Despite the enormous progress, face animation is still considered one of the toughest tasks in computer society. In many cases, the facial data come from real human individuals by various 3D coordinate measuring equipments to get more realistic models. The animation irrelevant parts in the scanned data make the automatic face correspondence, which is a key and difficult problem in face animation, even harder. We present a pipeline that can get quite reasonable animation result fully automatically from raw scanned facial meshes, applications of face morphing and expression cloning are demonstrated.

In this work we present several visualization approaches for analyzing acoustic behavior inside a room. Our methods are based on the results of the phonon tracing algorithm. For a simulated phonon map we examine the influence of the room surfaces on the wave fronts during their propagation from the sound source. Our visualization is based on individual phonon and surface representations as well as scattered data interpolation. Additionally, an observation of acoustic behavior at different positions inside the room using colored and deformed spheres is possible.

We present a comparative visualization of the acoustic simulation results obtained by two different approaches that were combined into a single simulation algorithm. The first method solves the wave equation on a volume grid based on finite elements. The second method, phonon tracing, is a geometric approach that we have previously developed for interactive simulation, visualization and modeling of room acoustics. Geometric approaches of this kind are more efficient than FEM in the high and medium frequency range. For low frequencies they fail to represent diffraction, which on the other hand can be simulated properly by means of FEM. When combining both methods we need to calibrate them properly and estimate in which frequency range they provide comparable results. For this purpose we use an acoustic metric called gain and display the resulting error. Furthermore we visualize interference patterns, since these depend not only on diffraction, but also exhibit phase-dependent amplification and neutralization effects.

This paper presents a shape-based approach in extracting thin structures, such as lines and sheets, from three-dimensional (3D) biomedical images. Of particular interest is the capability to recover cellular structures, such as microtubule spindle fibers and plasma membranes, from laser scanning confocal microscopic (LSCM) data. Hessian-based shape methods are reviewed. A synthesized linear structure is used to evaluate the sensitivity of the multiscale filtering approach in extracting closely positioned fibers. We find that the multiscale approach tends to fuse lines together, which makes it unsuitable for visualizing mouse egg spindle fibers. Single-scale Gaussian filters, balanced between sensitivity and noise resistance, are adopted instead. In addition, through an ellipsoidal Gaussian model, the eigenvalues of the Hessian matrix are quantitatively associated with the standard deviations of the Gaussian model. Existing shape filters are simplified and applied to LSCM data. A significant improvement in extracting closely positioned thin lines is demonstrated by the resultant images. Further, the direct association of shape models and eigenvalues makes the processed images more understandable qualitatively and quantitatively.

In this paper, we present a deformable surface geometric model for segmenting targets from volumetric data. This model deforms under external forces only, and changes its geometry and topology by using improved geometric constraints. External forces are calculated by using the sum of inflation forces, whose contributions take place on internal regions of objects, and the gradient forces, which play a key role when the surface is near the boundary of objects. A new set of geometric constraints is proposed which includes constraints on vertices, edges and faces. Once a constraint is broken, the corresponding topological transformation will occur to keep the geometric and topological integrity of the surface unaltered. We demonstrate that our model can efficiently segment complex anatomic structures from medical 3D images, and achieve the requirements of accuracy and geometry for image segmentation.

We describe a new technique for the parameterization of isosurfaces which result from the marching cubes (mc) algorithm. The motivation for the methods is based upon the method of chord length parameterization for curves. The method of extending the concept of curve parameterization to isosurface parameterization is based upon a relatively simple but very useful observation about a subset of the edge topology of a mc produced isosurface called the 4*-network. This is a collection of three mutually orthogonal planar polygons lying on and intersecting at the vertices of the isosurface. We illustrate the potential usefulness of this new parameterization method with examples from geometric modeling and medical imaging analysis.

Topological volume skeletons represent level-set graphs of 3D scalar fields, and have recently become crucial to visualizing the global isosurface transitions in the volume. However, it is still a time-consuming task to extract them, especially when input volumes are large-scale data and/or prone to small-amplitude noise. The paper presents an efficient method for accelerating the computation of such skeletons using adaptive tetrahedralization. The tetrahedralization is a top-down approach to linear interpolation of the scalar fields in that it selects tetrahedra to be subdivided adaptively using several criteria. As the criteria, the method employs a topological criterion as well as a geometric one in order to pursue all the topological isosurface transitions that may contribute to the global skeleton of the volume. The tetrahedralization also allows us to avoid unnecessary tracking of minor degenerate features that hide the global skeleton. Experimental results are included to demonstrate that the present method smoothes out the original scalar fields effectively without missing any significant topological features.

