We introduce novel multiscale 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. Additionally, the corresponding kernel distances and embeddings are convergent and efficiently computable. We introduce dual GMS signatures based
on the kernels and discuss the applicability of the multiscale distance and embedding. Collectively, we present a unified view of popular embeddings and distance metrics while recovering intuitive probabilistic interpretations
on discrete surface meshes.
Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object ModelingÃ¢â‚¬â€Geometric algorithms, languages, and systems