Fast and Robust Inversion‐Free Shape Manipulation

We present a shape manipulation technique capable of producing deformations of 2D and 3D meshes, guaranteeing that no elements will be inverted. We achieve this by augmenting the quadratic ex‐rotated elastic energy with additional convex terms that penalize the presence of inverted elements. Using a schedule of increasing penalty coefficients, we efficiently and robustly converge to an inversion free state by solving a sequence of unconstrained convex minimization problems. This process can be interpreted as a special purpose Semi‐Definite Programming (SDP) solver. We demonstrate that our method outperforms solvers used in previous work, including commercial‐grade SDP software (MOSEK). As an additional benefit, our method also converges to the solution via a more intuitive path, which can be used for quick preview. We demonstrate the efficacy of our scheme in a number of 2D and 3D shapes undergoing moderate to drastic deformation.     

Warp sculpting

The task of computer-based free-form shape design is fraught with practical and conceptual difficulties. Incorporating elements of traditional clay sculpting has long been recognized as a means of shielding the user from these complexities. We present warp sculpting, a variant of spatial deformation, which allows deformations to be initiated by the rigid body transformation or uniform scaling of volumetric tools. This is reminiscent of a tool imprinting, flexing, and molding clay. Unlike previous approaches, the deformation is truly interactive. Tools, encoded in a distance field, can have arbitrarily complex shapes. Although individual tools have a static shape, several tools can be applied simultaneously. We enhance the basic formulation of warp sculpting in two ways. First, deformation is toggled to automatically overcome the problem of "sticky" tools, where the object's surface clings to parts of a tool that are moving away. Second, unlike many other spatial deformations, we ensure that warp sculpting remains foldover-free and, hence, prevent self-intersecting objects.     

ProcDef: Local‐to‐global Deformation for Skeleton‐free Character Animation

Animations of characters with flexible bodies such as jellyfish, snails, and, hearts are difficult to design using traditional skeleton‐based approaches. A standard approach is keyframing, but adjusting the shape of the flexible body for each key frame is tedious. In addition, the character cannot dynamically adjust its motion to respond to the environment or user input. This paper introduces a new procedural deformation framework (ProcDef) for designing and driving animations of such flexible objects. Our approach is to synthesize global motions procedurally by integrating local deformations. ProcDef provides an efficient design scheme for local deformation patterns; the user can control the orientation and magnitude of local deformations as well as the propagation of deformation signals by specifying line charts and volumetric fields. We also present a fast and robust deformation algorithm based on shape‐matching dynamics and show some example animations to illustrate the feasibility of our framework.     

Pose space parameterization and style transfer of skin deformation

We present a technique to parameterize skin deformation by skeletal motion and to transfer the deformation style from one character to another. We decompose skin deformation into time‐varying signals and basis matrices by using dimension reduction techniques and then approximate the time‐varying signals by using radial basis functions with respect to joint angles that define skeletal motion. This decomposition reduces the size of deformation data to a small number of time‐varying signals that represent the complex role of muscle action. The subsequent parameterization yields a fast and intuitive control of characters; thus, it allows us to construct faithful skin deformations quickly as skeletal bones move. The representation of our parameterization allows us to capture and transfer a derived deformation style to another skeleton–skin structure without considering the input dimension of the deformation data. This style transfer can be used as a basis for realistically animating variants of sample characters that have the same skeletal topology. Parameterization of skin deformation and its style transfer can be performed within a small amount of error once the preprocessing time and control of the deformation is carried out in real time by our graphics processing unit implementation. Copyright © 2011 John Wiley & Sons, Ltd.     

