We present a novel approach to mesh deformation that enables simple context sensitive manipulation of 3D geometry. The method is based on locally anisotropic transformations and is extended to global control directions. This allows intuitive directional modeling within an easy to implement framework. The proposed method complements current sculpting paradigms by providing further possibilities for intuitive surface-based editing without the need for additional host geometries. We show the anisotropic deformation to be seamlessly transferable to free boundary parameterization methods, which allows us to solve the hard problem of flattening compression garments in the domain of apparel design.

We present a novel approach for real-time joint reconstruction of 3D scene motion and geometry from binocular stereo videos. Our approach is based on a novel variational halfway-domain scene flow formulation, which allows us to obtain highly accurate spatiotemporal reconstructions of shape and motion. We solve the underlying optimization problem at real-time frame rates using a novel data-parallel robust non-linear optimization strategy. Fast convergence and large displacement flows are achieved by employing a novel hierarchy that stores delta flows between hierarchy levels. High performance is obtained by the introduction of a coarser warp grid that decouples the number of unknowns from the input resolution of the images. We demonstrate our approach in a live setup that is based on two commodity webcams, as well as on publicly available video data. Our extensive experiments and evaluations show that our approach produces high-quality dense reconstructions of 3D geometry and scene flow at real-time frame rates, and compares favorably to the state of the art.

ABSTRACT We present a novel method for the interactive markerless reconstruction of human heads using a single commodity RGB‐D sensor. Our entire reconstruction pipeline is implemented on the graphics processing unit and allows to obtain high‐quality reconstructions of the human head using an interactive and intuitive reconstruction paradigm. The core of our method is a fast graphics processing unit‐based nonlinear quasi‐Newton solver that allows us to leverage all information of the RGB‐D stream and fit a statistical head model to the observations at interactive frame rates. By jointly solving for shape, albedo and illumination parameters, we are able to reconstruct high‐quality models including illumination corrected textures. All obtained reconstructions have a common topology and can be directly used as assets for games, films and various virtual reality applications. We show motion retargeting, retexturing and relighting examples. The accuracy of the presented algorithm is evaluated by a comparison against ground truth data. Copyright © 2014 John Wiley & Sons, Ltd.

Abstract We present a simple algorithm for computing a high‐quality personalized avatar from a single color image and the corresponding depth map which have been captured by Microsoft's Kinect sensor. Due to the low market price of our hardware setup, 3D face scanning becomes feasible for home use. The proposed algorithm combines the advantages of robust non‐rigid registration and fitting of a morphable face model. We obtain a high‐quality reconstruction of the facial geometry and texture along with one‐to‐one correspondences with our generic face model. This representation allows for a wide range of further applications such as facial animation or manipulation. Our algorithm has proven to be very robust. Since it does not require any user interaction, even non‐expert users can easily create their own personalized avatars. Copyright © 2011 John Wiley & Sons, Ltd.

Abstract The ability to extract spatial features from 3D objects is essential for applications such as shape matching and object classification. However, designing an effective feature vector which is invariant with respect to rotation, translation and scaling is a challenging task and is often solved by normalization techniques such as PCA, which can give rise to poor object alignment. In this paper, we introduce a novel method to extract robust and invariant 3D features based on rotational symmetry. By applying a rotation‐variant similarity function on two instances of the same 3D object, we can define an autocorrelation on the object in the space of rotations. We use a special representation of the SO(3) and determine significant rotation axes for an object by means of optimization techniques. By sampling the similarity function via rotations around these axes, we obtain robust and invariant features, which are descriptive for the underlying geometry. The resulting feature vector cannot only be used to characterize an object with respect to rotational symmetry but also to define a distance between 3D models. Because the features are compact and pre‐computable, our method is suitable to perform similarity searches in large 3D databases.

Abstract In this paper we analyze normal vector representations. We derive the error of the most widely used representation, namely 3D floating‐point normal vectors. Based on this analysis, we show that, in theory, the discretization error inherent to single precision floating‐point normals can be achieved by 2 50.2 uniformly distributed normals, addressable by 51 bits. We review common sphere parameterizations and show that octahedron normal vectors perform best: they are fast and stable to compute, have a controllable error, and require only 1 bit more than the theoretical optimal discretization with the same error.

