### Citations

2267 | Nonlinear total variation based noise removal algorithms
- Rudin, Osher, et al.
- 1992
(Show Context)
Citation Context ... image by the AMSS equation commutes with any affine transformation or contrast change. 2.2 The total variation minimization The Total variation minimization was introduced by Rudin, Osher and Fatemi =-=[70]-=-. Given a noisy image v(x), the above mentioned authors proposed to recover the originals2. Denoising algorithms 13 image u(x) as the solution of a constrained minimization problem � arg min |Du|, (0.... |

1800 |
Exploratory Data Analysis”,
- Tukey
- 1977
(Show Context)
Citation Context ...te and keeps the original values. Thus, it maintains dirt and sparkle. Since the neighborhood filters average pixels with a similar grey level value, they also keep these artifacts. The median filter =-=[80]-=- chooses the median value, that is, the value which has exactly the same number of grey level values above and below in a fixed neighborhood. This filter is optimal for the removal of impulse noise on... |

1154 | Bilateral filtering for gray and color images
- Tomasi, Manduchi
- 1998
(Show Context)
Citation Context ...arity and C(x) = � |u(y)−u(x)|2 Bρ(x) e− h2 dy is the normalization factor. The Yaroslavsky filter (2.1) is less known than more recent versions, namely the SUSAN filter [76] and the Bilateral filter =-=[79]-=-. Both algorithms, instead of considering a fixed spatial neighborhood Bρ(x), weigh the distance to the reference pixel x, where C(x) = � Ω SNFh,ρu(x) = 1 � |y−x|2 − u(y)e ρ C(x) Ω 2 |u(y)−u(x)|2 − e ... |

404 | The curvelet transform for image denoising.”
- Starck, Candes, et al.
- 2002
(Show Context)
Citation Context ...fect and an over smoothing of the image boundaries. More recent thresholding methods try to build redundant transforms more adapted to the geometry of the image as the bandlets [64] and the curvelets =-=[77]-=-. A different field of research is due to Cohen et al. [20, 3]. The authors introduce multiscale representations incorporating a specific geometric treatment of the edges. These ideas are closed to th... |

341 | Iterative methods for total variation denoising - Vogel, Oman - 1996 |

308 |
Anisotropic Diffusion
- Weickert
- 1998
(Show Context)
Citation Context ...normal system was first proposed for vector valued image analysis in [90]. Many PDE equations have been proposed for color image filtering using this system. We note the Coherence Enhancing Diffusion =-=[84]-=-, the Beltrami Flow [41] and an extension of the mean curvature motion [72]. Theorem 2.10 Suppose u ∈ C 2 (Ω, R n ), and let ρ, h, α > 0 such that ρ, h → 0 and h = O(ρ α ). Let ˜ f be the continuous f... |

273 | Susan - a new approach to low level image processing,”
- Smith, Brady
- 1997
(Show Context)
Citation Context ...ed, h controls the color similarity and C(x) = � |u(y)−u(x)|2 Bρ(x) e− h2 dy is the normalization factor. The Yaroslavsky filter (2.1) is less known than more recent versions, namely the SUSAN filter =-=[76]-=- and the Bilateral filter [79]. Both algorithms, instead of considering a fixed spatial neighborhood Bρ(x), weigh the distance to the reference pixel x, where C(x) = � Ω SNFh,ρu(x) = 1 � |y−x|2 − u(y)... |

231 | FRAME: Filters, random fields and maximum entropy—to a unified theory for texture modeling
- Zhu, Wu, et al.
- 1996
(Show Context)
Citation Context ...images is a very difficult task. The complexity of the geometry and the richness of textures and details make nearly impossible to generate a unified model. Despite of the advances made in this field =-=[91, 30]-=-, we will rarely have a statistical model for u. In that case, we deal with the single image and try to minimize the estimation error for it. The results of the Bayesian approach motivate the introduc... |

198 | Modeling textures with total variation minimization and oscillating patterns in image processing,”
- Vese, Osher
- 2003
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Citation Context ... by Meyer as the right space to model oscillatory patterns such as textures. The main focus of this method is not yet denoising. Because of the different and more ambitious scopes of the Meyer method =-=[5, 81, 62]-=-, which makes it parameter- and implementation-dependent, we could not draw it into the discussion. Last but not least, let us mention the bandlet [64] and curvelet [77] transforms for image analysis.... |

172 |
Anisotropic diffusion of multivalued images with applications to color filtering,”
- Sapiro, Ringach
- 1996
(Show Context)
Citation Context ...Many PDE equations have been proposed for color image filtering using this system. We note the Coherence Enhancing Diffusion [84], the Beltrami Flow [41] and an extension of the mean curvature motion =-=[72]-=-. Theorem 2.10 Suppose u ∈ C 2 (Ω, R n ), and let ρ, h, α > 0 such that ρ, h → 0 and h = O(ρ α ). Let ˜ f be the continuous function defined as ˜ f(0) = 1 6 , for t �= 0, where E(t) = 2 � t 0 e−s2 1. ... |

168 |
Total variation based image restoration with free local constraints
- Rudin, Osher
- 1994
(Show Context)
Citation Context ... and is experimentally patent in Figure 2.4. �s46 Local smoothing filters and PDEs. Neighborhood filters 2.4 Total variation The Total variation minimization was introduced by Rudin, Osher and Fatemi =-=[69, 70]-=-. The original image u is supposed to have a simple geometric description, namely a set of connected sets, the objects, along with their smooth contours, or edges. The image is smooth inside the objec... |

