometric features, especially at low coding bitrates. Feature‐oriented optimization in FOLProM is performed in hierarchy control and adaptive quantization. Efficient coordinate representation and prediction schemes are employed to reduce the entropy of data significantly. Furthermore, a simple yet efficient connectivity coding scheme is proposed. It is shown that FOLProM offers a significant rate‐distortion (R‐D) gain over the prior art, which is especially obvious at low bitrates.