Mean shift is an iterative algorithm that shifts each data point to the average of nearby points. This paper generalizes and analyzes mean shift, showing it as a mode-seeking process on a surface constructed with a "shadow" kernel. For Gaussian kernels, mean shift is a gradient mapping. The algorithm is studied for convergence and applied to clustering and Hough transform. Mean shift is also considered as an evolutionary strategy for global optimization. The paper generalizes mean shift by allowing non-flat kernels, weighted data points, and shifts on any subset of the space. It defines kernels with five operations and discusses how k-means clustering is a limit case of mean shift. A "shadow" kernel is defined, showing that mean shift on any kernel is equivalent to gradient ascent on the density estimated with its shadow. Convergence and rate are analyzed, and the algorithm's behavior in cluster analysis is discussed, with applications in Hough transform. Mean shift is shown to be a deterministic process for finding fixed points in cluster analysis. It is also transformed into a probabilistic evolutionary strategy for global optimization. The paper demonstrates that mean shift can be used for clustering and global optimization, with applications in data analysis and pattern recognition. The algorithm is shown to converge to local maxima of the data density function, and its effectiveness in adapting step size makes it more effective than gradient descent methods. The paper concludes that mean shift is a natural and effective method for data clustering and optimization, with potential applications in various fields.Mean shift is an iterative algorithm that shifts each data point to the average of nearby points. This paper generalizes and analyzes mean shift, showing it as a mode-seeking process on a surface constructed with a "shadow" kernel. For Gaussian kernels, mean shift is a gradient mapping. The algorithm is studied for convergence and applied to clustering and Hough transform. Mean shift is also considered as an evolutionary strategy for global optimization. The paper generalizes mean shift by allowing non-flat kernels, weighted data points, and shifts on any subset of the space. It defines kernels with five operations and discusses how k-means clustering is a limit case of mean shift. A "shadow" kernel is defined, showing that mean shift on any kernel is equivalent to gradient ascent on the density estimated with its shadow. Convergence and rate are analyzed, and the algorithm's behavior in cluster analysis is discussed, with applications in Hough transform. Mean shift is shown to be a deterministic process for finding fixed points in cluster analysis. It is also transformed into a probabilistic evolutionary strategy for global optimization. The paper demonstrates that mean shift can be used for clustering and global optimization, with applications in data analysis and pattern recognition. The algorithm is shown to converge to local maxima of the data density function, and its effectiveness in adapting step size makes it more effective than gradient descent methods. The paper concludes that mean shift is a natural and effective method for data clustering and optimization, with potential applications in various fields.