This paper generalizes and analyzes the mean shift algorithm, a simple iterative procedure that shifts each data point to the average of its neighborhood. The generalization includes nonflat kernels, weighted points, and the ability to perform shifts on any subset of the space while keeping the dataset fixed. The mean shift algorithm is shown to be equivalent to gradient ascent for density estimation using a "shadow" kernel. Convergence properties are studied, and the algorithm is treated as a deterministic problem of finding a fixed point that characterizes the data. Applications in clustering and Hough transform are demonstrated, and the mean shift algorithm is also considered as an evolutionary strategy for global optimization. The paper provides a comprehensive treatment of the mean shift algorithm, highlighting its properties and potential applications.This paper generalizes and analyzes the mean shift algorithm, a simple iterative procedure that shifts each data point to the average of its neighborhood. The generalization includes nonflat kernels, weighted points, and the ability to perform shifts on any subset of the space while keeping the dataset fixed. The mean shift algorithm is shown to be equivalent to gradient ascent for density estimation using a "shadow" kernel. Convergence properties are studied, and the algorithm is treated as a deterministic problem of finding a fixed point that characterizes the data. Applications in clustering and Hough transform are demonstrated, and the mean shift algorithm is also considered as an evolutionary strategy for global optimization. The paper provides a comprehensive treatment of the mean shift algorithm, highlighting its properties and potential applications.