This paper describes a prototype system for surgical planning and prediction of human facial shape after craniofacial and maxillofacial surgery for patients with facial deformities. For this purpose it combines, unifies, and extends various methods from geometric modeling, finite element analysis, and image processing to render highly realistic 3D images of the post surgical situation. The basic concept of the system is to join advanced geometric modeling and animation systems such as Alias with a special purpose finite element model of the human face developed under AVS . In contrast to existing facial models we acquire facial surface and soft tissue data both from photogrammetric and CT scans of the individual. After initial data preprocessing, reconstruction, and registration, a finite element model of the facial surface and soft tissue is provided which is based on triangular finite elements. Stiffness parameters of the soft tissue are computed using segmentations of the underlying...

We define the Morse-Smale complex of a Morse function over a 3-manifold as the overlay of the descending and ascending manifolds of all critical points. In the generic case, its 3-dimensional cells are shaped like crystals and are separated by quadrangular faces. In this paper, we give a combinatorial algorithm for constructing such complexes for piecewise linear data.

Since the introduction of standard techniques for isosurface extraction from volumetric datasets, one of the hardest problems has been to reduce the number of triangles (or polygons) generated. This paper presents an algorithm that considerably reduces the number of polygons generated by a Marching Cubes-like scheme without excessively increasing the overall computational complexity. The algorithm assumes discretization of the dataset space and replaces cell edge interpolation by midpoint selection. Under these assumptions, the extracted surfaces are composed of polygons lying within a finite number of incidences, thus allowing simple merging of the output facets into large coplanar polygons. An experimental evaluation of the proposed approach on datasets related to biomedical imaging and chemical modelling is reported. 1 Introduction The use of the Marching Cubes (MC) technique, originally proposed by W. Lorensen and H. Cline [7], is considered to be a standard approach to the proble...

Visualized data often have dubious origins and quality. Di erent forms of uncertainty and errors are also introduced as the data are derived, transformed, interpolated, and nally rendered. In the absence of integrated presentation of data and uncertainty, the analysis of the visualization is incomplete at best and often leads to inaccurate or incorrect conclusions. This paper surveys techniques for presenting data together with uncertainty. These uncertainty visualization techniques present data in such a manner that users are made aware of the locations and degree of uncertainties in their data so as to make more informed analyses and decisions. The techniques include adding glyphs, adding geometry, modifying geometry, modifying attributes, animation, soni cation, and psycho-visual approaches. We present our results in uncertainty visualization for environmental visualization, surface interpolation, global illumination with radiosity, ow visualization, and gure animation. We also present a classi cation of the possibilities in uncertainty visualization, and locate our contributions within this classi cation.

Abstract—Two important tools for manipulating polygonal models are simplification and repair and we present voxel-based methods for performing both of these tasks. We describe a method for converting polygonal models to a volumetric representation in a way that handles models with holes, double walls, and intersecting parts. This allows us to perform polygon model repair simply by converting a model to and from the volumetric domain. We also describe a new topology-altering simplification method that is based on 3D morphological operators. Visually unimportant features such as tubes and holes may be eliminated from a model by the open and close morphological operators. Our simplification approach accepts polygonal models as input, scan converts these to create a volumetric description, performs topology modification, and then converts the results back to polygons. We then apply a topologypreserving polygon simplification technique to produce a final model. Our simplification method produces results that are everywhere manifold. Index Terms—Mesh simplification, mesh repair, volumetric models, morphological operators. æ 1

We present a simple,robust, and practical method for object simplification for applications where gradual elimination of high frequency details is desired. This is accomplished by converting an object into multi-resolution volume rastersusing a controlled filtering and sampling technique.Amultiresolution triangle-mesh hierarchycan then be generated by applying the Marching Cubes algorithm. We f urther propose an adaptive surface generation algorithm to reduce the number of triangles generated by the standardMarching Cubes. Our method simplifies the topology of objects in a controlled fashion. In addition, at eachlevel of detail, multi-layered meshes can be used for an efficient antialiased rendering.

We are presenting a new method for adaptive surface meshing and triangulation which controls the local level-of-detail of the surface approximation by local spectral estimates. These estimates are figured out by a wavelet representation of the surface data. The basic idea is to decompose the initial data set by means of an orthogonal or semi-orthogonal tensor product wavelet transform (WT) and to analyze the resulting coefficients. In surface regions, where the partial energy of the resulting coefficients is low, the polygonial approximation of the surface can be performed with larger triangles without loosing too much fine grain details. However, since the localization of the WT is bound by the Heisenberg principle the meshing method has to be controlled by the detail signals rather than directly by the coefficients. The dyadic scaling of the WT stimulated us to build an hierachical meshing algorithm which transforms the initially regular data grid into a quadtree representation by...

Multiresolution methods are becoming increasingly important tools for the interactive visualization of very large data sets. Multiresolution isosurface visualization allows the user to explore volume data using simplified and coarse representations of the isosurface for overview images, and finer resolution in areas of high interest or when zooming into the data. Ideally, a coarse isosurface should have the same topological structure as the original. The topological genus of the isosurface is one important property which is often neglected in multiresolution algorithms. This results in uncontrolled topological changes which can occur whenever the level-of-detail is changed. The scope of this paper is to propose an efficient technique which allows preservation of topology as well as controlled topology simplification in multiresolution isosurface extraction. CR Categories: G.1.2 [Numerical Analysis]: Approximation--- Approximation of Surfaces and Contours I.3.5 [Computer Graphics ]: Co...

Abstract — Reconstructing an accurate and topologically correct representation of the cortical surface of the brain is an important objective in various neuroscience applications. Most cortical surface reconstruction methods either ignore topology or correct it using manual editing or methods that lead to inaccurate reconstructions. Shattuck and Leahy recently reported a fully-automatic method that yields a topologically correct representation with little distortion of the underlying segmentation. We provide an alternate approach that has several advantages over their approach, including the use of arbitrary digital connectivities, a flexible morphology-based multiscale approach, and the option of foreground-only or background-only correction. A detailed analysis of the method's performance on 15 magnetic resonance brain images is provided.

We present a new method for adaptive surface meshing and triangulation which controls the local level-of-detail of the surface approximation by local spectral estimates. These estimates are determined by a wavelet representation of the surface data. The basic idea is to decompose the initial data set by means of an orthogonal or semi-orthogonal tensor product wavelet transform (WT) and to analyze the resulting coefficients. In surface regions, where the partial energy of the resulting coefficients is low, the polygonal approximation of the surface can be performed with larger triangles without loosing too much fine grain details. However, since the localization of the WT is bound by the Heisenberg principle the meshing method has to be controlled by the detail signals rather than directly by the coefficients. The dyadic scaling of the WT stimulated us to build an hierarchical meshing algorithm which transforms the initially regular data grid into a quadtree representation by rejection of unimportant mesh vertices. The optimum triangulation of the resulting quadtree cells is carried out by selection from a look-up table. The tree grows recursively as controlled by detail signals which are computed from a modified inverse WT. In order to control the local level-of-detail, we introduce a new class of wavelet space filters acting as “magnifying glasses ” on the data. We show that our algorithm performs a low algorithmic complexity, so that surface meshing can be achieved at interactive rates, such as required by flight simulators. However, other applications are possible as well, such as mesh reduction in complex data, FEM or radiosity meshing. The method is applied on different types of data comprising both digital terrain models and laser range scans. In addition, quantitative investigations on error analysis are carried out.