Nonlinear Mean Shift over Riemannian Manifolds

Authors:
Raghav Subbarao;Peter Meer
Affiliations:
Electrical and Computer Engineering Department, Rutgers University, Piscataway, USA 08854-8058;Electrical and Computer Engineering Department, Rutgers University, Piscataway, USA 08854-8058
Venue:
International Journal of Computer Vision
Year:
2009

Citing 31
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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.