Heat Kernel Signature: Multiscale Visualization of Tensor Fields
The Identification of similar surfaces or shapes is an important problem in computational geometry. Here surfaces are considered as similar if there is an isometric mapping between them. This allows to identify characters in different poses, for example. One approach to deal with such problems are shape signatures. This project is concerned with the definition and analysis of such signatures for comparing surfaces and general metric tensors. The signatures developed in this project are based on the process of heat conduction on surfaces, which depends only on its metric. The time parameter of heat conduction allows a multiscale analysis in a natural way. The extension of this signatures to general tensor fields opens up a new area of application. For example, it enables the comparison of stress tensor fields which are of great importance in materials science. Further information is available in the detailed project description.
- Valentin Zobel, Jan Reiningshaus, Ingrid Hotz. Visualization of Two-Dimensional Symmetric Tensor Fields Using the Heat Kernel Signature. Topological Methods in Data Analysis and Visualization III, 2013
- Valentin Zobel, Jan Reininghaus, Ingrid Hotz. Generalized Heat Kernel Signature. Journal of WSCG, International Conference on Computer Graphics, Visualization and Computer Vision, pp. 93-100, 2011.
- Edmond Boyer, Alexander M. Bronstein, Michael M. Bronstein, Benjamin Bustos, Tal Darom, Radu Horaud, Ingrid Hotz, Yosi Keller, Johannes Keustermans, Artiom Kovnatsky, Roee Litman, Jan Reininghaus, Ivan Sipiran, Dirk Smeets, Paul Suetens, Dirk Vandermeulen, Andrei Zaharescu, Valentin Zobel. SHREC 2011: robust feature detection and description benchmark. Proc. Eurographics 2011 Workshop on 3D Object Retrieval (3DOR'11), pp. 71-78, Eurographics Association, 2011.
- Valentin Zobel. Spectral Analysis of the Hodge Laplacian on Discrete Manifolds. Diplomarbeit, Technische Universität Berlin (J. M. Sullivan) and ZIB (I. Hotz) 2010.