The exploration of biomedical data which involves heterogeneous sources coming from different spatial scales and medical domains is a challenging topic in current research. In this work, we combine efforts regarding multi-scale visualization, multimodal interaction and knowledge formalization for the exploration of multi-scale biomedical data. The knowledge formalization stores and organizes the information sources, the integrated visualization captures all relevant information for the domain expertise of the user and the multimodal interaction provides a natural exploration. We present a concrete example of use of the proposed exploratory system designed for a biologist investigating multi-scale pathologies.

Haptic exploration adds an additional dimension to working with 3D data: a sense of touch. This is especially useful in areas such as medical simulation, training and pre-surgical planning, as well as in museum display, sculpting, CAD, military applications, assistive technology for blind and visually impaired, entertainment and others. There exist different surface- and voxel-based haptic rendering methods. Unaddressed practical problems for almost all of them are that no guarantees for collision detection could be given and/or that a special topological structure of objects is required. Here we present a novel and robust approach based on employing the ray casting technique to collision detection, which does not have the aforementioned drawbacks while guaranteeing nearly constant time complexity independent of data resolution. This is especially important for such delicate procedures as pre-operation planning. A collision response in the presented prototype system is rigid and operates on voxel data, and no precalculation is needed. Additionally, our collision response uses an implicit surface representation "on the fly", which can be used with dynamically changing objects.

A haptic exploration adds an additional dimension to working with 3D data: a sense of touch (figure 1). This is especially useful in areas such as medical training and pre-surgical planning, entertainment, CAD and others. Each haptic rendering frame consists of three stages: collision detection, collision response and force-feedback generation. In order to feel the 3D data smoothly, an update rate of at least 1 kHz is required [Brooks Jr. et al. 1990]. Unaddressed practical problems for almost all haptic rendering methods are that no guarantees for collision detection could be given and/or that a special topological structure of objects is required. Here we present an approach which does not have these drawbacks. Furthermore our algorithm has nearly constant time complexity independent of data resolution and does not require any additional precomputed structures. We focus on volumetric voxel data, since that is the direct input from the scanning devices. Other data types could be transformed to this one, if necessary.

Hot metal forging and precision-forging of machine parts are important production techniques. Forging processes generally consist of several steps and have to be designed from top down. Beginning with the final product, the design engineer derives the intermediate steps of the process in inverse order, using simulations to evaluate and validate them. The simulations are generally based on the finite element method, a widely employed technique in engineering. Two problems exist with this method: 1. The run-time of the simulations is often very long, depending on the spatial and temporal resolution of the simulated process. 2. The simulation progresses from one intermediate step to the next, while the engineer has to lay out the steps in inverse order. We propose a technique which addresses these problems, by following an approach relying on the geometry of the form and elementary plasticity theory. This method allows for a coarse approximation of the material flow that can be inverted.

Real-time cloth simulation involves many computational challenges to be solved, particularly in the context of haptic applications, where high frame rates are necessary for obtaining a satisfying experience. In this paper, we present an interactive cloth simulation system that offers a compromise between a realistic physics-based simulation of fabrics and a haptic application meeting high requirements in terms of computation speed. Our system allows the user to interact with the fabric using two fingers. The required performance of the system is achieved by introducing an intermediate layer responsible for the simulation of the small section of the surface being in contact with the fingers. We compare several contact models to obtain the best compromise in the context of haptic applications.

The EU funded RTD project "HAPTEX" addresses the challenge of developing a Virtual Reality (VR) system for the realistic and accurate rendering of the physical interactions of humans with textiles, through the real-time generation of artificial visual and haptic stimuli. This challenge concerns the development of both the SW and the HW components of the VR system, as well as it implies a substantial advancement in the understanding of the mechanisms underlying the human haptic perception of fine physical properties like those of textiles. This paper reports some important details relating to the technical implementation of the developed HW and SW components with special emphasis on the issues related to their integration into a single VR system. Furthermore some preliminary results relating to the functional tests carried out on the integrated system are also reported.

The main contribution of this work is the generalisation of the medial axis transform (MAT) and the medial axis inverse transform MAIT) on complete Riemannian manifolds. It is known that almost every solid can be reconstructed from its medial axis and the corresponding radius function. In the past this reconstruction scheme has only been implemented in Euclidean spaces. We will use the concepts of Fermi coordinates that represent a natural generalisation of normal coordinates. However, this concept only works out properly if some substantial conditions for the radius function are established. Several approaches for the computation of the medial axis have been implemented so far but almost all of them lack good numerical results. Usually numerical errors occur because the approaches operate on a discretised model of the corresponding objects. In this work we will assume that both the 3D Riemannian space and the modelled object can be represented by smooth mappings and coordinate charts respectively. Therefore, we can introduce the so called medial equations that will allow us to compute medial surface patches using the implicit function theorem. Finally we will give examples for the MAT and the MAIT and show to what extent the inverse transform is applicable in the context of computer aided geometric design. The geodesic medial modeller is one of those applications.

