Multi‐Scale Kernels Using Random Walks

Sinha, A.; Ramani, K.

Multi‐Scale Kernels Using Random Walks

Date

2014

Authors

Sinha, A.
Ramani, K.

Publisher

The Eurographics Association and John Wiley and Sons Ltd.

Abstract

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.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.

        @article{10.1111:cgf.12264
,
journal = {Computer Graphics Forum},
title = {{Multi‐Scale Kernels Using Random Walks
}},
author = {Sinha, A. and 
Ramani, K.
},
year = {2014
},
publisher = {The Eurographics Association and John Wiley and Sons Ltd.
},
ISSN = {1467-8659
},
DOI = {10.1111/cgf.12264
}
}

URI

https://doi.org/10.1111/cgf.12264

Collections

33-Issue 1

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