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222
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 1455 (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.
Fast Bilateral Filtering for the Display of HighDynamicRange Images
, 2002
"... We present a new technique for the display of highdynamicrange images, which reduces the contrast while preserving detail. It is based on a twoscale decomposition of the image into a base layer, encoding largescale variations, and a detail layer. Only the base layer has its contrast reduced, the ..."
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Cited by 296 (10 self)
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We present a new technique for the display of highdynamicrange images, which reduces the contrast while preserving detail. It is based on a twoscale decomposition of the image into a base layer, encoding largescale variations, and a detail layer. Only the base layer has its contrast reduced, thereby preserving detail. The base layer is obtained using an edgepreserving filter called the bilateral filter. This is a nonlinear filter, where the weight of each pixel is computed using a Gaussian in the spatial domain multiplied by an influence function in the intensity domain that decreases the weight of pixels with large intensity differences. We express bilateral filtering in the framework of robust statistics and show how it relates to anisotropic diffusion. We then accelerate bilateral filtering by using a piecewiselinear approximation in the intensity domain and appropriate subsampling. This results in a speedup of two orders of magnitude. The method is fast and requires no parameter setting.
Fields of experts: A framework for learning image priors
 In CVPR
, 2005
"... We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach extends traditional Markov Random Field (MRF) models by learning potential functions over extended pixel neighborhood ..."
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Cited by 226 (3 self)
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We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach extends traditional Markov Random Field (MRF) models by learning potential functions over extended pixel neighborhoods. Field potentials are modeled using a ProductsofExperts framework that exploits nonlinear functions of many linear filter responses. In contrast to previous MRF approaches all parameters, including the linear filters themselves, are learned from training data. We demonstrate the capabilities of this Field of Experts model with two example applications, image denoising and image inpainting, which are implemented using a simple, approximate inference scheme. While the model is trained on a generic image database and is not tuned toward a specific application, we obtain results that compete with and even outperform specialized techniques. 1.
Random walks for image segmentation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2006
"... Abstract—A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with userdefined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach on ..."
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Cited by 215 (18 self)
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Abstract—A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with userdefined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a highquality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs. Index Terms—Image segmentation, interactive segmentation, graph theory, random walks, combinatorial Dirichlet problem, harmonic functions, Laplace equation, graph cuts, boundary completion. Ç 1
Prior Learning and Gibbs ReactionDiffusion
, 1997
"... This article addresses two important themes in early visual computation: rst it presents a novel theory for learning the universal statistics of natural images { a prior model for typical cluttered scenes of the world { from a set of natural images, second it proposes a general framework of designi ..."
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Cited by 147 (18 self)
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This article addresses two important themes in early visual computation: rst it presents a novel theory for learning the universal statistics of natural images { a prior model for typical cluttered scenes of the world { from a set of natural images, second it proposes a general framework of designing reactiondiusion equations for image processing. We start by studying the statistics of natural images including the scale invariant properties, then generic prior models were learned to duplicate the observed statistics, based on the minimax entropy theory studied in two previous papers. The resulting Gibbs distributions have potentials of the form U(I; ; S) = P K I)(x; y)) with S = fF g being a set of lters and = f the potential functions. The learned Gibbs distributions con rm and improve the form of existing prior models such as lineprocess, but in contrast to all previous models, inverted potentials (i.e. (x) decreasing as a function of jxj) were found to be necessary. We nd that the partial dierential equations given by gradient descent on U(I; ; S) are essentially reactiondiusion equations, where the usual energy terms produce anisotropic diusion while the inverted energy terms produce reaction associated with pattern formation, enhancing preferred image features. We illustrate how these models can be used for texture pattern rendering, denoising, image enhancement and clutter removal by careful choice of both prior and data models of this type, incorporating the appropriate features. Song Chun Zhu is now with the Computer Science Department, Stanford University, Stanford, CA 94305, and David Mumford is with the Division of Applied Mathematics, Brown University, Providence, RI 02912. This work started when the authors were at ...
Kernel regression for image processing and reconstruction
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2007
"... In this paper, we make contact with the field of nonparametric statistics and present a development and generalization of tools and results for use in image processing and reconstruction. In particular, we adapt and expand kernel regression ideas for use in image denoising, upscaling, interpolation, ..."
