Ulf Labsik

Interpolatory √ 3-Subdivision

We present a new interpolatory subdivision scheme for triangle meshes. Instead of splitting each edge and performing a 1‐to‐4 split for every triangle we compute a new vertex for every triangle and retriangulate the old and the new vertices. Using this refinement operator the number of triangles only triples in each step. New vertices are computed with a Butterfly like scheme. In order to obtain overall smooth surfaces special rules are necessary in the neighborhood of extraordinary vertices. The scheme is suitable for adaptive refinement by using an easy forward strategy. No temporary triangles are produced here which allows simpler data structures and makes the scheme easy to implement.

Remeshing triangulated surfaces with optimal parameterizations

The use of polygonal meshes, especially triangle meshes, is manifold, but a lot of algorithms require the mesh to be structured in a certain way and cannot be applied to an arbitrarily structured mesh. The process of replacing an arbitrarily structured mesh by a structured one is called remeshing and the most important class of structured meshes are triangle meshes with subdivision connectivity. In this paper, we present an algorithm for remeshing triangle meshes with boundary that is based on parameterizing the mesh over a planar domain. We discuss what kind of parameterizations are optimal for the purpose of remeshing and show the advantages of our approach in a series of examples.

Progressive transmission of subdivision surfaces

Abstract Triangle meshes are a standard representation for surface geometry in computer graphics and virtual reality applications. To achieve high realism of the modeled objects, the meshes typically consist of a very large number of faces. For broadcasting virtual environments over low-bandwidth data connections like the Internet it is highly important to develop efficient algorithms which enable the progressive transmission of such large meshes. In this paper we introduce a special representation for storing and transmitting meshes with subdivision connectivity which allows random access to the detail information. We present algorithms for the decomposition and the reconstruction of subdivision surfaces. With this technique, the receiver can reconstruct smooth approximations of the original surface from a rather small amount of data received.

Fast and Adaptive Finite Element Approach for Modeling Brain Shift

Objective: In this paper we introduce a finite element-based strategy for simulation of brain deformation occurring during neurosurgery. The phenomenon, known as brain shift, causes a decrease in the accuracy of neuronavigation systems that rely on preoperatively acquired data. This can be compensated for with a computational model of the brain deformation process. By applying model calculations to preoperative images, an update within the operating room can be performed. Methods: One of the crucial concerns in the context of developing a physical-based model is the choice of governing equations describing the physics of the phenomenon. In this work, deformation of brain tissue is expressed in terms of a 3D consolidation model for a linearly elastic and porous fluid. The next crucial issue is ensuring stable calculations within the chosen model. For this purpose, we developed a special technique for generating the underlying geometry for the simulation. With this technique an unstructured grid consisting of regular tetrahedra is created, whereupon time-dependent finite element simulation is performed in an adaptive manner. Results: We applied our algorithm to preoperative MR scans and investigated the value of the method. Due to the adaptivity of the method, only 5-10% of the computing time was needed as compared to traditional finite element approaches based on a uniformly subdivided grid. The results of the experiments were compared to the corresponding intraoperative MR scans. A close match between the computed deformation of the brain and the displacement resulting from the intraoperative data was observed. Conclusion: A model-based approach for the simulation of brain shift is presented. In this computational model the brain tissue is described as an elastic and porous material using Biot consolidation theory. Validating experiments conducted with MR data provided promising results.

REPAIRING NON-MANIFOLD TRIANGLE MESHES USING SIMULATED ANNEALING

In the field of reverse engineering one often faces the problem of repairing triangulations with holes, intersecting triangles, Mobius-band-like structures or other artifacts. In this paper we present a novel approach for generating manifold triangle meshes from such incomplete or imperfect triangulations. Even for heavily damaged triangulations, representing closed surfaces with arbitrary genus, our algorithm results in correct manifold triangle meshes. The algorithm is based on a randomized optimization technique from probability calculus called simulated annealing.

Hierarchical extraction of iso-surfaces with semi-regular meshes

In this paper we present a novel approach to iso-surface extraction which is based on a multiresolution volume data representation and hierarchically approximates the iso-surface with a semi-regular mesh. After having generated a hierarchy of volumes, we extract the iso-surface from the coarsest resolution with a standard Marching Cubes algorithm, apply a simple mesh decimation strategy to improve the shape of the triangles, and use the result as a base mesh. Then we iteratively fit the mesh to the iso-surface at the finer volume levels, thereby subdividing it adaptively in order to be able to correctly reconstruct local features. We also take care of generating an even vertex distribution over the iso-surface so that the final result consists of triangles with good aspect ratio. The advantage of this approach as opposed to the standard method of extracting the iso-surface from the finest resolution with Marching Cubes is that it generates a mesh with subdivision connectivity which can be utilized by several multiresolution algorithms. As an application of our method we show how to reconstruct the surface of archaeological items.

Hierarchical Iso-Surface Extraction

The extraction and display of iso-surfaces is a standard method for the visualization of volume data sets. In this paper we present a novel approach that utilizes a hierarchy on both the input and the output data. For the generation of a coarse base mesh, we construct a hierarchy of volumes and extract an iso-surface from the coarsest resolution with a standard Marching Cubes algorithm. We additionally apply a simple mesh decimation algorithm to improve the shape of the triangles. We iteratively fit this mesh to the iso-surface at the finer volume levels. To be able to reconstruct fine detail of the iso-surface we thereby adaptively subdivide the mesh. To evenly distribute the vertices of the triangle mesh over the iso-surface and generate a triangle mesh with evenly shaped triangles, we have integrated a mesh smoothing algorithm into the fitting process. The advantage of this approach is that it generates a mesh with subdivision connectivity which can be utilized by several multiresolution algorithms such as compression and progressive transmission. As applications of our method we show how to reconstruct the surface of archaeological artifacts and the reconstruction of the brain surface for the simulation of the brain shift phenomenon.

Using most isometric parameterizations for remeshing polygonal surfaces

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.

Progressive isosurface extraction from tetrahedral meshes

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.