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247
Mean shift: A robust approach toward feature space analysis
 In PAMI
, 2002
"... A general nonparametric 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. We prove for discrete data the convergence ..."
Abstract

Cited by 1487 (34 self)
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A general nonparametric 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. We prove for discrete data 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 equivalence of the mean shift procedure to the Nadaraya–Watson estimator from kernel regression and the robust Mestimators of location is also established. Algorithms for two lowlevel 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.
An Efficient Approach to Clustering in Large Multimedia Databases with Noise
, 1998
"... Several clustering algorithms can be applied to clustering in large multimedia databases. The effectiveness and efficiency of the existing algorithms, however, is somewhat limited, since clustering in multimedia databases requires clustering highdimensional feature vectors and since multimedia data ..."
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Cited by 207 (9 self)
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Several clustering algorithms can be applied to clustering in large multimedia databases. The effectiveness and efficiency of the existing algorithms, however, is somewhat limited, since clustering in multimedia databases requires clustering highdimensional feature vectors and since multimedia databases often contain large amounts of noise. In this paper, we therefore introduce a new algorithm to clustering in large multimedia databases called DENCLUE (DENsitybased CLUstEring). The basic idea of our new approachis to model the overall point density analytically as the sum of influence functions of the data points. Clusters can then be identified by determining densityattractors and clusters of arbitrary shape can be easily described by a simple equation based on the overall density function. The advantages of our new approach are (1) it has a firm mathematical basis, (2) it has good clustering properties in data sets with large amounts of noise, (3) it allows a compact mathematical ...
Mean Shift Analysis and Applications
, 1999
"... A nonparametric estimator of density gradient, the mean shift, is employed in the joint, spatialrange (value) domain of gray level and color images for discontinuity preserving filtering and image segmentation. Properties of the mean shift are reviewed and its convergence on lattices is proven. The ..."
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Cited by 157 (8 self)
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A nonparametric estimator of density gradient, the mean shift, is employed in the joint, spatialrange (value) domain of gray level and color images for discontinuity preserving filtering and image segmentation. Properties of the mean shift are reviewed and its convergence on lattices is proven. The proposed filtering method associates with each pixel in the image the closest local mode in the density distribution of the joint domain. Segmentation into a piecewise constant structure requires only one more step, fusion of the regions associated with nearby modes. The proposed technique has two parameters controlling the resolution in the spatial and range domains. Since convergence is guaranteed, the technique does not require the intervention of the user to stop the filtering at the desired image quality. Several examples, for gray and color images, show the versatilityofthe method and compare favorably with results described in the literature for the same images.
Improved fast Gauss transform and efficient kernel density estimation
 In ICCV
, 2003
"... Evaluating sums of multivariate Gaussians is a common computational task in computer vision and pattern recognition, including in the general and powerful kernel density estimation technique. The quadratic computational complexity of the summation is a significant barrier to the scalability of this ..."
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Cited by 105 (7 self)
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Evaluating sums of multivariate Gaussians is a common computational task in computer vision and pattern recognition, including in the general and powerful kernel density estimation technique. The quadratic computational complexity of the summation is a significant barrier to the scalability of this algorithm to practical applications. The fast Gauss transform (FGT) has successfully accelerated the kernel density estimation to linear running time for lowdimensional problems. Unfortunately, the cost of a direct extension of the FGT to higherdimensional problems grows exponentially with dimension, making it impractical for dimensions above 3. We develop an improved fast Gauss transform to efficiently estimate sums of Gaussians in higher dimensions, where a new multivariate expansion scheme and an adaptive space subdivision technique dramatically improve the performance. The improved FGT has been applied to the mean shift algorithm achieving linear computational complexity. Experimental results demonstrate the efficiency and effectiveness of our algorithm. 1
Distribution Free Decomposition of Multivariate Data
 Pattern Analysis and Applications
, 1998
"... We present a practical approach to nonparametric cluster analysis of large data sets. The number of clusters and the cluster centers are automatically derived by mode seeking with the mean shift procedure on a reduced set of points randomly selected from the data. The cluster boundaries are delineat ..."
