Results 1  10
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62
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 ..."
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Cited by 2375 (40 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.
Local adaptivity to variable smoothness for exemplarbased image denoising and representation
, 2005
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Channel smoothing: Efficient robust smoothing of lowlevel signal features
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2006
"... In this paper, we present a new and efficient method to implement robust smoothing of lowlevel signal features: Bspline channel smoothing. This method consists of three steps: encoding of the signal features into channels, averaging of the channels, and decoding of the channels. We show that line ..."
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Cited by 36 (22 self)
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In this paper, we present a new and efficient method to implement robust smoothing of lowlevel signal features: Bspline channel smoothing. This method consists of three steps: encoding of the signal features into channels, averaging of the channels, and decoding of the channels. We show that linear smoothing of channels is equivalent to robust smoothing of the signal features if we make use of quadratic Bsplines to generate the channels. The linear decoding from Bspline channels allows the derivation of a robust error norm, which is very similar to Tukey’s biweight error norm. We compare channel smoothing with three other robust smoothing techniques: nonlinear diffusion, bilateral filtering, and meanshift filtering, both theoretically and on a 2D orientationdata smoothing task. Channel smoothing is found to be superior in four respects: It has a lower computational complexity, it is easy to implement, it chooses the global minimum error instead of the nearest local minimum, and it can also be used on nonlinear spaces, such as orientation space.
On robust estimation and smoothing with spatial and tonal kernels
 Proc. Dagstuhl Seminar: Geometric Properties from Incomplete Data
, 2004
"... This paper deals with establishing relations between a number of widelyused nonlinear filters for digital image processing. We cover robust statistical estimation with (local) Mestimators, local mode filtering in image or histogram space, bilateral filtering, nonlinear diffusion, and regularisatio ..."
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Cited by 32 (8 self)
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This paper deals with establishing relations between a number of widelyused nonlinear filters for digital image processing. We cover robust statistical estimation with (local) Mestimators, local mode filtering in image or histogram space, bilateral filtering, nonlinear diffusion, and regularisation approaches. Although these methods originate in different mathematical theories, we show that their implementation reveals a highly similar structure. We demonstrate that all these methods can be cast into a unified framework of functional minimisation combining nonlocal data and nonlocal smoothness terms. This unification contributes to a better understanding of the individual methods, and it opens the way to new techniques combining the advantages of known filters. Keywords: image analysis, Mestimators, mode filtering, nonlinear diffusion, bilateral filter, regularisation
Image Denoising: Pointwise Adaptive Approach
 Annals of Statistics
, 1998
"... A new method of pointwise adaptation has been proposed and studied in Spokoiny (1998) in context of estimation of piecewise smooth univariate functions. The present paper extends that method to estimation of bivariate greyscale images composed of large homogeneous regions with smooth edges and obse ..."
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Cited by 31 (0 self)
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A new method of pointwise adaptation has been proposed and studied in Spokoiny (1998) in context of estimation of piecewise smooth univariate functions. The present paper extends that method to estimation of bivariate greyscale images composed of large homogeneous regions with smooth edges and observed with noise on a gridded design. The proposed estimator # f(x) at a point x is simply the average of observations over a window # U(x) selected in a datadriven way. The theoretical properties of the procedure are studied for the case of piecewise constant images. We present a nonasymptotic bound for the accuracy of estimation at a specific grid point x as a function of the number of pixel n, of the distance from the point of estimation to the closest boundary and of smoothness properties and orientation of this boundary. It is also shown that the proposed method provides a near optimal rate of estimation near edges and inside homogeneous regions. We briefly discuss algorithmic aspects and the complexity of the procedure. The numerical examples demonstrate a reasonable performance of the method and they are in agreement with the theoretical issues. An example from satellite (SAR) imaging illustrates the applicability of the method. # The authors thank A.Juditski, O. Lepski, A.Tsybakov and Yu.Golubev for important remarks and discussion. polzehl, j. and spokoiny, v. 1 1
Smoothers for discontinuous signals
 J. Nonpar. Statist
, 2002
"... First we explain the interplay between robust loss functions, nonlinear lters and Bayes smoothers for edgepreserving image reconstruction. Then we prove the surprising fact that maximum posterior smoothers are nonlinear lters. A (generalized) Potts prior for segmentation and piecewise smoothing of ..."