Abstract In this paper we address the problem of optimal centre placement for scattered data approximation using radial basis functions (RBFs) by introducing the concept of floating centres. Given an initial least‐squares solution, we optimize the positions and the weights of the RBF centres by minimizing a non‐linear error function. By optimizing the centre positions, we obtain better approximations with a lower number of centres, which improves the numerical stability of the fitting procedure. We combine the non‐linear RBF fitting with a hierarchical domain decomposition technique. This provides a powerful tool for surface reconstruction from oriented point samples. By directly incorporating point normal vectors into the optimization process, we avoid the use of off‐surface points which results in less computational overhead and reduces undesired surface artefacts. We demonstrate that the proposed surface reconstruction technique is as robust as recent methods, which compute the indicator function of the solid described by the point samples. In contrast to indicator function based methods, our method computes a global distance field that can directly be used for shape registration.

Abstract We present a novel method to animate a static geometry by cloning a captured animation sequence. More precisely, given a sequence of range scans of a deforming object which has been captured by a real‐time 3D scanner, we describe a novel algorithm to clone the animation of the recorded geometry onto another triangle mesh. To achieve this, we reconstruct a coherent animated mesh of the input sequence using a template deformation approach. Then we employ a new algorithm for robust marker‐less non‐rigid registration to deform one frame of the generated animation such that it matches a different 3D model. The resulting registration is further used to find correspondences between the animation and the target object which are in turn used to transfer the animation of the recorded sequence onto the target shape. Transferring the entire geometry of the animations results in very convincing facial expressions since even the smallest expression wrinkles are preserved. We evaluate the robustness and the performance of the proposed algorithms using a variety of data sets, including facial animations and whole body animations. Copyright © 2010 John Wiley & Sons, Ltd.

Abstract In this paper, we describe a novel approach for the reconstruction of animated meshes from a series of time‐deforming point clouds. Given a set of unordered point clouds that have been captured by a fast 3‐D scanner, our algorithm is able to compute coherent meshes which approximate the input data at arbitrary time instances. Our method is based on the computation of an implicit function in ℝ4 that approximates the time‐space surface of the time‐varying point cloud. We then use the four‐dimensional implicit function to reconstruct a polygonal model for the first time‐step. By sliding this template mesh along the time‐space surface in an as‐rigid‐as‐possible manner, we obtain reconstructions for further time‐steps which have the same connectivity as the previously extracted mesh while recovering rigid motion exactly. The resulting animated meshes allow accurate motion tracking of arbitrary points and are well suited for animation compression. We demonstrate the qualities of the proposed method by applying it to several data sets acquired by real‐time 3‐D scanners.

Diffusion tensor imaging is of high value in neurosurgery, providing information about the location of white matter tracts in the human brain. For their reconstruction, streamline techniques commonly referred to as fiber tracking model the underlying fiber structures and have therefore gained interest. To meet the requirements of surgical planning and to overcome the visual limitations of line representations, a new real-time visualization approach of high visual quality is introduced. For this purpose, textured triangle strips and point sprites are combined in a hybrid strategy employing GPU programming. The triangle strips follow the fiber streamlines and are textured to obtain a tube-like appearance. A vertex program is used to orient the triangle strips towards the camera. In order to avoid triangle flipping in case of fiber segments where the viewing and segment direction are parallel, a correct visual representation is achieved in these areas by chains of point sprites. As a result, a high quality visualization similar to tubes is provided allowing for interactive multimodal inspection. Overall, the presented approach is faster than existing techniques of similar visualization quality and at the same time allows for real-time rendering of dense bundles encompassing a high number of fibers, which is of high importance for diagnosis and surgical planning.

A new technique is presented to increase the performance of volume splatting by using hardware accelerated point sprites. This allows creating screen aligned elliptical splats for high quality volume splatting at very low cost on the GPU. Only one vertex per splat is stored on the graphics card. GPU generated point sprite texture coordinates are used for computing splats and per-fragment 3D-texture coordinates on the fly. Thus, only 6 bytes per splat are stored on the GPU and vertex shader load is 25% in comparison to applying textured quads. For eight predefined viewing directions, depth-sorting of the splats is performed in a pre-processing step where the resulting indices are stored on the GPU. Thereby, there is no data transfer between CPU and GPU during rendering. Post-classificative two dimensional transfer functions with lighting for scalar data and tagged volumes were implemented. Thereby, we focused on the visualization of neurovascular structures, where typically no more than 2% of the voxels contribute to the resulting 3D-representation. A comparison with a 3D-texture-based slicing algorithm showed frame rates up to 11 times higher for the presented approach on current CPUs. The presented technique was evaluated with a broad medical database and its value for highly sparse volume visualization is shown.