Multi‐View Stereo on Consistent Face Topology

We present a multi‐view stereo reconstruction technique that directly produces a complete high‐fidelity head model with consistent facial mesh topology. While existing techniques decouple shape estimation and facial tracking, our framework jointly optimizes for stereo constraints and consistent mesh parameterization. Our method is therefore free from drift and fully parallelizable for dynamic facial performance capture. We produce highly detailed facial geometries with artist‐quality UV parameterization, including secondary elements such as eyeballs, mouth pockets, nostrils, and the back of the head. Our approach consists of deforming a common template model to match multi‐view input images of the subject, while satisfying cross‐view, cross‐subject, and cross‐pose consistencies using a combination of 2D landmark detection, optical flow, and surface and volumetric Laplacian regularization. Since the flow is never computed between frames, our method is trivially parallelized by processing each frame independently. Accurate rigid head pose is extracted using a PCA‐based dimension reduction and denoising scheme. We demonstrate high‐fidelity performance capture results with challenging head motion and complex facial expressions around eye and mouth regions. While the quality of our results is on par with the current state‐of‐the‐art, our approach can be fully parallelized, does not suffer from drift, and produces face models with production‐quality mesh topologies.     

Direct Visualization of Deformation in Volumes

Deformation is a topic of interest in many disciplines. In particular in medical research, deformations of surfaces and even entire volumetric structures are of interest. Clear visualization of such deformations can lead to important insight into growth processes and progression of disease.
We present new techniques for direct focus+context visualization of deformation fields representing transformations between pairs of volumetric datasets. Typically, such fields are computed by performing a non-rigid registration between two data volumes. Our visualization is based on direct volume rendering and uses the GPU to compute and interactively visualize features of these deformation fields in real-time. We integrate visualization of the deformation field with visualization of the scalar volume affected by the deformations. Furthermore, we present a novel use of texturing in volume rendered visualizations to show additional properties of the vector field on surfaces in the volume.     

Real-time elastic deformations of soft tissues for surgerysimulation

We describe a novel method for surgery simulation including a volumetric model built from medical images and an elastic modeling of the deformations. The physical model is based on elasticity theory which suitably links the shape of deformable bodies and the forces associated with the deformation. A real time computation of the deformation is possible thanks to a preprocessing of elementary deformations derived from a finite element method. This method has been implemented in a system including a force feedback device and a collision detection algorithm. The simulator works in real time with a high resolution liver model     

Creating and Animating Subject‐Specific Anatomical Models

Creating and animating subject‐specific anatomical models is traditionally a difficult process involving medical image segmentation, geometric corrections and the manual definition of kinematic parameters. In this paper, we introduce a novel template morphing algorithm that facilitates three‐dimensional modelling and parameterization of skeletons. Target data can be either medical images or surfaces of the whole skeleton. We incorporate prior knowledge about bone shape, the feasible skeleton pose and the morphological variability in the population. This allows for noise reduction, bone separation and the transfer, from the template, of anatomical and kinematical information not present in the input data. Our approach treats both local and global deformations in successive regularization steps: smooth elastic deformations are represented by an as‐rigid‐as‐possible displacement field between the reference and current configuration of the template, whereas global and discontinuous displacements are estimated through a projection onto a statistical shape model and a new joint pose optimization scheme with joint limits.     

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.     

Fast Corotated FEM using Operator Splitting

In this paper we present a novel operator splitting approach for corotated FEM simulations. The deformation energy of the corotated linear material model consists of two additive terms. The first term models stretching in the individual spatial directions and the second term describes resistance to volume changes. By formulating the backward Euler time integration scheme as an optimization problem, we show that the first term is invariant to rotations. This allows us to use an operator splitting approach and to solve both terms individually with different numerical methods. The stretching part is solved accurately with an optimization integrator, which can be done very efficiently because the system matrix is constant over time such that its Cholesky factorization can be precomputed. The volume term is solved approximately by using the compliant constraints method and Gauss‐Seidel iterations. Further, we introduce the analytic polar decomposition which allows us to speed up the extraction of the rotational part of the deformation gradient and to recover inverted elements. Finally, this results in an extremely fast and robust simulation method with high visual quality that outperforms standard corotated FEMs by more than two orders of magnitude and even the fast but inaccurate PBD and shape matching methods by more than one order of magnitude without having their typical drawbacks. This enables a very efficient simulation of complex scenes containing more than a million elements.     