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Cited by 26 (8 self)
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First we explain the interplay between robust loss functions, nonlinear lters and Bayes smoothers for edgepreserving image reconstruction. Then we prove the surprising fact that maximum posterior smoothers are nonlinear lters. A (generalized) Potts prior for segmentation and piecewise smoothing of noisy signals and images is adopted. For onedimensional signals, an exact solution for the maximum posterior mode based on dynamic programming is derived. After, some results on the performance of nonlinear lters on jumps and ramps we nally introduce a cascade of nonlinear lters with varying scale parameters and discuss the choice of parameters for segmentation and piecewise smoothing.
Noise Reduction in Images: Some Recent EdgePreserving Methods
, 1999
"... We introduce some recent and very recent smoothing methods which focus on the preservation of boundaries, spikes and canyons in presence of noise. We try to point out basic principles they have in common; the most important one is the robustness aspect. It is reflected by the use of `cup functions&a ..."
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Cited by 23 (5 self)
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We introduce some recent and very recent smoothing methods which focus on the preservation of boundaries, spikes and canyons in presence of noise. We try to point out basic principles they have in common; the most important one is the robustness aspect. It is reflected by the use of `cup functions' in the statistical loss functions instead of squares; such cup functions were introduced early in robust statistics to downweight outliers. Basically, they are variants of truncated squares. We discuss all the methods in the common framework of `energy functions', i.e we associate to (most of ) the algorithms a `loss function' in such a fashion that the output of the algorithm or the `estimate' is a global or local minimum of this loss function. The third aspect we pursue is the correspondence between loss functions and their local minima and nonlinear filters. We shall argue that the nonlinear filters can be interpreted as variants of gradient descent on the loss functions. This way we can ...
Jump surface estimation, edge detection, and image restoration
 Journal of the American Statistical Association
, 2007
"... Surface estimation is important in many applications. When conventional smoothing procedures, such as the running averages, local polynomial kernel smoothing procedures, and smoothing spline procedures, etc., are used for estimating jump surfaces from noisy data, jumps would be blurred at the same t ..."
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Cited by 15 (6 self)
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Surface estimation is important in many applications. When conventional smoothing procedures, such as the running averages, local polynomial kernel smoothing procedures, and smoothing spline procedures, etc., are used for estimating jump surfaces from noisy data, jumps would be blurred at the same time when noise is removed. In recent years, new smoothing methodologies have been proposed in the statistical literature for detecting jumps in surfaces and for estimating jump surfaces with jumps preserved. We provide a review of these methodologies in this paper. Because a monochrome image can be regarded as a jump surface of the image intensity function, with jumps at the outlines of objects, edge detection and image restoration problems in image processing are closely related to the jump surface estimation problem in statistics. In this paper, we also review major methodologies on edge detection and image restoration, and discuss about connections and differences between these methods and the related methods in the statistical literature.
Consistencies and Rates of Convergence of JumpPenalized Least Squares Estimators
"... We study the asymptotics for jumppenalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L 2 ([0,1)) our results cover other metrics like Skorokhod metric on the spac ..."
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Cited by 14 (6 self)
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We study the asymptotics for jumppenalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L 2 ([0,1)) our results cover other metrics like Skorokhod metric on the space of càdlàg functions and uniform metrics on C([0,1]) as well as convergence of the scale spaces, the family of estimates under varying smoothing parameter. We will show that the estimates used are in an adaptive sense rate optimal over the class of functions of bounded variation, (piecewise) Hölder continuous functions of order 1 ≥ α> 0 and the class of step functions. In the latter setting, we will also deduce the rates known from changepoint analysis for detecting the jumps. 1
On detecting jumps in time series  Nonparametric setting
 Journal of Nonparametric Statistics
, 2004
"... Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle ..."
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Cited by 12 (9 self)
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Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle