Nonlinear Mean Shift over Riemannian Manifolds |
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Authors: | Raghav Subbarao and Peter Meer |
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Affiliation: | (1) Electrical and Computer Engineering Department, Rutgers University, 94 Brett Road, Piscataway, NJ 08854-8058, USA |
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Abstract: | The original mean shift algorithm is widely applied for nonparametric clustering in vector spaces. In this paper we generalize
it to data points lying on Riemannian manifolds. This allows us to extend mean shift based clustering and filtering techniques
to a large class of frequently occurring non-vector spaces in vision. We present an exact algorithm and prove its convergence
properties as opposed to previous work which approximates the mean shift vector. The computational details of our algorithm
are presented for frequently occurring classes of manifolds such as matrix Lie groups, Grassmann manifolds, essential matrices
and symmetric positive definite matrices. Applications of the mean shift over these manifolds are shown. |
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Keywords: | Mean shift Clustering Riemannian manifolds |
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