@misc{TycowiczAmbellanMukhopadhyayetal.2016, author = {Tycowicz, Christoph von and Ambellan, Felix and Mukhopadhyay, Anirban and Zachow, Stefan}, title = {A Riemannian Statistical Shape Model using Differential Coordinates}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61175}, year = {2016}, abstract = {We propose a novel Riemannian framework for statistical analysis of shapes that is able to account for the nonlinearity in shape variation. By adopting a physical perspective, we introduce a differential representation that puts the local geometric variability into focus. We model these differential coordinates as elements of a Lie group thereby endowing our shape space with a non-Euclidian structure. A key advantage of our framework is that statistics in a manifold shape space become numerically tractable improving performance by several orders of magnitude over state-of-the-art. We show that our Riemannian model is well suited for the identification of intra-population variability as well as inter-population differences. In particular, we demonstrate the superiority of the proposed model in experiments on specificity and generalization ability. We further derive a statistical shape descriptor that outperforms the standard Euclidian approach in terms of shape-based classification of morphological disorders.}, language = {en} } @misc{ZoecklerStallingHege1999, author = {Z{\"o}ckler, Malte and Stalling, Detlev and Hege, Hans-Christian}, title = {Fast and Intuitive Generation of Geometric Shape Transitions}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4219}, number = {SC-99-33}, year = {1999}, abstract = {We describe a novel method for continuously transforming two triangulated models of arbitrary topology into each other. Equal global topology for both objects is assumed, extensions for genus changes during metamorphosis are provided. The proposed method addresses the major challenge in 3D metamorphosis, namely specifying the morphing process intuitively, with minimal user interaction and sufficient detail. Corresponding regions and point features are interactively identified. These regions are parametrized automatically and consistently, providing a basis for smooth interpolation. Utilizing suitable 3D interaction techniques a simple and intuitive control over the whole morphing process is offered.}, language = {en} } @misc{LangePolthier2005, author = {Lange, Carsten and Polthier, Konrad}, title = {Anisotropic Smoothing of Point Sets}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8508}, number = {05-16}, year = {2005}, abstract = {The use of point sets instead of meshes became more popular during the last years. We present a new method for anisotropic fairing of a point sampled surface using an anisotropic geometric mean curvature flow. The main advantage of our approach is that the evolution removes noise from a point set while it detects and enhances geometric features of the surface such as edges and corners. We derive a shape operator, principal curvature properties of a point set, and an anisotropic Laplacian of the surface. This anisotropic Laplacian reflects curvature properties which can be understood as the point set analogue of Taubin's curvature-tensor for polyhedral surfaces. We combine these discrete tools with techniques from geometric diffusion and image processing. Several applications demonstrate the efficiency and accuracy of our method.}, language = {en} } @misc{HildebrandtPolthier2004, author = {Hildebrandt, Klaus and Polthier, Konrad}, title = {Anisotropic Filtering of Non-Linear Surface Features}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8003}, number = {04-25}, year = {2004}, abstract = {A new method for noise removal of arbitrary surfaces meshes is presented which focuses on the preservation and sharpening of non-linear geometric features such as curved surface regions and feature lines. Our method uses a prescribed mean curvature flow (PMC) for simplicial surfaces which is based on three new contributions: 1. the definition and efficient calculation of a discrete shape operator and principal curvature properties on simplicial surfaces that is fully consistent with the well-known discrete mean curvature formula, 2. an anisotropic discrete mean curvature vector that combines the advantages of the mean curvature normal with the special anisotropic behaviour along feature lines of a surface, and 3. an anisotropic prescribed mean curvature flow which converges to surfaces with an estimated mean curvature distribution and with preserved non-linear features. Additionally, the PMC flow prevents boundary shrinkage at constrained and free boundary segments.}, language = {en} } @misc{KaelbererPolthierReitebuchetal.2004, author = {K{\"a}lberer, Felix and Polthier, Konrad and Reitebuch, Ulrich and Wardetzky, Max}, title = {Compressing Triangle Meshes using Geometric Infomation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8016}, number = {04-26}, year = {2004}, abstract = {We introduce FreeLence, a lossless single-rate connectivity compression algorithm for triangle surface meshes. Based upon a geometry-driven traversal scheme we present two novel and simple concepts: free-valence connectivity encoding and entropy coding based on geometric context. Together these techniques yield significantly smaller rates for connectivity compression than current state of the art approaches - valence-based algorithms and Angle- Analyzer, with an average of \$36\\%\$ improvement over the former and an average of \$18\\%\$ over the latter on benchmark 3D models, combined with the ability to well adapt to the regularity of meshes. We also prove that our algorithm exhibits a smaller worst case entropy for a class of "'well-behaved"' triangle meshes than valence-driven connectivity encoding approaches.}, language = {en} } @misc{SanderRunge2000, author = {Sander, Oliver and Runge, Daniel}, title = {Fast Surface Reconstruction Using a Probe Sphere}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6181}, number = {00-50}, year = {2000}, abstract = {We introduce a new method for reconstructing a triangular surface from an unorganized set of points in space. It is based on placing a probe sphere on the point set and rolling it around, connecting all triples of points with a triangle that the sphere comes to rest on. Therefore, the algorithm interpolates, rather than approximates, the input points. The method needs considerably less running time than previous algorithms and yields good results on point sets that are reasonably well-behaved.}, language = {en} }