Markov random field modeling in image analysis
Markov random field modeling in image analysis
Mean Shift: A Robust Approach Toward Feature Space Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms
International Journal of Computer Vision
Mean Shift, Mode Seeking, and Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Mean Shift Analysis and Applications
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Mean Shift Based Clustering in High Dimensions: A Texture Classification Example
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Mean Shift Is a Bound Optimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Understanding and Using Linear Programming (Universitext)
Understanding and Using Linear Programming (Universitext)
A novel and quick SVM-based multi-class classifier
Pattern Recognition
A note on the convergence of the mean shift
Pattern Recognition
Gaussian Mean-Shift Is an EM Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Pose Estimation and Recognition Using Non-Gaussian Modeling of Appearance Subspaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Recognition
Mean shift spectral clustering
Pattern Recognition
Nonlinear Mean Shift over Riemannian Manifolds
International Journal of Computer Vision
Deformed Lattice Detection in Real-World Images Using Mean-Shift Belief Propagation
IEEE Transactions on Pattern Analysis and Machine Intelligence
The estimation of the gradient of a density function, with applications in pattern recognition
IEEE Transactions on Information Theory
Improved neural solution for the Lyapunov matrix equation based on gradient search
Information Processing Letters
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The Mean-Shift (MS) algorithm and its variants have wide applications in pattern recognition and computer vision tasks such as clustering, segmentation, and tracking. In this paper, we study the dynamics of the algorithm with Gaussian kernels, based on a Generalized MS (GMS) model that includes the standard MS as a special case. First, we prove that the GMS has solutions in the convex hull of the given data points. By the principle of contraction mapping, a sufficient condition, dependent on a parameter introduced into Gaussian kernels, is provided to guarantee the uniqueness of the solution. It is shown that the solution is also globally stable and exponentially convergent under the condition. When the condition does not hold, the GMS algorithm can possibly have multiple equilibriums, which can be used for clustering as each equilibrium has its own attractive basin. Based on this, the condition can be used to estimate an appropriate parameter which ensures the GMS algorithm to have its equilibriums suitable for clustering. Examples are given to illustrate the correctness of the condition. It is also shown that the use of the multiple-equilibrium property for clustering, on the data sets such as IRIS, leads to a lower error rate than the standard MS approach, and the K-Means and Fuzzy C-Means algorithms.