2018-08-27, 17:15, ZIB (Hörsaal): An adapted orthonormal

frame along a space curve incorporates the curve tangent at each point as one basis vector, and the frame is said to

be rotation-minimizing if its angular velocity maintains a zero component in the tangent direction, i.e., the two normalplane

vectors exhibit no instantaneous rotation about the tangent. Such frames are important in applications such as computer animation, swept surface constructions, path planning for robotics, and 5-axis CNC machining. The theory of polynomial space curves with rational rotation-minimizing

adapted frames (which form a proper subset of the spatial Pythagorean-hodograph curves) is presented, together with algorithms for their construction and examples of their applications. Some generalizations to other types of rotation-

minimizing frames are also briefly discussed.

2017-12-04, 17:15, ZIB (Hörsaal): Many tasks in information visualization can be considered as Mathematical Optimization problems, calling for the development of numerical solution procedures. In this presentation, we will illustrate this for a collection of information visualization tasks.

To start with, the complex data consists of a set of individuals with a real positive value (“magnitude”) assigned to each individual and a real positive value (“dissimilarity”) to each pair of individuals. These values may vary over time. The task is to visualize the individuals together with the magnitudes and the dissimilarities. As visual design, we choose to represent each individual as a 2D glyph, spread over the visualization region, the magnitudes as glyph areas and the dissimilarities as spatial distances between the glyphs. The temporal variation is depicted by the animation of a collection of snapshots. To preserve the mental map during the temporal development we ensure that the movement from one snapshot to the next one in time of the glyph associated with an individual is small. The mathematical optimization problem to build this visual design is approached by means of difference of convex optimization techniques and nonconvex quadratic binary optimization.

We will continue with a modification of the setting above, where we consider the “magnitude” assigned to each individual to be normalized, yielding a “frequency”. The task is to visualize the individuals together with the frequencies and the dissimilarities is approached by means of a space-filling visual design. The visualization region is now a 2D square, the glyphs representing the individuals are rectangles that form a partition of the visualization region. The mathematical optimization problem to build this visual design is approached by mixed integer linear optimization.

The procedures have been successfully tested on datasets of diverse nature.

2017-06-06, 17:15, ZIB (Hörsaal): Frame shapes, which are made of struts, have been widely used in many fields, such as art, sculpture, architecture and geometric modeling, etc. An interest in robotic fabrication of frame shapes via spatial thermoplastic extrusion has been increasingly growing in recent years. In this talk, we present a novel algorithm to generate a feasible fabrication sequence for general frame shapes. To solve this non-trivial combinatorial problem, we develop a divide-and-conquer strategy that first decomposes the input frame shape into stable layers via a constrained sparse optimization model. Then we search a feasible sequence for each layer via a local optimization method together with a backtracking strategy. The generated sequence guarantees that the already-printed part is in a stable equilibrium state at all stages of fabrication, and that the 3D printing extrusion head does not collide with the printed part during the fabrication. Our algorithm has been validated utilizing a prototype robotic fabrication system made of a 6-axis KUKA robotic arm with a customized extrusion head. Experimental results demonstrate the feasibility and applicability of our algorithm.

2017-04-03, 17:15, ZIB (Hörsaal): Numerical optimisation algorithms are at the core of most intensity-based image registration methods. Efficient optimisation means efficient image registration. In this presentation I will focus on a particular class of optimisation methods: stochastic gradient descent (SGD). Based on SGD, highly efficient registration algorithms can be constructed. SGD is widely used in other fields as well, for example for deep learning to train the weights of a neural network. I will discuss the basic principles of SGD and explain how it enables very fast image registration by random subsampling. Next, I will present several variations of the basic algorithm, introducing randomness in different components of the registration algorithm, aimed at achieving further acceleration or at improving registration accuracy.

2017-03-20, 15:00, FU (Hörsaal Mathematik): Splines and subdivision curves are flexible tools in the design and manipulation of curves in Euclidean space. We study generalizations of interpolating splines and subdivision schemes to the Riemannian manifold of shell surfaces in which the associated metric measures both bending and membrane distortion. This enables the animation of shells via the smooth interpolation of a given set of key frame control meshes. Using a variational time discretization of geodesics efficient numerical implementations can be derived. These are based on a discrete geodesic interpolation, discrete geometric logarithm, discrete exponential map, and discrete parallel transport.