156 |
A note on the gradient of a multi-image,”
- Zenzo
- 1986
(Show Context)
Citation Context ...ighborhood filters corresponding eigenvectors are orthogonal leading to the above defined normal and tangent directions. This orthonormal system was first proposed for vector valued image analysis in =-=[90]-=-. Many PDE equations have been proposed for color image filtering using this system. We note the Coherence Enhancing Diffusion [84], the Beltrami Flow [41] and an extension of the mean curvature motio... |

132 |
Curvature and the Evolution of Fronts,
- Sethian
- 1985
(Show Context)
Citation Context ..., endowed in a more general shape analysis framework, the simplest equation of the list, � � Du ut = |Du|div = uξξ. |Du| This equation had been proposed some time before in another context by Sethian =-=[73]-=- as a tool for front propagation algorithms. This last equation is a “pure” diffusion in the tangent direction to the level line passing through x. It can be shown that the evolution of the image by t... |

107 |
The mathematical theory of communication.
- EC, Weaver
- 1949
(Show Context)
Citation Context ... accuracy are categorized as blur and noise. Blur is intrinsic to image acquisition systems, as digital images have a finite number of samples and must satisfy the Shannon–Nyquist sampling conditions =-=[75]-=-. The second main image perturbation is noise. In any digital image, the measurement of the three observed color values is subject to some perturbations. Each one of the pixel values u(i) is the resul... |

105 |
Variational optic flow computation with a spatio-temporal smoothness constraint”,
- Weickert, Schnorr
- 2001
(Show Context)
Citation Context ... for instance [58]. This type of algorithms is local in time, and two frames are in general enough to compute the optical flow. In this work, we shall use the method developed by Weickert and Schnorr =-=[85]-=-. The spatial regularization term is replaced by a spatiotemporal one. The minimized energy is now a three dimensional integral whose solution is the optical flow for all the frames t ∈ [O, T ]: � E(v... |

99 | Universal discrete denoising: Known channel
- Weissman, Ordentlich, et al.
- 2005
(Show Context)
Citation Context ...n the image values in a window around a pixel and the pixel value at the window center.s3.1. Statistical neighborhood approaches 77 3.1.1 DUDE, a universal denoiser The recent work by Weissman et al. =-=[86]-=- has led to the proposition of a “universal denoiser” for digital images. The authors assume that the noise model is fully known, namely the probability transition matrix Π(a, b), where a, b ∈ A, the ... |

71 | A multiscale image representation using hierarchical (BV,L2) decompositions.
- Tadmor, Nezzar, et al.
- 2004
(Show Context)
Citation Context ...e removed noise, v(x) − u(x), is treated as an error and is no longer studied. In practice, some structures and texture are present in this error. Several recent works have tried to avoid this effect =-=[60, 78]-=-. The Tadmor et al. approach In [78], the authors have proposed to use the Rudin-Osher-Fatemi iteratively. They decompose the noisy image, v = u0 + n0 by the total variation model. So taking u0 to con... |

38 |
Digital Picture Processing - An Introduction”,
- Yaroslavsky
- 1985
(Show Context)
Citation Context ...exactly the technique of the sigma-filter. This famous algorithm is generally attributed to J.S. Lee [46] in 1983 but can be traced back to L. Yaroslavsky and the Soviet Union image processing school =-=[89]-=-. The idea is to average neighboring pixels which also have a similar color value. The filtered value by this strategy can be written YNFh,ρu(x) = 1 C(x) � Bρ(x) |u(y)−u(x)|2 − u(y)e h2 dy, (0.2)s2. D... |

16 |
Local adaptive image restoration and enhancement with the use of dft and dct in a running window
- Yaroslavsky
- 1996
(Show Context)
Citation Context ...moment, the way seems to be a dictionary of basis instead of one single basis, [51]. 1.3.1 Local adaptive filters in transform Domain The local adaptive filters have been introduced by L. Yaroslavsky =-=[87, 88]-=-. The noisy image is analyzed in a moving window and in each position of the window its spectrum is computed and modified. Finally, an inverse transform is used to estimate only the signal value in th... |

9 |
An adaptive image sequence filtering scheme based on motion detection”,
- Samy
- 1985
(Show Context)
Citation Context ...t , j0 + w t ). Following this scheme, all of the previous static filters can be compensated. Many of these motion compensated denoising algorithms have been directly proposed in the literature. Samy =-=[71]-=- and Sezan et al. [74] proposed the LMMSE filter which is a motion compensation of the statistical correction of the mean filter. Ozkan et al [63] proposed the AWA filter which is in fact a motion com... |

8 |
Smooth regression analysis, The Indian
- Watson
- 1964
(Show Context)
Citation Context ...be taken as small as possible. Let X and Y be distributed as X1 and Y1. Under this form the NL-means algorithm can be seen as an instance for the exponential operator of the Nadaraya–Watson estimator =-=[57, 83]-=-. This is an estimator of the conditional expectation r(x) = E[φ(Y ) | X = x]. Probability Framework The NL-means algorithm is intuitively consistent under stationarity conditions, saying that one can... |

6 |
Temporally adaptive filtering of noisy sequences using a robust motion estimation algorithm”,
- Sezan, Ozkan, et al.
- 1991
(Show Context)
Citation Context ...ing this scheme, all of the previous static filters can be compensated. Many of these motion compensated denoising algorithms have been directly proposed in the literature. Samy [71] and Sezan et al. =-=[74]-=- proposed the LMMSE filter which is a motion compensation of the statistical correction of the mean filter. Ozkan et al [63] proposed the AWA filter which is in fact a motion compensation of the neigh... |