Multi-Scale Kernels Using Random Walks
Article first published online: 21 NOV 2013
© 2013 The Authors Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd.
Computer Graphics Forum
Volume 33, Issue 1, pages 164–177, February 2014
How to Cite
Sinha, A. and Ramani, K. (2014), Multi-Scale Kernels Using Random Walks. Computer Graphics Forum, 33: 164–177. doi: 10.1111/cgf.12264
- Issue published online: 24 FEB 2014
- Article first published online: 21 NOV 2013
- geometric analysis;
- random walks;
- shape signatures;
- I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms;
- and systems
We introduce novel multi-scale kernels using the random walk framework and derive corresponding embeddings and pairwise distances. The fractional moments of the rate of continuous time random walk (equivalently diffusion rate) are used to discover higher order kernels (or similarities) between pair of points. The formulated kernels are isometry, scale and tessellation invariant, can be made globally or locally shape aware and are insensitive to partial objects and noise based on the moment and influence parameters. In addition, the corresponding kernel distances and embeddings are convergent and efficiently computable. We introduce dual Green's mean signatures based on the kernels and discuss the applicability of the multi-scale distance and embedding. Collectively, we present a unified view of popular embeddings and distance metrics while recovering intuitive probabilistic interpretations on discrete surface meshes.