2017-01-16, 01:00, ZIB (Hörsaal): Triply-periodic minimal surfaces are symmetric saddle surfaces that divide space into two components, each resembling a three-dimensional labyrinth, and are hence called bicontinuous. While many triply-periodic minimal surfaces are known, one particular surface is particularly often found in natural nanostructures or synthetic membrane systems. This surface is Allan Schoen's Gyroid surface. The geometric reason for this prevalence is its homogeneity in terms of curvature and domain sizes, that is, the fact that variations of the Gauss curvature throughout this surface are smaller for the Gyroid than for most other triply-periodic minimal surfaces. We will discuss this argument in this seminar, demonstrating that -in a loose and maybe controversial sense, the Gyroid is nature's best (albeit not perfect) attempt at embedding the hyperbolic plane in Euclidean three-space. We then briefly consider a generalisation of the bicontinuous gyroid to tri-continuous structures. These consist of three entangled labyrinth-like domains with a branched (non-manifold) surface that obeys Plateau's foam laws forming the interface between the domains. We discuss that homogeneity arguments similar to the curvature variations provide a rationale for why these structures may form in chemical systems.

2017-01-09, 17:15, ZIB (Hörsaal): We present an algorithm to extract topologically correct and manifold isosurfaces from volume data. We show how to describe the geometry and topologically classify the inter- section of the level set with a reference unit cell. The solutions of three quadratic equations are used to correctly triangulate the level set withinthe cell satisfying the conditions imposed by the asymptotic decider.

This way the triangulation of isosurfaces across cell borders is manifold and topologically correct. Finally, we brieflydescribe a GPU implementation of the algorithm.

2016-05-02, ZIB (Hörsaal): Taking pictures is easy, but editing them is not. In 2012 Facebook reported that people were uploading photos at a rate of more than 10 million per hour. The overwhelming majority of these pictures are casual - they effectively chronicle a moment, but without much work on the part of the photographer. In contrast, professional artists and designers expend great care and effort in pursuit of composing and editing aesthetically-pleasing, impactful imagery. Commercial and research software offers a powerful array of tools for manipulating photos. Some of these tools are easy to understand but offer a limited range of expressiveness. Other more expressive tools are time consuming for experts and inscrutable to novices. I will describe several methods designed to make photo manipulation easier for everyone. [...]

2016-04-18, ZIB (Hörsaal): One of the major challenges in scientific visualization is to deal with the huge amount of information contained in scientific data. A typical concept in visualization refers to the notion of dominant or important features as basis for the visualization. However, there is often still a high feature density overwhelming the user and unfortunately there doesn’t exist a silver bullet to solve this challenge for all cases. Solutions must be found in close collaboration with the domain experts generating the data specifically targeted to their needs. Though there are tools and concepts that can be adapted to many applications. [...]

2016-02-09, ZIB (Hörsaal): In this talk I will discuss an algorithm that generates a surface triangle mesh from an input tolerance volume. The mesh is guaranteed to be within the tolerance, intersection free and topologically correct. A pliant meshing algorithm is used to capture the topology then discover the anisotropy in the input tolerance volume in order to generate a concise output. We first refine a 3D Delaunay triangulation over the tolerance volume while maintaining a piecewise-linear function on this triangulation, until an isosurface of this function matches the topology sought after. [...]

2015/11/02, ZIB (Hörsaal): This talk will describe new technology to automatically annotate skeletal structures in radiographic images, aiming to rapidly transform image data into useful medical information.

Musculoskeletal diseases affect millions of people globally, posing a major cost to healthcare systems worldwide. In clinical practise and research into musculoskeletal diseases, 2D X-ray images are the imaging modality of choice due to wide availability, speed of acquisition and low cost. [...]

2015/05/26, ZIB (Hörsaal): This talk will be devoted to the study of rational geometric objects possessing special rational properties. In particular, we focus on rational curves and surfaces with rational offsets, rational curvature functions, rational convolutions with other objects, rational normal

fields and frames. In the univariate case, we also study curves with polynomial or rational speed, which are traditionally called Pythagorean hodograph curves. In the bivariate case, we investigate surfaces with rational area element which are called, by analogy, Pythagorean hodograph surfaces.