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Cited by 110 (50 self)
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In this paper, we make contact with the field of nonparametric statistics and present a development and generalization of tools and results for use in image processing and reconstruction. In particular, we adapt and expand kernel regression ideas for use in image denoising, upscaling, interpolation, fusion, and more. Furthermore, we establish key relationships with some popular existing methods and show how several of these algorithms, including the recently popularized bilateral filter, are special cases of the proposed framework. The resulting algorithms and analyses are amply illustrated with practical examples.
The Variable Bandwidth Mean Shift and DataDriven Scale Selection
 in Proc. 8th Intl. Conf. on Computer Vision
, 2001
"... We present two solutions for the scale selection problem in computer vision. The first one is completely nonparametric and is based on the the adaptive estimation of the normalized density gradient. Employing the sample point estimator, we define the Variable Bandwidth Mean Shift, prove its converge ..."
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Cited by 97 (9 self)
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We present two solutions for the scale selection problem in computer vision. The first one is completely nonparametric and is based on the the adaptive estimation of the normalized density gradient. Employing the sample point estimator, we define the Variable Bandwidth Mean Shift, prove its convergence, and show its superiority over the fixed bandwidth procedure. The second technique has a semiparametric nature and imposes a local structure on the data to extract reliable scale information. The local scale of the underlying density is taken as the bandwidth which maximizes the magnitude of the normalized mean shift vector. Both estimators provide practical tools for autonomous image and quasi realtime video analysis and several examples are shown to illustrate their effectiveness. 1 Motivation for Variable Bandwidth The efficacy of Mean Shift analysis has been demonstrated in computer vision problems such as tracking and segmentation in [5, 6]. However, one of the limitations of the mean shift procedure as defined in these papers is that it involves the specification of a scale parameter. While results obtained appear satisfactory, when the local characteristics of the feature space differs significantly across data, it is difficult to find an optimal global bandwidth for the mean shift procedure. In this paper we address the issue of locally adapting the bandwidth. We also study an alternative approach for datadriven scale selection which imposes a local structure on the data. The proposed solutions are tested in the framework of quasi realtime video analysis. We review first the intrinsic limitations of the fixed bandwidth density estimation methods. Then, two of the most popular variable bandwidth estimators, the balloon and the sample point, are introduced and...
Robust Principal Component Analysis for Computer Vision
, 2001
"... Principal Component Analysis (PCA) has been widely used for the representation of shape, appearance, and motion. One drawback of typical PCA methods is that they are least squares estimation techniques and hence fail to account for "outliers" which are common in realistic training sets. In computer ..."
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Cited by 95 (3 self)
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Principal Component Analysis (PCA) has been widely used for the representation of shape, appearance, and motion. One drawback of typical PCA methods is that they are least squares estimation techniques and hence fail to account for "outliers" which are common in realistic training sets. In computer vision applications, outliers typically occur within a sample (image) due to pixels that are corrupted by noise, alignment errors, or occlusion. We review previous approaches for making PCA robust to outliers and present a new method that uses an intrasample outlier process to account for pixel outliers. We develop the theory of Robust Principal Component Analysis (RPCA) and describe a robust Mestimation algorithm for learning linear multivariate representations of high dimensional data such as images. Quantitative comparisons with traditional PCA and previous robust algorithms illustrate the benefits of RPCA when outliers are present. Details of the algorithm are described and a software implementation is being made publically available.
A Framework for Robust Subspace Learning
 International Journal of Computer Vision
, 2003
"... Many computer vision, signal processing and statistical problems can be posed as problems of learning low dimensional linear or multilinear models. These models have been widely used for the representation of shape, appearance, motion, etc, in computer vision applications. ..."
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Cited by 93 (6 self)
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Many computer vision, signal processing and statistical problems can be posed as problems of learning low dimensional linear or multilinear models. These models have been widely used for the representation of shape, appearance, motion, etc, in computer vision applications.
Variational Problems and Partial Differential Equations on Implicit Surfaces: The Framework and Examples in Image Processing and Pattern Formation
, 2000
"... this paper. The key ..."