## Edge-preserving image denoising and estimation of discontinuous surfaces (2006)

Venue: | IEEE Transactions on Pattern Analysis and Machine Intelligence |

Citations: | 12 - 6 self |

### BibTeX

@ARTICLE{Gijbels06edge-preservingimage,

author = {Irène Gijbels and Re Lambert and Peihua Qiu},

title = {Edge-preserving image denoising and estimation of discontinuous surfaces},

journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},

year = {2006},

volume = {28},

pages = {1075--1087}

}

### OpenURL

### Abstract

In this paper, we are interested in the problem of estimating a discontinuous surface from noisy data. A novel procedure for this problem is proposed based on local linear kernel smoothing, in which local neighbourhoods are adapted to the local smoothness of the surface measured by the observed data. The procedure can therefore remove noise correctly in continuity regions of the surface, and preserve discontinuities at the same time. Since an image can be regarded as a surface of the image intensity function and such a surface has discontinuities at the outlines of objects, this procedure can be applied directly to image denoising. Numerical studies show that it works well in applications, compared to some existing procedures. Index Terms Corners, edges, jump-preserving estimation, local linear fit, noise, nonparametric regression,

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Citation Context ...s from noisy data. The procedure is constructed in the framework of statistical jump regression analysis (JRA), which is a research area handling regression models involving jumps and discontinuities =-=[1]-=-. Since an image can be regarded as a surface of the image intensity function, this work can be used directly for image restoration, especially for image denoising. Other possible applications include... |

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Citation Context ...r of the true image. To simplify its computation, Besag [6] suggested the iterated conditional modes (ICM) algorithm. Numerous other generalizations and modifications exist in the literature, see [9]-=-=[14]-=-. Image denoising by robust estimation, adaptive smoothing, and bilateral filtering attracts much attention in the literature. Median filtering was first suggested in the statistical literature [15], ... |

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Citation Context ...n the statistical literature [15], and it has become a popular pre-smoothing tool in image processing, because it has a certain ability of preserving edges while removing noise [16], [17], [18], [19]-=-=[21]-=-. To avoid pixels located on two different sides of an edge segment from being averaged in local smoothing, Saint-Marc et al. [22] suggested an adaptive smoothing filter which can adapt to the edge st... |

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Citation Context ...ate the surface with a discontinuity-preserving spline smoothing procedure. Discontinuity-preserving and viewpoint invariant surface estimation procedures have been proposed by several authors (e.g., =-=[38]-=-, [39]). Surface estimation from noisy data can be regarded as a special case of 2-D statistical regression problem (see Section II-A). There are several procedures in the statistical literature for e... |

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Citation Context ...ecial case of 2-D statistical regression problem (see Section II-A). There are several procedures in the statistical literature for estimating surfaces with possible jumps preserved. For example, Qiu =-=[40]-=- proposed a three-stage procedure for this purpose, in which jumps are preserved by fitting local principal component lines. Chu et al. [41] studied the sigma filter and M-smoother. Both of them are b... |

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Citation Context ...y edge preserving regularization methods, i.e. by minimizing an objective function that enforces a roughness penalty, in addition to a term measuring fidelity of the estimator to the data (e.g. [34], =-=[35]-=-, [36]). Discontinuity-preserving surface estimation can be regarded as a more general problem than image denoising, in the sense that image pixels are usually regularly spaced in rows and columns but... |

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Citation Context ...one-sided WRMS’s would be smaller than WRMSc, and thus diff(x, y) would be relatively large. Therefore, diff(x, y) can be used to judge whether there are edge pixels around (x, y). See Gijbels et al. =-=[45]-=- for related discussion. In (5), the case WRMS1(x, y) = WRMS2(x, y) has, for n tending to infinity, probability zero to occur under some regularity conditions. It is included just for completeness. Th... |

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Citation Context ...mator of the true image. To simplify its computation, Besag [6] suggested the iterated conditional modes (ICM) algorithm. Numerous other generalizations and modifications exist in the literature, see =-=[9]-=--[14]. Image denoising by robust estimation, adaptive smoothing, and bilateral filtering attracts much attention in the literature. Median filtering was first suggested in the statistical literature [... |

6 |
Discontinuity-preserving and viewpoint invariant reconstruc- tion of visible surface using a first order regularization
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(Show Context)
Citation Context ...e surface with a discontinuity-preserving spline smoothing procedure. Discontinuity-preserving and viewpoint invariant surface estimation procedures have been proposed by several authors (e.g., [38], =-=[39]-=-). Surface estimation from noisy data can be regarded as a special case of 2-D statistical regression problem (see Section II-A). There are several procedures in the statistical literature for estimat... |

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(Show Context)
Citation Context ...e of the image intensity function, this work can be used directly for image restoration, especially for image denoising. Other possible applications include early vision [2] and computer aided design =-=[3]-=-. In the literature, there are many existing procedures for image restoration. Early work involves mainly Fourier and inverse Fourier transformations and other algebraic manipulations (see e.g., Chapt... |

5 |
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(Show Context)
Citation Context ...ng surfaces with possible jumps preserved. For example, Qiu [40] proposed a three-stage procedure for this purpose, in which jumps are preserved by fitting local principal component lines. Chu et al. =-=[41]-=- studied the sigma filter and M-smoother. Both of them are based on robust estimation and closely related to adaptive smoothing and bilateral filterings4 mentioned above. Polzehl and Spokoiny [42] pro... |

5 | The local piecewisely linear kernel smoothing procedure for fitting jump regression surfaces
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(Show Context)
Citation Context ... Polzehl and Spokoiny [42] proposed the adaptive weights smoothing algorithm, which is an iterative procedure in which the size of a neighbourhood is adaptive to the surface smoothness. Recently, Qiu =-=[43]-=- suggested estimating jump surfaces by local piecewise linear kernel smoothing. The proposed discontinuity-preserving surface estimation procedure is based on local linear kernel smoothing. Its basic ... |

3 |
Gibbs and Markov systems with constraints
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(Show Context)
Citation Context ...eling and the maximum a posteriori (MAP) estimation (e.g., [5], [6]). In these Bayesian image restoration procedures, the equivalence between Gibbs distributions and MRFs plays an important role [7], =-=[8]-=-. Geman and Geman [5] suggested using a stochastic relaxation algorithm and an annealing schedule for computing the MAP estimator of the true image. To simplify its computation, Besag [6] suggested th... |

2 | Constrained restoration and the recovery of distributions - Geman, Reynolds - 1992 |