Refine
Year of publication
Document Type
- Article (9)
- In Proceedings (8)
- Book chapter (3)
- ZIB-Report (2)
- Doctoral Thesis (1)
- In Collection (1)
Language
- English (24)
Is part of the Bibliography
- no (24)
We introduce a scheme for real-time nonlinear interpolation of a set of shapes. The scheme exploits the structure of the shape interpolation problem, in particular, the fact that the set of all possible interpolated shapes is a low-dimensional object in a high-dimensional shape space. The interpolated shapes are defined as the minimizers of a nonlinear objective functional on the shape space. Our approach is to construct a reduced optimization problem that approximates its unreduced counterpart and can be solved in milliseconds. To achieve this, we restrict the optimization to a low-dimensional subspace that is specifically designed for the shape interpolation problem. The construction of the subspace is based on two components: a formula for the calculation of derivatives of the interpolated shapes and a Krylov-type sequence that combines the derivatives and the Hessian of the objective functional. To make the computational cost for solving the reduced optimization problem independent of the resolution of the example shapes, we combine the dimensional reduction with schemes for the efficient approximation of the reduced nonlinear objective functional and its gradient. In our experiments, we obtain rates of 20-100 interpolated shapes per second even for the largest examples which have 500k vertices per example shape.
Many efficient computational methods for physical simulation are based on model reduction. We propose new model reduction techniques for the approximation of reduced forces and for the construction of reduced shape spaces of deformable objects that accelerate the construction of a reduced dynamical system, increase the accuracy of the approximation, and simplify the implementation of model reduction. Based on the techniques, we introduce schemes for real-time simulation of deformable objects and interactive deformation-based editing of triangle or tet meshes. We demonstrate the effectiveness of the new techniques in different experiments with elastic solids and shells and compare them to alternative approaches.
The limited spatial resolution of standard computer displays impedes the legibility of text. To improve the rendering, we have developed a number of strategies that employ GPU-based shader programs and appropriate preprocessing steps. We devised and implemented a set of methods that may be used alone or in combination ranging from simple measures such as gamma-correct MIPmapping to complex ones such as RGB subpixel rendering combined with supersampling. We have researched into their performance in terms of both legibility and speed. We difinded a psychovisual test that quantifies legibility quickly enough to compare a selection of promising techniques. The results allow to choose the optimum blend of rendering methods for a given set of requirements.
Multiresolution meshes provide an efficient and structured representation of geometric objects. To increase the mesh resolution only at vital parts of the object, adaptive refinement is widely used. We propose a lossless compression scheme for these adaptive structures that exploits the parent-child relationships inherent to the mesh hierarchy. We use the rules that correspond to the adaptive refinement scheme and store bits only where some freedom of choice is left, leading to compact codes that are free of redundancy. Moreover, we extend the coder to sequences of meshes with varying refinement. The connectivity compression ratio of our method exceeds that of state-of-the-art coders by a factor of 2 to 7. For efficient compression of vertex positions we adapt popular wavelet-based coding schemes to the adaptive triangular and quadrangular cases to demonstrate the compatibility with our method. Akin to state-of-the-art coders, we use a zerotree to encode the resulting coefficients. Using improved context modeling we enhanced the zerotree compression, cutting the overall geometry data rate by 7% below those of the successful Progressive Geometry Compression. More importantly, by exploiting the existing refinement structure we achieve compression factors that are 4 times greater than those of coders which can handle irregular meshes.
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.
This thesis concerns model reduction techniques for the efficient numerical treatment
of physical systems governing the deformation behavior of geometrically complex shapes.
We present new strategies for the construction of simplified,
low-dimensional models that capture the main features of the original complex system
and are suitable for use in interactive computer graphics applications.
To demonstrate the effectiveness of the new techniques we propose frameworks
for real-time simulation and interactive deformation-based modeling
of elastic solids and shells and compare them to alternative approaches.
In addition, we investigate differential operators that are derived from
the physical models and hence can serve as alternatives to the Laplace-Beltrami
operator for applications in modal shape analysis.
Furthermore, this thesis addresses the compression of digital shapes.
In particular, we present a lossless compression scheme that is adapted to
the special characteristics of adaptively refined, hierarchical meshes.
We propose a new framework for spacetime optimization that can generate artistic motion with a long planning horizon for complex virtual characters. The scheme can be used for generating general types of motion and neither requires motion capture data nor an initial motion that satisfies the constraints. Our modeling of the spacetime optimization combines linearized dynamics and a novel warping scheme for articulated characters. We show that the optimal motions can be described using a combination of vibration modes, wiggly splines, and our warping scheme. This enables us to restrict the optimization to low-dimensional spaces of explicitly parametrized motions. Thereby the computation of an optimal motion is reduced to a low-dimensional non-linear least squares problem, which can be solved with standard solvers. We show examples of motions created by specifying only a few constraints for positions and velocities.
We propose a scheme for animating deformable objects based on spacetime optimization. The main feature is that it robustly and quickly (within a few seconds) generates interesting motion from a sparse set of spacetime constraints. Providing only partial (as opposed to full) keyframes for positions and velocities is sufficient. The computed motion satisfies the constraints and the remaining degrees of freedom are determined by physical principles using elasticity and the spacetime constraints paradigm. Our modeling of the spacetime optimization problem combines dimensional reduction, modal coordinates, wiggly splines, and rotation strain warping. Controlling the warped motion requires the derivative of the warp map. We derive a representation of the derivative that can be efficiently and robustly evaluated. Our solver is based on a theorem that characterizes the solutions of the optimization problem and allows us to restrict the optimization to very low-dimensional search spaces. This treatment of the optimization problem avoids a time discretization and the resulting method can robustly deal with sparse input and wiggly motion.
Geometry processing
(2014)