Multi‐layer Lattice Model for Real‐Time Dynamic Character Deformation

Due to the recent advancement of computer graphics hardware and software algorithms, deformable characters have become more and more popular in real‐time applications such as computer games. While there are mature techniques to generate primary deformation from skeletal movement, simulating realistic and stable secondary deformation such as jiggling of fats remains challenging. On one hand, traditional volumetric approaches such as the finite element method require higher computational cost and are infeasible for limited hardware such as game consoles. On the other hand, while shape matching based simulations can produce plausible deformation in real‐time, they suffer from a stiffness problem in which particles either show unrealistic deformation due to high gains, or cannot catch up with the body movement. In this paper, we propose a unified multi‐layer lattice model to simulate the primary and secondary deformation of skeleton‐driven characters. The core idea is to voxelize the input character mesh into multiple anatomical layers including the bone, muscle, fat and skin. Primary deformation is applied on the bone voxels with lattice‐based skinning. The movement of these voxels is propagated to other voxel layers using lattice shape matching simulation, creating a natural secondary deformation. Our multi‐layer lattice framework can produce simulation quality comparable to those from other volumetric approaches with a significantly smaller computational cost. It is best to be applied in real‐time applications such as console games or interactive animation creation.     

Real‐Time Symmetry‐Preserving Deformation

In this paper, we address the problem of structure‐aware shape deformation: We specifically consider deformations that preserve symmetries of the shape being edited. While this is an elegant approach for obtaining plausible shape variations from minimal assumptions, a straightforward optimization is numerically expensive and poorly conditioned. Our paper introduces an explicit construction of bases of linear spaces of shape deformations that exactly preserve symmetries for any user‐defined level of detail. This permits the construction of low‐dimensional spaces of low‐frequency deformations that preserve the symmetries. We obtain substantial speed‐ups over alternative approaches for symmetry‐preserving shape editing due to (i) the sub‐space approach, which permits low‐res editing, (ii) the removal of redundant, symmetric information, and (iii) the simplification of the numerical formulation due to hard‐coded symmetry preservation. We demonstrate the utility in practice by applying our framework to symmetry‐preserving co‐rotated iterative Laplace surface editing of models with complex symmetry structure, including partial and nested symmetry.     

Multiresolution free form object modeling with point sampled geometry

In this paper an efficient framework for the creation of 3D digital content with point sampled geometry is proposed. A new hierarchy of shape representations with three levels is adopted in this framework. Based on this new hierarchical shape representation, the proposed framework offers concise integration of various volumetric- and surface-based modeling techniques, such as Boolean operation, offset, blending, free-form deformation, parameterization and texture mapping, and thus simplifies the complete modeling process. Previously to achieve the same goal, several separated algorithms had to be used independently with inconsistent volumetric and surface representations of the free-form object. Both graphics and industrial applications are presented to demonstrate the effectiveness and efficiency of the proposed framework.     

Adaptive Space Deformations Based on Rigid Cells

We propose a new adaptive space deformation method for interactive shape modeling. A novel energy formulation based on elastically coupled volumetric cells yields intuitive detail preservation even under large deformations. By enforcing rigidity of the cells, we obtain an extremely robust numerical solver for the resulting nonlinear optimization problem. Scalability is achieved using an adaptive spatial discretization that is decoupled from the resolution of the embedded object. Our approach is versatile and easy to implement, supports thin-shell and solid deformations of 2D and 3D objects, and is applicable to arbitrary sample-based representations, such as meshes, triangle soups, or point clouds.     