We describe a new technique for fitting scattered point cloud data. Given a scattered point cloud of 3D data points and associated normal vectors, our new method produces an implicit volume model whose zero level isosurface interpolates the given points and associated normal vectors. We concentrate on certain application of these new volume modeling techniques. We take existing polygon mesh surfaces and use the present methods to construct implicit volume models for these surfaces. Implicit models allow for the application of Boolean operations on these surfaces through the techniques of constructive solid geometry. Also, standard wavelet and filter operators can be applied to the implicit volume model leading to effective smoothing and filtering algorithms, which are simple to implement.

We present the definition and computational algorithms for a new class of surfaces which are dual to the isosurface produced by the widely used marching cubes (MC) algorithm. These new isosurfaces have the same separating properties as the MC surfaces but they are comprised of quad patches that tend to eliminate the common negative aspect of poorly shaped triangles of the MC isosurfaces. Based upon the concept of this new dual operator, we describe a simple, but rather effective iterative scheme for producing smooth separating surfaces for binary, enumerated volumes which are often produced by segmentation algorithms. Both the dual surface algorithm and the iterative smoothing scheme are easily implemented.

Direct volume rendering is a standard technique for projecting all the optically-encoded samples onto the screen at once to allow us to peer into the inner structures involved in a volume data. Datacentric approaches to the design of transfer functions (TFs) have recently been well-established, which perform mathematical analysis of the data prior to pertinent rendering. The advent of multidimensional TFs is one of the latest major achievements in the volume visualization research. As opposed to the traditional onedimensional TFs that only consider a voxel’s scalar field value, the multi-dimensional TFs assign auxiliary attributes to the voxels to construct their sophisticated parametric domains. For example, when visualizing volumes obtained by scientific simulations, the observers can utilize their own knowledge about the simulation settings to extract the global characteristics of the volumes and to locate regions of particular interest. If they are allowed to design multi-dimensional TFs using staff attributes so as to encapsulate such advance knowledge, they can readily yield visualization results to fulfill their purposes. Nevertheless, nearly all attributes for the conventional multi-dimensional TFs are based on local features, such as differentials and curvatures, and are difficult to capture the global structure of the volume contrary to the observer’s purposes. This paper therefore introduces a new set of topological attributes to establish a new framework that is intended to realize objective-based assistance. Topological attributes proposed herein are derived from the level-set graph, which delineates the topological evolution of an isosurface with respect to the scalar field.

We present a new method for smoothly interpolating orientation matrices. It is based upon quaternions and a particular construction of upsilon-spline curves. The new method has tension parameters and variable knot (time) spacing which both prove to be effective in designing and controlling key frame animations.

We describe a modification of the widely used marching cubes method that leads to the useful property that the resulting isosurfaces are locally single valued functions. This implies that conventional interpolation and approximation methods can be used to locally represent the surface. These representations can be used for computing approximations for local surface properties. We utilize this possibility in order to develop algorithms for locally approximating Gaussian and mean curvature, methods for constrained smoothing of isosurface, and techniques for the parameterization of isosurfaces.

This paper presents a coarse-grain approach for segmentation of objects with gray levels appearing in volume data. The input data is on a 3D structured grid of vertices v(i. j. k), each associated with a scalar value. In this paper, we consider a voxel as a /spl kappa/ /spl times/ /spl kappa/ /spl times/ /spl kappa/ cube and each voxel is assigned two values: expectancy and standard deviation (E-SD). We use the Weibull noise index to estimate the noise in a voxel and to obtain more precise E-SD values for each voxel. We plot the frequency of voxels which have the same E-SD, then 3D segmentation based on the Weibull E-SD field is presented. Our test bed includes synthetic data as well as real volume data from a confocal laser scanning microscope (CLSM). Analysis of these data all show distinct and defining regions in their E-SD fields. Under the guide of the E-SD field, we can efficiently segment the objects embedded in real and simulated 3D data.

A characterization and classification of the isosurfaces of trilinear functions is presented. Based upon these results, a new algorithm for computing a triangular mesh approximation to isosurfaces for data given on a 3D rectilinear grid is presented. The original marching cubes algorithm is based upon linear interpolation along edges of the voxels. The asymptotic decider method is based upon bilinear interpolation on faces of the voxels. The algorithm of this paper carries this theme forward to using trilinear interpolation on the interior of voxels. The algorithm described here will produce a triangular mesh surface approximation to an isosurface which preserves the same connectivity/separation of vertices as given by the isosurface of trilinear interpolation.

Differential geometry and topology are the areas of higher mathematics, which particularly require visual representation of studying objects for better understanding of the material. On the other hand, the complex structure of such objects makes their visualization a challenge for modern graphical systems. In this video we demonstrate real-time methods for adequate representation of topologically non-trivial objects in virtual environment systems, particularly the acceleration of standard mechanisms for rendering of transparent surfaces, applicable for complex cases of self-intersecting time-dependent surfaces, not necessarily admitting continuous fields of normal vectors. We also use the technique of image-based rendering, which places stereo-photographs of real environments as static background for 3D virtual scenes. The methods are implemented in educational application, which demonstrates the main properties of elementary topological objects (Möbius band, Klein bottle, projective plane etc) and gives a possibility to explore interactively the complex constructions, arising in higher mathematics.