The Voronoi diagram has been investigated intensively throughout the last decades. This has been done not only in the context of Euclidean geometry but also in curved spaces. Except for [KWR97] these methods typically make use of some fast marching cube algorithms. In this work we will focus on the computation of Voronoi diagrams including Voronoi objects that are contained in a Riemannian manifold M. Further, we assume throughout this paper that M has a differentiable structure consisting of smooth parametrisation functions fi, i 2 I. This is the reason why the approach presented in this work differs from the aforementioned algorithms. More accurate algorithms can be obtained by using to some medial equations that heavily involve normal coordinates. This approach relies on the precise computation of shortest joins of any two given points , q 2 M. For these computations we did not apply shooting methods or related methods. Instead, we used a new perturbation method that operates on a family of deformed manifolds Mt, assuming that M0 has constant sectional curvature. To reduce time and space complexity of the introduced algorithm we suggest to use a randomised incremental construction scheme (RICS). Our approach assumes that those points fulfil a general position requirement for computing the geodesic Voronoi diagram for a set of points. Finally results of some computed Voronoi diagrams will be presented.

In this work we present an approach to generate a tactile representation from an image that may be a photograph or a scan of cloth. A large class of fabrics can be generated by repetition of a parallelogram primitive. That means there are two non-collinear directions where the pattern is periodically repeated. The method we present is based on analysing the repetitive structure of the sample, that is to find the two principle directions of repetition, and building a model from that analysis. We compare our method to a technique developed by Gang Huang.

Modern multimedia applications generate vast amounts of image data. With the availability of cheap photo hardware and affordable rendering software even more such data is being collected. In order to manage huge collections of image data one needs short representations of the data sets, or to be more precise invariant features being appropriate to identify a specific voxel data set using just a few numbers. This paper describes a variation of a method introduced by Reuter, Wolter and Peinecke based on the computation of the spectrum of the Laplace operator for the image for generating an invariant feature vector - a fingerprint. Oppose to previous techniques interpreting the image as a height function we make use of the representation of the image as a density function. We discuss the use of the spectrum of eigenvalues of the Laplace mass density operator as a fingerprint and show the usability of this approach in several cases. Instead of using the discrete Laplace-Kirchhoff operator the approach presented in this paper is based on the continuous Laplace operator allowing better results in comparing the resulting spectra and deeper insights into the problems arising when comparing two spectra generated using discrete Laplacians.

This paper proposes to use the volumetric Laplace spectrum as a global shape descriptor for medical shape analysis. The approach allows for shape comparisons using minimal shape preprocessing. In particular, no registration, mapping, or remeshing is necessary. All computations can be performed directly on the voxel representations of the shapes. The discriminatory power of the method is tested on a population of female caudate shapes (brain structure) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the volumetric Laplace spectrum are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann spectra. Both, the computations of spectra on 3D voxel data for shape matching as well as the use of the Neumann spectrum for shape analysis are completely new.

This paper introduces a method to extract fingerprints of any surface or solid object by taking the eigenvalues of its respective Laplace-Beltrami operator. Using an object's spectrum (i.e. the family of its eigenvalues) as a fingerprint for its shape is motivated by the fact that the related eigenvalues are isometry invariants of the object. Employing the Laplace-Beltrami spectra (not the spectra of the mesh Laplacian) as fingerprints of surfaces and solids is a novel approach in the field of geometric modeling and computer graphics. Those spectra can be calculated for any representation of the geometric object (e.g. NURBS or any parametrized or implicitly represented surface or even for polyhedra). Since the spectrum is an isometry invariant of the respective object this fingerprint is also independent of the spatial position. Additionally the eigenvalues can be normalized so that scaling factors for the geometric object can be obtained easily. Therefore checking if two objects are isometric needs no prior alignment (registration/localization) of the objects, but only a comparison of their spectra. With the help of such fingerprints it is possible to support copyright protection, database retrieval and quality assessment of digital data representing surfaces and solids.

Gives an overview of some recent methods useful for local and global shape analysis and for the design of solids. These methods include, as new tools for global and local shape analysis, the spectra of the Laplace and Laplace-Beltrami operators and the concept of stable umbilical points, i.e. stable singularities of the "principal curvature line" wire-frame model of the solid's boundary surface. Most of the material in this paper deals with the medial axis transform as a tool for shape interrogation, reconstruction, modification and design. We show that it appears to be possible to construct an intuitive user interface that allows one to mould shapes by employing the medial axis transform. We also explain that the medial axis and Voronoi diagram can also be defined and computed on free surfaces in a setting where the geodesic distance between two points p and q on a surface S is defined by the shortest surface path on S joining the two points p, q. This leads to the natural and computable generalized concepts of the geodesic medial axis and geodesic Voronoi diagram on free-form surfaces. Both can be computed with a reasonable speed and with high accuracy (of about 12 digits when double floating-point arithmetic is used for the computations).

In this paper we extend the concept of Voronoi diagrams to parameterized surfaces where distance between two points is defined as infimum over the lengths of surface paths connecting these points. We present a method to compute Voronoi diagrams on these surfaces.