TL;DR: It is proved the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and, thus, its utility in detecting the modes of the density.
Abstract: A general non-parametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure: the mean shift. For discrete data, we prove the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and, thus, its utility in detecting the modes of the density. The relation of the mean shift procedure to the Nadaraya-Watson estimator from kernel regression and the robust M-estimators; of location is also established. Algorithms for two low-level vision tasks discontinuity-preserving smoothing and image segmentation - are described as applications. In these algorithms, the only user-set parameter is the resolution of the analysis, and either gray-level or color images are accepted as input. Extensive experimental results illustrate their excellent performance.
TL;DR: A new approach toward target representation and localization, the central component in visual tracking of nonrigid objects, is proposed, which employs a metric derived from the Bhattacharyya coefficient as similarity measure, and uses the mean shift procedure to perform the optimization.
Abstract: A new approach toward target representation and localization, the central component in visual tracking of nonrigid objects, is proposed. The feature histogram-based target representations are regularized by spatial masking with an isotropic kernel. The masking induces spatially-smooth similarity functions suitable for gradient-based optimization, hence, the target localization problem can be formulated using the basin of attraction of the local maxima. We employ a metric derived from the Bhattacharyya coefficient as similarity measure, and use the mean shift procedure to perform the optimization. In the presented tracking examples, the new method successfully coped with camera motion, partial occlusions, clutter, and target scale variations. Integration with motion filters and data association techniques is also discussed. We describe only a few of the potential applications: exploitation of background information, Kalman tracking using motion models, and face tracking.
TL;DR: Mean shift, a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed and makes some k-means like clustering algorithms its special cases.
Abstract: Mean shift, a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper. This generalization makes some k-means like clustering algorithms its special cases. It is shown that mean shift is a mode-seeking process on the surface constructed with a "shadow" kernal. For Gaussian kernels, mean shift is a gradient mapping. Convergence is studied for mean shift iterations. Cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data. Applications in clustering and Hough transform are demonstrated. Mean shift is also considered as an evolutionary strategy that performs multistart global optimization. >
TL;DR: The theoretical analysis of the approach shows that it relates to the Bayesian framework while providing a practical, fast and efficient solution for real time tracking of non-rigid objects seen from a moving camera.
Abstract: A new method for real time tracking of non-rigid objects seen from a moving camera is proposed. The central computational module is based on the mean shift iterations and finds the most probable target position in the current frame. The dissimilarity between the target model (its color distribution) and the target candidates is expressed by a metric derived from the Bhattacharyya coefficient. The theoretical analysis of the approach shows that it relates to the Bayesian framework while providing a practical, fast and efficient solution. The capability of the tracker to handle in real time partial occlusions, significant clutter, and target scale variations, is demonstrated for several image sequences.
TL;DR: Applications of gradient estimation to pattern recognition are presented using clustering and intrinsic dimensionality problems, with the ultimate goal of providing further understanding of these problems in terms of density gradients.
Abstract: Nonparametric density gradient estimation using a generalized kernel approach is investigated. Conditions on the kernel functions are derived to guarantee asymptotic unbiasedness, consistency, and uniform consistency of the estimates. The results are generalized to obtain a simple mcan-shift estimate that can be extended in a k -nearest-neighbor approach. Applications of gradient estimation to pattern recognition are presented using clustering and intrinsic dimensionality problems, with the ultimate goal of providing further understanding of these problems in terms of density gradients.