Publications

We present a deformable model to reconstruct a surface from a point cloud. The model is based on an explicit mesh representation composed of multiple competing evolving fronts. These fronts adapt to the local feature size of the target shape in a coarse-to-fine manner. Hence, they approach towards the finer (local) features of the target shape only after the reconstruction of the coarse (global) features has been completed. This conservative approach leads to a better control and interpretation of the reconstructed topology. The use of an explicit representation for the deformable model guarantees water-tightness and simple tracking of topological events. Furthermore, the coarse-to-fine nature of reconstruction enables adaptive handling of non-homogenous sample density, including robustness to missing data in defected areas.

We present a new volumetric method for reconstructing watertight triangle meshes from arbitrary, unoriented point clouds. While previous techniques usually reconstruct surfaces as the zero level-set of a signed distance function, our method uses an unsigned distance function and hence does not require any information about the local surface orientation. Our algorithm estimates local surface confidence values within a dilated crust around the input samples. The surface which maximizes the global confidence is then extracted by computing the minimum cut of a weighted spatial graph structure. We present an algorithm, which efficiently converts this cut into a closed, manifold triangle mesh with a minimal number of vertices. The use of an unsigned distance function avoids the topological noise artifacts caused by misalignment of 3D scans, which are common to most volumetric reconstruction techniques. Due to a hierarchical approach our method efficiently produces solid models of low genus even for noisy and highly irregular data containing large holes, without loosing fine details in densely sampled regions. We show several examples for different application settings such as model generation from raw laser-scanned data, image-based 3D reconstruction, and mesh repair.

We present a new method for 3D shape modeling that achieves intuitive and robust deformations by emulating physically plausible surface behavior inspired by thin shells and plates. The surface mesh is embedded in a layer of volumetric prisms, which are coupled through non-linear, elastic forces. To deform the mesh, prisms are rigidly transformed to satisfy user constraints while minimizing the elastic energy. The rigidity of the prisms prevents degenerations even under extreme deformations, making the method numerically stable. For the underlying geometric optimization we employ both local and global shape matching techniques. Our modeling framework allows for the specification of various geometrically intuitive parameters that provide control over the physical surface behavior. While computationally more involved than previous methods, our approach significantly improves robustness and simplifies user interaction for large, complex deformations.

We propose a new technique for quad-dominant remeshing which separates the local regularity requirements from the global alignment requirements by working in two steps. In the first step, we apply a slight variant of variational shape approximation in order to segment the input mesh into patches which capture the global structure of the processed object. Then we compute an optimized quad-mesh for every patch by generating a finite set of candidate curves and applying a combinatorial optimization procedure. Since the optimization is performed independently for each patch, we can afford more complex operations while keeping the overall computation times at a reasonable level. Our quad-meshing technique is robust even for noisy meshes and meshes with isotropic or flat regions since it does not rely on the generation of curves by integration along estimated principal curvature directions. Instead we compute a conformal parametrization for each patch and generate the quad-mesh from curves with minimum bending energy in the 2D parameter domain. Mesh consistency between patches is guaranteed by simply using the same set of sample points along the common boundary curve. The resulting quad-meshes are of high-quality locally (shape of the quads) as well as globally (global alignment) which allows us to even generate fairly coarse quad-meshes that can be used as Catmull-Clark control meshes.

In this article we present a new multiscale surface representation based on point samples. Given an unstructured point cloud as input, our method first computes a series of point-based surface approximations at successively higher levels of smoothness, that is, coarser scales of detail, using geometric low-pass filtering. These point clouds are then encoded relative to each other by expressing each level as a scalar displacement of its predecessor. Low-pass filtering and encoding are combined in an efficient multilevel projection operator using local weighted least squares fitting.

Our representation is motivated by the need for higher-level editing semantics which allow surface modifications at different scales. The user would be able to edit the surface at different approximation levels to perform coarse-scale edits on the whole model as well as very localized modifications on the surface detail. Additionally, the multiscale representation provides a separation in geometric scale which can be understood as a spectral decomposition of the surface geometry. Based on this observation, advanced geometric filtering methods can be implemented that mimic the effects of Fourier filters to achieve effects such as smoothing, enhancement, or band-bass filtering.

