Mean Shift: Construction and Convergence Proof

In most low-level computer vision problems, very little information (if any) is known about the true underlying probability density function, such as its shape, number of mixture components, etc.. Due to this lack of knowledge, parametric approaches are less relevant, rather one has to rely on non-parametric methods. In this note we consider the construction and convergence proof of the non-parametric mean shift method which was developed by Fukunaga and Hostetler (Fukunaga & Hostetler, 1975), later adapted by Cheng (Cheng, 1995) for the purpose of image analysis and more recently popularized in the computer vision literature by Comaniciu and Meer (Comaniciu & Meer, 2002). The mean shift procedure represents a simple iterative non-parametric procedure for density mode seeking. For a general treatment of density estimation the reader is referred to (Silverman, 1998).