Polynomial-time approximation schemes for geometric min-sum median clustering
Journal of the ACM (JACM)
Mean Shift: A Robust Approach Toward Feature Space Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Some extensions of Tukey's depth function
Journal of Multivariate Analysis
Mean Shift, Mode Seeking, and Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust analysis of feature spaces: color image segmentation
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Locality-sensitive hashing scheme based on p-stable distributions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Efficient Image Segmentation by Mean Shift Clustering and MDL-Guided Region Merging
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
Efficient Mean-Shift Tracking via a New Similarity Measure
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
On k-Median clustering in high dimensions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Nonlinear Mean Shift for Clustering over Analytic Manifolds
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Pattern Recognition
Computational Statistics & Data Analysis
Geometric Mean for Subspace Selection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear Mean Shift over Riemannian Manifolds
International Journal of Computer Vision
Performance evaluation of density-based clustering methods
Information Sciences: an International Journal
Camera calibration and geo-location estimation from two shadow trajectories
Computer Vision and Image Understanding
Geometric median-shift over Riemannian manifolds
PRICAI'10 Proceedings of the 11th Pacific Rim international conference on Trends in artificial intelligence
Enhanced clustering of biomedical documents using ensemble non-negative matrix factorization
Information Sciences: an International Journal
Contour Detection and Hierarchical Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Artificial immune multi-objective SAR image segmentation with fused complementary features
Information Sciences: an International Journal
Segmentation of multiple sclerosis lesions in brain MRI: A review of automated approaches
Information Sciences: an International Journal
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The mean shift algorithms have been successfully applied to many areas, such as data clustering, feature analysis, and image segmentation. However, they still have two limitations. One is that they are ineffective in clustering data with low dimensional manifolds because of the use of the Euclidean distance for calculating distances. The other is that they sometimes produce poor results for data clustering and image segmentation. This is because a mean may not be a point in a data set. In order to overcome the two limitations, we propose a novel approach for the median shift over Riemannian manifolds that uses the geometric median and geodesic distances. Unlike the mean, the geometric median of a data set is one of points in the set. Compared to the Euclidean distance, the geodesic distances can better describe data points distributed on Riemannian manifolds. Based on these two facts, we first present a novel density function that characterizes points on a manifold with the geodesic distance. The shift of the geometric median over the Riemannian manifold is derived from maximizing this density function. After this, we present an algorithm for geometric median shift over Riemannian manifolds, together with theoretical proofs of its correctness. Extensive experiments have demonstrated that our method outperforms the state-of-the-art algorithms in data clustering, image segmentation, and noise filtering on both synthetic data sets and real image databases.