Discontinuity Preserving Filtering over Analytic Manifolds.
Raghav Subbarao and Peter Meer
Department of Electrical and Computer Engineering
Rutgers University, Piscataway, NJ 08854, USA
Discontinuity preserving filtering of images is an important
low-level vision task. With the development of new imaging
techniques like diffusion tensor imaging (DTI), where the data
does not lie in a vector space, previous methods like the original
mean shift are not applicable. In this paper, we use the nonlinear
mean shift algorithm to develop filtering methods for data lying
on analytic manifolds. We work out the computational details of
using mean shift on $Sym_n^+$, the manifold of $n\times n$
symmetric positive definite matrices. We apply our algorithm to
chromatic noise filtering, which requires mean shift over the
Grassmann manifold $G_{3,1}$, and obtain better results then
standard mean shift filtering. We also use our method for DTI
filtering, which requires smoothing over $Sym_3^+$.
2007 Computer Vision and Pattern Recognition Conference,
Minneapolis, MN, June 2007.
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