In wireless network planning, much effort is spent on the improvement of the network and transport layer -- especially for Mobile Ad Hoc Networks. Although in principle real-world measurements are necessary for this, their setup is often too complex and costly. Hence good and reliable simulation tools are needed. In this work we present a new physical layer simulation algorithm based on the extension and adaptation of recent techniques for global illumination simulation. By combining and improving these highly efficient algorithms from the field of Computer Graphics, it is possible to build a fast and flexible utility to be used for wireless network simulation. We compute a discrete sampling of the volumetric electromagnetic field by tracing stochastically generated photon paths through the scene. This so called Photon Path Map is then used to estimate the field density at any point in space and also provides local information about the delay spread. The algorithm can be applied to three dimensional indoor as well as outdoor scenarios without any changes and the path-tracing costs scale only logarithmically with the growing complexity of the underlying scene geometry.

The simulation of wireless networks has been an important tool for researchers and the industry in the last years. Especially in the field of Mobile Ad Hoc Networking, most current results have been achieved using simulators. The need for reproducible results and easy to observe environments limits the use of real world measurements for those kind of networks. It is stated here that the radio wave propagation model has a strong impact on the results of the simulation run. This work shows the limitations of current simulation environments and describes a high accuracy propagation model based on the use of a ray-tracer. By using a parallelized preprocessing step we made this propagation model feasible for usage in network simulators. Based on two examples, the effects on characteristic performance properties in Mobile Ad Hoc Networks are shown. We found that the physical layer simulation has a great impact on routing protocol efficiency.

In this work we present a method to visualize the wave propagation mechanisms of wireless networks at interactive rates. The user can move around transmitting nodes and immediately sees the resulting field strength for the complete scenario. This can be used for rapid optimization of antenna placement, or for visualizing the coverage of mobile stations, as they move through a simulation. In a preprocessing step we compute the wave propagation for a distinct set of transmitter positions. Whereas in the visualization phase we use these precomputed maps to do a fast interpolation using a current graphics card.

We present a method for the reconstruction of 3D planes from calibrated 2D images. Given a set of pixels Ω in a reference image, our method computes a plane which best approximates that part of the scene which has been projected to Ω by exploiting additional views. Based on classical image alignment techniques we derive linear matching equations minimally parameterized by the three parameters of an object-space plane. The resulting iterative algorithm is highly robust because it is able to integrate over large image regions due to the correct object-space approximation and hence is not limited to comparing small image patches. Our method can be applied to a pair of stereo images but is also able to take advantage of the additional information provided by an arbitrary number of input images. A thorough experimental validation shows that these properties enable robust convergence especially under the influence of image sensor noise and camera calibration errors.

We present an interactive system for fragment-based image completion which exploits information about the approximate 3D structure in a scene in order to estimate and apply perspective corrections when copying a source fragment to a target position. Even though implicit 3D information is used, the interaction is strictly 2D which makes the user interface very simple and intuitive. We propose different interaction metaphors in our system for providing 3D information interactively. Our search and matching procedure is done in the Fourier domain and hence it is very fast and it allows us to use large fragments and multiple source images with high resolution while still obtaining interactive response times. Our image completion technique also takes user-specified structure information into account where we generalize the concept of feature curves to arbitrary sets of feature pixels. We demonstrate our technique on a number of difficult completion tasks.

This paper presents a new volumetric stereo algorithm to reconstruct the 3D shape of an arbitrary object. Our method is based on finding the minimum cut in an octahedral graph structure embedded into the vol umetric grid, which establishes a well defined relationship between the integrated photo-consistency function of a region in space and the corresponding edge weights of the embedded graph. This new graph structure allows for a highly efficient hierarchical implementation supporting high volumetric resolutions and large numbers of input images. Furthermore we will show how the resulting cut surface can be directly converted into a consistent, closed and manifold mesh. Hence this work provides a complete multi-view stereo reconstruction pipeline. We demonstrate the robustness and efficiency of our technique by a number of high quality reconstructions of real objects.

Estimating photo-consistency is one of the most important ingredients for any 3D stereo reconstruction technique that is based on a volumetric scene representation. This paper presents a new, illumination invariant photo-consistency measure for high quality, volumetric 3D reconstruction from calibrated images. In contrast to current standard methods such as normalized cross-correlation it supports unconstrained camera setups and non-planar surface approximations. We show how this measure can be embedded into a highly efficient, completely hardware accelerated volumetric reconstruction pipeline by exploiting current graphics processors. We provide examples of high quality reconstructions with computation times of only a few seconds to minutes, even for large numbers of cameras and high volumetric resolutions.

We propose an algorithm to construct a set of interfaces that separate the connected components of a multi-valued volume dataset. While each single interface is a manifold triangle mesh, two or more interfaces may join consistently along their common boundaries, i.e. there are no T-junctions or gaps. In contrast to previous work, our algorithm classifies and removes the topological ambiguities from the volume before extracting the interfaces. This not only allows for a simple and stable extraction algorithm, but also makes it possible to include user constraints.