We present some new methods for computing estimates of normal vectors at the vertices of a triangular mesh surface approximation to an isosurface which has been computed by the marching cube algorithm. These estimates are required for the smooth rendering of triangular mesh surfaces. The conventional method of computing estimates based upon divided difference approximations of the gradient can lead to poor estimates in some applications. This is particularly true for isosurfaces obtained from a field function, which is defined only for values near to the isosurface. We describe some efficient methods for computing the topology of the triangular mesh surface, which is used for obtaining local estimates of the normals. In addition, a new, one pass, approach for these types of applications is described and compared to existing methods.

We present a new method for the modeling of freehand collected three-dimensional ultrasound data. The model is piecewise linear and based upon progressive tetrahedral domains created by a subdivision scheme which splits a tetrahedron on on its longest edge and guarantees a valid tetrahedrization. Least squares error is used to characterize the model and an effective iterative technique is used to compute the values of the model at the vertices of the tetrahedral grid. Since the subdivision strategy is adaptive, the complexity of the model conforms to the complexity of the data leading to an extremely efficient and highly compressed volume model. The model is evaluated in real time using piecewise linear interpolation, and gives a medical professional the chance to see images which would not be possible using conventional ultrasound techniques.

We present a novel approach to solving the cracking problem. The cracking problem arises in many contexts in scientific visualization and computer graphics modeling where there is need for an approximation based upon domain decomposition that is fine in certain regions and coarse in others. This includes surface rendering approximation of images and multiresolution terrain visualization. In general, algorithms based upon adaptive refinement strategies must deal with this problem. The approach presented here is simple and general. It is based upon the use of a triangular Coons patch. Both the basic idea of using a triangular Coons patch in this context and the particular Coons patch that is used constitute the novel contributions of the paper.

We present some very efficient and accurate methods for computing tangent curves for three-dimensional flows. Our methods work directly in physical coordinates, eliminating the usual need to switch back and forth with computational coordinates. Unlike conventional methods, such as Runge-Kutta, for computing tangent curves which give only approximations, our methods produce exact values based upon piecewise linear variation over a tetrahedrization of the domain of interest. We use balycentric coordinates in order to efficiently track cell-to-cell movement of the tangent curves.

We develop multiresolution models for analyzing and visualizing two-dimensional flows over curvilinear grids. Our models are based upon nested spaces of piecewise defined functions defined over nested curvilinear grid domains. The nested domains are selected so as to maintain the original geometry of the inner boundary. We first give the refinement and decomposition equations for Haar wavelets over these domains. Next, using lifting techniques we develop and show examples of piecewise linear wavelets over curvilinear grids.

An algorithm for computing a triangulated surface which separates a collection of data points that have been segmented into a number of different classes is presented. The problem generalizes the concept of an isosurface which separates data points that have been segmented into only two classes: those for which data function values are above the threshold and those which are below the threshold value. The algorithm is very simple, easy to implement and applies without limit to the number of classes.

Some new piecewise constant wavelets defined over nested triangulated domains are presented and applied to the problem of multiresolution analysis of flow over a spherical domain. These new, nearly orthogonal wavelets have advantages over the existing weaker biorthogonal wavelets. In the planar case of uniform areas, the wavelets converge to one of two fully orthogonal Haar wavelets. These new, fully orthogonal wavelets are proven to be the only possible wavelets of this type.

The interval volume is a generalization of the isosurface commonly associated with the marching cubes algorithm. Based upon samples at the locations of a 3D rectilinear grid, the algorithm produces a triangular approximation to the surface defined by F(x,y,z)=c. The interval volume is defined by /spl alpha//spl les/F(x,y,z)/spl les//spl beta/. The authors describe an algorithm for computing a tetrahedrization of a polyhedral approximation to the interval volume.

In the last five years, there has been numerous applications of wavelets and multiresolution analysis in many fields of computer graphics as different as geometric modelling, volume visualization or illumination modelling. Classical multiresolution analysis is based on the knowledge of a nested set of functional spaces in which the successive approximations of a given function converge to that function, and can be efficiently computed. This paper first proposes a theoretical framework which enables multiresolution analysis even if the functional spaces are not nested, as long as they still have the property that the successive approximations converge to the given function. Based on this concept, we finally introduce a new multiresolution analysis with exact reconstruction for large data sets defined on uniform grids. We construct a one-parameter family of multiresolution analyses which is a blending of Haar and linear multiresolution, using BLaC (Blending of Linear and Constant) wavelets.

