Browsing by Author "Rumpf, Martin"
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- ItemMathematical Imaging and Surface Processing(Zürich : EMS Publ. House, 2016) Rumpf, Martin; Schröder, PeterWithin the last decade image and geometry processing have become increasingly rigorous with solid foundations in mathematics. Both areas are research fields at the intersection of different mathematical disciplines, ranging from geometry and calculus of variations to PDE analysis and numerical analysis. The workshop brought together scientists from all these areas and a fruitful interplay took place. There was a lively exchange of ideas between geometry and image processing applications areas, characterized in a number of ways in this workshop. For example, optimal transport, first applied in computer vision is now used to define a distance measure between 3d shapes, spectral analysis as a tool in image processing can be applied in surface classification and matching, and so on. We have also seen the use of Riemannian geometry as a powerful tool to improve the analysis of multivalued images. This volume collects the abstracts for all the presentations covering this wide spectrum of tools and application domains.
- ItemMini-Workshop: Analytical and Numerical Methods in Image and Surface Processing(Zürich : EMS Publ. House, 2005) Reif, Ulrich; Rumpf, Martin; Schröder, PeterThe workshop successfully brought together researchers from mathematical analysis, numerical mathematics, computer graphics and image processing. The focus was on variational methods in image and surface processing such as active contour models, Mumford-Shah type functionals, image and surface denoising based on geometric evolution problems in image and surface fairing, physical modeling of surfaces, the restoration of images and surfaces using higher order variational formulations.
- ItemShape space – a paradigm for character animation in computer graphics(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2020) Heeren, Behrend; Rumpf, MartinNowadays 3D computer animation is increasingly realistic as the models used for the characters become more and more complex. These models are typically represented by meshes of hundreds of thousands or even millions of triangles. The mathematical notion of a shape space allows us to effectively model, manipulate, and animate such meshes. Once an appropriate notion of dissimilarity measure between different triangular meshes is defined, various useful tools in character modeling and animation turn out to coincide with basic geometric operations derived from this definition.
- ItemTrends in Mathematical Imaging and Surface Processing(Zürich : EMS Publ. House, 2011) Rumpf, Martin; Sapiro, Guillermo; Schröder, PeterMotivated both by industrial applications and the challenge of new problems, one observes an increasing interest in the field of image and surface processing over the last years. It has become clear that even though the applications areas differ significantly the methodological overlap is enormous. Even if contributions to the field come from almost any discipline in mathematics, a major role is played by partial differential equations and in particular by geometric and variational modeling and by their numerical counterparts. The aim of the workshop was to gather a group of leading experts coming from mathematics, engineering and computer graphics to cover the main developments.