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Robust Statistics over Analytic Manifolds for Computer Vision

Raghav Subbarao

Monday, November 12, 2007, 01:00pm - 02:00pm

Rutgers University, Center for Advanced Information Processing (CAIP)

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Many low-level and mid-level vision tasks involve the estimation of parameters in the presence of noise and outliers. The use of parametric models at this stage may lead to incorrect results which are compounded by the high-level modules of a vision system. An alternative to this is the use of nonparametric techniques for the analysis of visual data. The original mean shift algorithm is one such nonparametric method which has been widely used in computer vision for tracking, robust fusion, smoothing and segmentation. In all previous applications of mean shift, it has always been applied to vector spaces. However, in practice the geometric constraints involved in the problem and the nature of the imaging device, lead to feature spaces which are not vector spaces. Most of these feature spaces still exhibit a regular geometry and belong to the class of analytic manifolds, which have been well studied in fields such as differential geometry. We develop a Nonlinear Mean Shift algorithm which is a generalization of mean shift to analytic manifolds. Applications of nonlinear mean shift include motion segmentation and image filtering. We present examples of commonly occurring manifolds and show the results of motion segmentation and image filtering. Theoretical properties of nonlinear mean shift are also discussed.


Background Reading:">

O. Tuzel, R. Subbarao, P. Meer:  Simultaneous multiple 3D motion estimation via mode finding on Lie groups.
R. Subbarao, P. Meer:  Nonlinear mean shift for clustering over analytic manifolds.
R. Subbarao, P. Meer:  Discontinuity Preserving Filtering over Analytic Manifolds.

Raghav Subbarao