Inverse adaptation of a Hex-dominant mesh for large deformation finite element analysis

In the finite element analysis of metal forming processes, many mesh elements are usually deformed severely in the later stage of the analysis because of the corresponding large deformation of the geometry. Such highly distorted elements are undesirable in finite element analysis because they introduce error into the analysis results, and, in the worst case, inverted elements can cause the analysis to terminate prematurely. This paper proposes a new inverse-adaptation method that reduces or eliminates the number of inverted mesh elements created in the later stage of finite element analysis, thereby lessening the chances of early termination and improving the accuracy of the analysis results. By this method, a simple uniform mesh is created initially, and a pre-analysis is run in order to observe the deformation behavior of the elements. Next, an input hex-dominant mesh is generated in which each element is “inversely adapted”, or pre-deformed in such a way that it has approximately the opposite shape of the final shape that normal analysis would deform it into. Thus, when finite element analysis is performed, the analysis starts with an input mesh of inversely adapted elements whose shapes are not ideal. As the analysis continues, the element shape quality improves to almost ideal, and then, toward the final stage of analysis, degrades again, but much less than would be the case without the inverse adaptation. This method permits the analysis to run to the end, or to a further stage, with no inverted elements. Besides its pre-skewing the element shape, the proposed method is also capable of controlling the element size according to the equivalent plastic strain information collected from the pre-analysis. The proposed inverse adaptation can be repeated iteratively until reaching the final stage of deformation.     

Poisson‐Based Weight Reduction of Animated Meshes

While animation using barycentric coordinates or other automatic weight assignment methods has become a popular method for shape deformation, the global nature of the weights limits their use for real‐time applications. We present a method that reduces the number of control points influencing a vertex to a user‐specified number such that the deformations created by the reduced weight set resemble that of the original deformation. To do so we show how to set up a Poisson minimization problem to solve for a reduced weight set and illustrate its advantages over other weight reduction methods. Not only does weight reduction lower the amount of storage space necessary to deform these models but also allows GPU acceleration of the resulting deformations. Our experiments show that we can achieve a factor of 100 increase in speed over CPU deformations using the full weight set, which makes real‐time deformations of large models possible.     

Compact inverted index storage using general‐purpose compression libraries

Efficient storage of large inverted indexes is one of the key technologies that support current web search services. Here we re‐examine mechanisms for representing document‐level inverted indexes and within‐document term frequencies, including comparing specialized methods developed for this task against recent fast implementations of general‐purpose adaptive compression techniques. Experiments with the Gov2‐URL collection and a large collection of crawled news stories show that standard compression libraries can provide compression effectiveness as good as or better than previous methods, with decoding rates only moderately slower than reference implementations of those tailored approaches. This surprising outcome means that high‐performance index compression can be achieved without requiring the use of specialized implementations.     

Automatic Generation of Vivid LEGO Architectural Sculptures

Brick elements are very popular and have been widely used in many areas, such as toy design and architectural fields. Designing a vivid brick sculpture to represent a three‐dimensional (3D) model is a very challenging task, which requires professional skills and experience to convey unique visual characteristics. We introduce an automatic system to convert an architectural model into a LEGO sculpture while preserving the original model's shape features. Unlike previous legolization techniques that generate a LEGO sculpture exactly based on the input model's voxel representation, we extract the model's visual features, including repeating components, shape details and planarity. Then, we translate these visual features into the final LEGO sculpture by employing various brick types. We propose a deformation algorithm in order to resolve discrepancies between an input mesh's continuous 3D shape and the discrete positions of bricks in a LEGO sculpture. We evaluate our system on various architectural models and compare our method with previous voxelization‐based methods. The results demonstrate that our approach successfully conveys important visual features from digital models and generates vivid LEGO sculptures.     

A level-set approach for the metamorphosis of solid models

We present a new approach to 3D shape metamorphosis. We express the interpolation of two shapes as a process where one shape deforms to maximize its similarity with another shape. The process incrementally optimizes an objective function while deforming an implicit surface model. We represent the deformable surface as a level set (iso-surface) of a densely sampled scalar function of three dimensions. Such level-set models have been shown to mimic conventional parametric deformable surface models by encoding surface movements as changes in the grayscale values of a volume data set. Thus, a well-founded mathematical structure leads to a set of procedures that describes how voxel values can be manipulated to create deformations that are represented as a sequence of volumes. The result is a 3D morphing method that offers several advantages over previous methods, including minimal need for user input, no model parameterization, flexible topology, and subvoxel accuracy     

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.