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Cited by 65 (16 self)
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We present a practical approach to nonparametric cluster analysis of large data sets. The number of clusters and the cluster centers are automatically derived by mode seeking with the mean shift procedure on a reduced set of points randomly selected from the data. The cluster boundaries are delineated using a knearest neighbor technique. The proposed algorithm is stable and efficient, a 10000 point data set being decomposed in only a few seconds. Complex clustering examples and applications are discussed, and convergence of the gradient ascent mean shift procedure is demonstrated for arbitrary distribution and cardinality of the data. Keywords: Nonparametric cluster analysis, mode seeking, gradient density estimation, mean shift procedure, convergence, range searching. 1 Introduction In image understanding the feature spaces derived from real data most often have a complex structure and a priori information to guide the analysis may not be available. The significant features whose ...
Video Tooning
, 2004
"... We describe a system for transforming an input video into a highly abstracted, spatiotemporally coherent cartoon animation with a range of styles. To achieve this, we treat video as a spacetime volume of image data. We have developed an anisotropic kernel mean shift technique to segment the video ..."
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Cited by 60 (3 self)
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We describe a system for transforming an input video into a highly abstracted, spatiotemporally coherent cartoon animation with a range of styles. To achieve this, we treat video as a spacetime volume of image data. We have developed an anisotropic kernel mean shift technique to segment the video data into contiguous volumes. These provide a simple cartoon style in themselves, but more importantly provide the capability to semiautomatically rotoscope semantically meaningful regions.
An EMlike algorithm for colorhistogrambased object tracking, in
 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition
"... The iterative procedure called ’meanshift ’ is a simple robust method for finding the position of a local mode (local maximum) of a kernelbased estimate of a density function. A new robust algorithm is given here that presents a natural extension of the ’meanshift ’ procedure. The new algorithm s ..."
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Cited by 54 (5 self)
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The iterative procedure called ’meanshift ’ is a simple robust method for finding the position of a local mode (local maximum) of a kernelbased estimate of a density function. A new robust algorithm is given here that presents a natural extension of the ’meanshift ’ procedure. The new algorithm simultaneously estimates the position of the local mode and the covariance matrix that describes the approximate shape of the local mode. We apply the new method to develop a new 5degrees of freedom (DOF) color histogram based nonrigid object tracking algorithm. 1.
Image and Video Segmentation by Anisotropic Kernel Mean Shift
 In Proc. ECCV
, 2004
"... Mean shift is a nonparametric estimator of density which has been applied to image and video segmentation. Traditional mean shift based segmentation uses a radially symmetric kernel to estimate local density, which is not optimal in view of the often structured nature of image and more particula ..."
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Cited by 47 (1 self)
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Mean shift is a nonparametric estimator of density which has been applied to image and video segmentation. Traditional mean shift based segmentation uses a radially symmetric kernel to estimate local density, which is not optimal in view of the often structured nature of image and more particularly video data. In this paper we present an anisotropic kernel mean shift in which the shape, scale, and orientation of the kernels adapt to the local structure of the image or video. We decompose the anisotropic kernel to provide handles for modifying the segmentation based on simple heuristics. Experimental results show that the anisotropic kernel mean shift outperforms the original mean shift on image and video segmentation in the following aspects: 1) it gets better results on general images and video in a smoothness sense; 2) the segmented results are more consistent with human visual saliency; 3) the algorithm is robust to initial parameters.
Quick shift and kernel methods for mode seeking
 In European Conference on Computer Vision, volume IV
, 2008
"... Abstract. We show that the complexity of the recently introduced medoidshift algorithm in clustering N points is O(N 2), with a small constant, if the underlying distance is Euclidean. This makes medoid shift considerably faster than mean shift, contrarily to what previously believed. We then explo ..."
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Cited by 43 (6 self)
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Abstract. We show that the complexity of the recently introduced medoidshift algorithm in clustering N points is O(N 2), with a small constant, if the underlying distance is Euclidean. This makes medoid shift considerably faster than mean shift, contrarily to what previously believed. We then exploit kernel methods to extend both mean shift and the improved medoid shift to a large family of distances, with complexity bounded by the effective rank of the resulting kernel matrix, and with explicit regularization constraints. Finally, we show that, under certain conditions, medoid shift fails to cluster data points belonging to the same mode, resulting in overfragmentation. We propose remedies for this problem, by introducing a novel, simple and extremely efficient clustering algorithm, called quick shift, that explicitly trades off under and overfragmentation. Like medoid shift, quick shift operates in nonEuclidean spaces in a straightforward manner. We also show that the accelerated medoid shift can be used to initialize mean shift for increased efficiency. We illustrate our algorithms to clustering data on manifolds, image segmentation, and the automatic discovery of visual categories. 1