Mean shift, mode seeking, and clustering

Key Points

• Generalize the mean shift algorithm, establish its theoretical properties in mode seeking and gradient mapping, and examine its convergence behavior in clustering applications.
• Formulated a generalized mean shift procedure using shadow kernels and evaluated its mathematical properties as a gradient mapping under Gaussian kernels.
• Analyzed the convergence of mean shift iterations toward deterministic fixed points and applied the method to clustering and the Hough transform.
• Proved that mean shift operates as a mode-seeking process on kernel-defined surfaces, encompassing k-means-like algorithms as special cases.
• Established convergence of mean shift iterations, showing the procedure acts as an evolutionary multistart global optimization strategy.