Abstract For analyzing and interpreting results of flow simulations, particle tracing is a well established visualization method. In addition, it is a preliminary step for more advanced techniques such as line integral convolution. For interactive exploration of large data sets, a very efficient and reliable particle tracing method is needed. For wind channel experiments or flight simulations, large unstructured computational grids have become common practice. Traditional approachs, based on numerical integration methods of ordinary differential equations however fail to deliver sufficiently accurate path calculation at the speed required for interactive use. In this paper we extend the local exact approach of Nielson and Jung in such a way that it can be used for interactive particle tracing in large data sets of steady flow simulation experiments. This will be achieved by sophisticated preprocessing using additional memory. For further visual enhancement of the streamline we construct an implicitly defined smooth Bézier curve that is used for ray tracing. This allows us to visualize additional scalar values of the simulation as attributes to the trajectory and enables the display of high‐quality smooth curves without creating any visualization geometry and providing a good impression of the spatial situation at the same time. ACM CSS: I.3.3 Computer Graphics—Line and curve generation; I .3.7 Computer Graphics—Raytracing; G.1.2 Numerical Analysis—Spline and piecewise polynomial approximation

The authors present a technique for transforming a tetrahedral mesh into a progressive representation based on half edge collapses. This allows the efficient transmission of the mesh from a remote computer where the simulation was computed to a visualization computer. During the transmission, the user can start visualizing while the transmission is still in progress. We show a technique for progressively extracting isosurfaces from the progressive mesh. Starting with the base mesh, an isosurface for a specific value is computed and will locally be improved where a vertex is inserted into the mesh.

The importance of triangle meshes with a special kind of connectivity, the so-called subdivision connectivity is still growing. Therefore it is important to develop efficient algorithms for converting a given mesh with arbitrary connectivity into one with subdivision connectivity. We focus on 2-manifold triangle meshes with a boundary and no holes. We discuss the importance of a parametrization with minimal distortion for the process of remeshing. Based on the concept of most isometric parameterizations we have developed a remeshing algorithm for the given class of triangle meshes. A series of examples shows the advantages of our approach.

Inspection of reflection line patterns is a standard way to check the quality of free form surfaces. In this paper, we describe an approach which enables the designer to control during the modeling process the reflection line pattern by approximating a specified family of reflection lines. Our method directly operates on the commonly used B-spline format, and produces fair surfaces. The approach is based on the minimization of a suitable error functional. A minimization algorithm based on data dependent quadratic error functionals provides an efficient numerical solution. The potential of the method will be demonstrated by applying it to two standard modeling problems: "surface fairing" and "surface reconstruction".

An algorithm for adaptive refinement of 3D meshes is presented. This algorithm can be applied for the generation of mesh hierarchies used for efficient volume visualization algorithms, e.g. iso-surface extraction or direct volume rendering, as well as for multilevel finite element computations. The aim was to construct an algorithm which generates as few congruence classes as possible. The main idea is to work with consistent partitions of the domain into tetrahedra and octahedra. The refinement consists of regular refinement rules which produce per element type one congruence class. In the case of local mesh refinement, for generating consistent subdivisions a temporary (virtual) closure is done based on suitable irregular refinement rules.

Clipping 2D polygons is one of the basic routines in computer graphics. In rendering complex 3D images it has to be done several thousand times. Efficient algorithms are therefore very important. We present such an efficient algorithm for clipping arbitrary 2D-polygons. The algorithm can handle arbitrary closed polygons, specifically where the clip and subject polygons may self-intersect. The algoirthm is simple and faster that Vatti's (1992) algorithm, which was designed for the general case as well. Simple modifications allow determination of union and set-theoretic differences of two arbitrary polygons.

Abstract When modeling spline surfaces of complex shape, one has to deal with an overwhelming number of control points. Modeling by direct manipulation of the control points is a tedious task. In particular, it is very difficult to maintain a generally pleasant looking surface shape. It becomes therefore increasingly important to build tools that allow the designer to specify only a few geometric constraints while automatically determining the explicit representation of the surface. The basic concept of such a tool is simple. In a first step one has to somehow measure the “fairness” (=quality) of a surface. Once this is achieved, an optimization process selects the one surface with optimal fairness from all surfaces satisfying the user specified geometric constraints. To measure the fairness, thin plate energy functionals are a good choice. However, for interactive use these functionals are far too complex. W e will present appropriate approximations to these functionals that allow an optimization nearly in real time. Thefunctionals are obtained by introducing reference surfaces thus leading to data dependent, quadratic approximations to the exact thin plate energy functionals. We apply the method to interactive surface manipulations based on energy constraints.

Abstract Variational principles have become quite popular in the design of free form surfaces. Among others they are used for fairing purposes. The choice of the ‘right’ fairness functional is a crucial step. There is always a tradeoff between high quality and computational effort. In this paper we present fairness functionals that allow fairing efficiently, i.e., produce high quality surfaces in a reasonable amount of time. These functionals can be considered as simplified thin plate energy functionals for parametric surfaces or as simplified MVC functionals.