It will be a pleasure to welcome in Seville three invited speakers:
Title of the talk: Stable length estimates of tube-like shapes.
Abstract. Mathematical objects can be measured unambiguously, but not so objects from our physical world. Even the total length of tube-like shapes has its difficulties. We introduce a combination of geometric, probabilistic, and topological methods to design a stable length estimate for tube-like shapes; that is: one that is insensitive to small shape changes. Joint work with Florian Pausinger.Title of the talk: The complexity of discrete objects
Abstract. In this paper we explore how to quantify the complexity of discrete objects (images, meshes, networks) which can be encoded in terms of graphs, digraphs or hypergraphs. Herein we present our Heat Flow-Thermodynamic Depth approach which combines ingredients of spectral graph theory, information theory and information projection. We illustrate the approach with several applications: image exploration (image complexity), mesh regularization and selection of optimal map functions in Extended Reeb Graphs (graph and digraph complexity) and structural categorization (hypergraph complexity).
Title of the talk: Differential-Based Geometry Modeling
Abstract. We present an interactive modeling framework for 3D shapes and for texture maps. The technique combines a differential-based deformation method with the idea of geometry brushes that allow to interactively apply modifications by painting on the geometry. Whereas most other deformation techniques demand the designer to define and move hard constrained regions on the surface, the proposed modeling process is similar to sculpting. Geometry brushes allow the user to locally manipulate the metric, enlarge, shrink or rotate parts of the surface and to generate bumps. In a similar way it is possible to modify texture maps, or more generally, arbitrary tensor maps on surfaces. The local changes are globally integrated and visualized in real-time. The presented mathematical techniques such as discrete differential forms, discrete Hodge decomposition, and integrability issues are fundamental also for a wide range of local and global applications in geometry processing including recent progress in surface parametrization.
March 20-22, 2013, Sevilla, Spain