2014/06/23, ZIB (Hörsaal): Modern medical imaging techniques enable to

acquire patient-related data with unprecedented accuracy. Both anatomical and functional data are acquired that provide, for example, information about brain function. The high temporal resolution of modern CT scanners allows to acquire even dynamic data. While the data obtained are often used in diagnosis, also minimally heavily. In such procedures, the surgeons often have only limited possibilities to get an overview of the surgical site and to orient themselves – which strengthens the role of visualization techniques. [...]

2014/04/28, ZIB (Hörsaal): Several natural and man-made objects exhibit symmetry in different forms, both in their geometry and in the material distribution. The study of symmetry plays an important role in understanding both the structure of these objects and their physical properties. The notion of symmetry with respect to the geometry of an object or domain is well understood. In this talk, I will introduce the problem of symmetry detection in a scalar field, a real-valued function defined on a spatial domain of interest. [...]

2014/03/20, ZIB (Hörsaal): Despite many great advances in visualization research, we are still far from being able to intuitively convey the behavior of complex scalar data through images. Part of the solution resides in developing theoretical and computing tools to extract and display meaningful features. It is equally crucial to take into account the strengths and the limitations of the human visual perception to derive efficient visualizations. This talk will describe several works we have been conducted in these two complementary directions.

2014/02/28, ZIB (Hörsaal): In this talk, we first provide a group theoretical background of spherical harmonics, and using this, we propose a possible geometry preserving algebraic framework, which might slightly accelerate the (numerical and exact) computations for spherical harmonic lighting.

2014/02/17, ZIB (Seminarraum): CGAL - The Computational Geometry Algorithms Library

The CGAL C++ library, developed by the CGAL Open Source Project, offers geometric data structures and algorithms that are reliable, efficient, easy to use, and easy to integrate in existing software.

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2013/05/06, ZIB (Hörsaal): In the first part of the talk, I will present a novel sparse modeling approach to nonrigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so the correspondence between the regions is not know, nor do we known how many regions correspond in the two shapes. [...]

2013/04/29, ZIB (Hörsaal): The model-based, analysis-by-synthesis approach has served as a rich source of ideas for computer vision. The conceptual appeal of this approach is however marred by the computational complexity of the resulting ‘inverse’ optimization problems. [...]

2012/08/06, ZIB (Hörsaal): The applications of two-dimensional (2D) X-ray imaging in orthopaedics are pervasive, both pre-operatively and intra-operatively. However, due to the projective character of 2D X-ray imaging, the accuracy of an X-ray image based application is restricted. One way to address this limitation is to learn a statistical model and to adapt the learned model to the patient’s individual anatomy based on a limited number of calibrated X-ray images. [...]

2012/06/25, ZIB (Hörsaal): In the mid 1800s, Hermann Grassmann discovered an important field of mathematics that he called Extension Theory. However, his insights were largely forgotten as the vector analysis and linear algebra that we consider standard today rose to popularity. Recently, the utility of Grassmann’s theory has been rediscovered in the field of computer graphics by researchers who understand how it can unify many of the geometric operations that are used every day. [...]

2012/06/11, ZIB (Hörsaal): Shape deformation and editing has received much research attention in the past decade. Many works have proposed to formulate deformation as a variational problem and have achieved impressive deformation quality via nonlinear elastic energy minimization. However, usually such high deformation quality comes at a significant computational price. In this talk I will discuss a series of works that reformulate shape deformation as a skinning problem. [...]

2012/05/07, ZIB (Hörsaal): Die Astronomie ist der Inbegriff einer klassischen Naturwissenschaft, die es mit abzählbaren, klar umrissenen Objekten zu tun hat, und ein Planetarium visualisiert dieses klassische astronomische Wissen auf perfekte Weise. Was gäbe es also weiter darüber zu sagen? Das am Fachgebiet Literaturwissenschaft der TU Berlin angesiedelte DFG-Projekt “Zeit-Bild-Raum” erforscht das 1923 in den Jenaer Zeiss-Werken erfundene Projektionsplanetarium aus kulturwissenschaftlicher Sicht. [...]

2012/04/02, ZIB (Hörsaal): The human face plays a critical role in almost all aspects of human interaction and face-to-face communication. As such, face modeling has long been considered a grand challenge in In this talk, I will present on our recent research efforts in acquiring and modeling deformable materials, with a special focus on human faces. Furthermore, based on these tech I will talk about a data-driven process for designing the field of computer graphics. [...]