Welcome to this theme issue on Visualization. This is the sixth in a series of theme issues. The first four appeared in Computer Graphics and Applications (CGbA vol. 11, no. 3; vol. 12, no. 4; vol. 13, no. 4; vol. 14, no. 5) and the fifth appeared last June in the inaugural year of TVCG. All of these theme issues are based upon topics that were previously presented at the IEEE-sponsored Visualization Conference. For all these theme issues, authors were invited to submit papers based upon their conference papers, but containing significant new research results. These papers were then subjected to an extensive and complete evaluation and review process, and the very best papers were then selected for publication. In the past, the collection of papers that survive this rigorous winnowing have constituted some of the most widely read and influential papers in visualization. They are often cited, and they are often the recipients of awards. We assume the same satisfactory outcome will hold for the present set of papers based upon papers presented at Visualization '95 held October 29 to November 3,1995, in Atlanta, Georgia.

A method for computing isovalue or contour surfaces of a trivariate function is discussed. The input data are values of the trivariate function, F/sub ijk/, at the cuberille grid points (x/sub i/, y/sub j/, z/sub k/), and the output of a collection of triangles representing the surface consisting of all points where F(x,y,z) is a constant value. The method is a modification that is intended to correct a problem with a previous method.>

Abstract This bibliography evolved as a network using the papers in the volume Visualization of Scientific Computing edited by Gregory M. Nielson and Bruce Shriver and published by IEEE Computer Society Press, 1990 as the root nodes. From there, the supplied reference lists were recursively traversed until a closure resulted either from the common links or from the effective grounding by the highly technical literature of application specializations. As usual, the standard disclaimers apply; so, for example, this collection is hopefully complete (in the sense that subsets of papers form research vectors that span the space of scientific visualization), but obviously not exhaustively comprehensive. Some of the entries are of a general survey nature, whereas others are quite specific and technical. Pivotal and often quoted works comprise the bulk of the material, but works of historical and developmental significance are also included especially where they point to researchers, research centres and journals where important work has been, and is being, performed and recorded. The annotations accompanying the references tend to be impressionistic and apologies to the authors are hereby noted for those instances where omissions, misunderstandings and whimsy have resulted in misinterpretations. The support of the U.S. Department of Energy is appreciated.

Some ideas and techniques for visualizing volumetric data are introduced. The methods presented are different from both the volume rendering techniques and surface contour methods. Volumetric data is data with a domain of three independent variables. The independent variables do not have to indicate a position in space and can be abstract in the sense that they can represent any quantity. The authors cover only the case where the dependent data is a single scalar. The authors describe a collection of techniques and ideas for graphing cuberille grid data. All of these techniques are quite simple and rather easy to implement. During the development of these techniques, the authors were particularly concerned with allowing the user to interact with the system in order to interrogate and analyze the relationships indicated by the volumetric data.>

Abstract Ray‐tracing volumetric data may take several minutes to compute a single image from a fixed viewpoint. We present techniques that generate approximate ray‐traced volumetric images in less than one second per image, after a lengthy initialization process is performed. These approximate images are based on methods that interpolate data sampled at locations on a sphere.

Abstract This bibliography evolved as a network using the papers in the volume Visualization of Scientific Computing edited by Gregory M. Nielson and Bruce Shriver and published by IEEE Computer Society Press, 1990 as the root nodes. From there, the supplied reference lists were recursively traversed until a closure resulted either from the common links or from the effective grounding by the highly technical literature of application specializations. As usual, the standard disclaimers apply; so, for example, this collection is hopefully complete (in the sense that subsets of papers form research vectors that span the space of scientific visualization), but obviously not exhaustively comprehensive. Some of the entries are of a general survey nature, whereas others are quite specific and technical. Pivotal and often quoted works comprise the bulk of the material, but works of historical and developmental significance are also included especially where they point to researchers, research centres and journals where important work has been, and is being, performed and recorded. The annotations accompanying the references tend to be impressionistic and apologies to the authors are hereby noted for those instances where omissions, misunderstandings and whimsy have resulted in misinterpretations.

The major process affecting the configuration and evolution of terrain is erosion by flowing water. Landscapes thus reflect the branching patterns of river and stream networks. The network patterns contain information that is characteristic of the landscape's topographic features. It is therefore possible to create an approximation to natural terrain by simulating the erosion of stream networks on an initially uneroded surface. Empirical models of stream erosion were used as a basis for the model presented here. Stream networks of various sizes and shapes are created by the model from a small number of initial parameters. The eroded surface is represented as a surface under tension, using the tension parameter to shape the profiles of valleys created by the stream networks. The model can be used to generate terrain databases for flight simulation and computer animation applications.