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## Image thresholding based on the EM algorithm and the generalized Gaussian distribution, Pattern Recognition 40 (2 (2007)

Citations: | 20 - 1 self |

### Citations

11693 | Maximum Likelihood from Incomplete Data via the EM Algorithm
- Dempster, Laird, et al.
- 1977
(Show Context)
Citation Context ...as it is an intrinsically ill-posed problem (many-to-one mapping) that can result in different solutions. A possible choice to obtain ML estimates of the mixture parameters is to use the EM algorithm =-=[29]-=-. It is based on the interpretation of X as incomplete data, where the missing part is Y (i.e., the thresholded image). In other words, the missing part can be evaluated as a set of L labels Z = {z(x)... |

10040 |
Genetic Algorithms
- Goldberg
- 1989
(Show Context)
Citation Context ...t each iteration of the optimization process, they retain a large number of candidate solutions and (ii) they do not base the search on the gradient principle but directly on the function to optimize =-=[36,37]-=-. The choice to adopt GAs for initializing the parameters of the distributions of classes mainly depends on the aforementioned properties of this optimization method. Since the initial values of the s... |

2761 |
Pattern Classification
- Duda, Hart, et al.
- 2001
(Show Context)
Citation Context ...han the proposed method. Another advantage of the proposed method lies in the possibility of applying any kind of decision rule (e.g., minimum cost, minimum risk, spatial context-based decision rules =-=[41]-=-) for selecting the optimal threshold value thanks to its explicit unbiased estimation of the class statistical parameters. Fig. 15. Change-detection maps obtained by thresholding the log-ratio image ... |

2170 |
A threshold selection method from gray-level histograms”, in proceedings of
- Otsu
- 1979
(Show Context)
Citation Context ...right-hand side of the 620 Y. Bazi et al. / Pattern Recognition 40 (2007) 619–634 threshold estimated at the previous iteration. This iterative process continues until convergence is reached. In Ref. =-=[11]-=-, the authors propose to select the optimal threshold value through a discriminant criterion that defines a separability measure between the object and background classes on the basis of second-order ... |

1687 |
Finite Mixture Models
- McLachlan, Peel
(Show Context)
Citation Context ...e of multiple random initial conditions to generate multiple solutions and then chose the one that produces the highest likelihood [33,34]. Others are based on initialization by clustering algorithms =-=[33,35]-=- or under a tree structure scheme [27]. In this paper, we propose to use GAs as an alternative solution to the problem of initialization. GAs represent a well-known family of methods for global optimi... |

1519 | Handbook of Genetic Algorithms
- Davis
- 1991
(Show Context)
Citation Context ...r than the user-defined probability of mutation PM . Then, a position in the offspring is selected randomly and the corresponding value is perturbed by a random noise following a uniform distribution =-=[38]-=-. At the end of the mutation operation, a new generation of the S/2 chromosomes selected from the previous generation and their corresponding S/2 offspring is obtained. (4) Convergence criterion: The ... |

1430 |
The EM Algorithm and Extensions
- McLachlan, Krishnan
- 2008
(Show Context)
Citation Context ...igin of the realization x. It is a binary vector given by z(x) = {z1(x), z2(x)} with zi(x) = 1 if x belongs to the component i and zi(x)=0 otherwise. The complete data log likelihood function becomes =-=[30]-=-: L(X,Z, ) = 2∑ i=1 L−1∑ x=0 zi(x)h(x) ln[Pipi(x|i )], (7) where i = [i , i , i]. In the case of a GG distribution, it is possible to prove that the complete log likelihood is given by L(X,Z, )... |

423 | A survey over image thresholding techniques and quantitative performance evaluation - Sankur, Sezgin - 2004 |

241 | Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance
- Do, Vetterli
- 2002
(Show Context)
Citation Context ...this paper for modeling the two class-conditional densities Fig. 1. GG distribution plotted for different shape parameters in the assumption of zero mean and scale parameter equal to one. is given by =-=[28]-=- pi(x|i ) = i2i(1/i ) e−[|x−i |/i ]i , i = 1, 2, (3) where i , i and i are the mean, the scale, and the shape parameters of the ith class-conditional distribution, respectively, and (·) is... |

237 |
A new method for gray-level picture thresholding using the entropy of the histogram
- Kapur, Sahoo, et al.
- 1985
(Show Context)
Citation Context ...d on the moment preserving principle is presented, in which the threshold value is selected in such a way that the first three moments of the original image are preserved in the binary image. In Ref. =-=[13]-=-, the threshold value is identified by maximizing the sum of entropies of object and background classes of the image. In Ref. [14], a method that optimizes a criterion function based on the Bayes clas... |

207 | Discriminant analysis by gaussian mixtures
- Hastie, Tibshirani
- 1994
(Show Context)
Citation Context ...ods are reported in the literature. Some of these are based on the use of multiple random initial conditions to generate multiple solutions and then chose the one that produces the highest likelihood =-=[33,34]-=-. Others are based on initialization by clustering algorithms [33,35] or under a tree structure scheme [27]. In this paper, we propose to use GAs as an alternative solution to the problem of initializ... |

171 |
Picture thresholding using an iterative selection method
- Ridler, Calvard
- 1978
(Show Context)
Citation Context ...c approach does not make any assumption about the class statistical distributions. Among the early global thresholding techniques available in the literature, one can find the work presented in Refs. =-=[9,10]-=-. In this iterative method, the threshold value is first initialized with the mean of the entire histogram. Then at each iteration the new threshold value is computed as the average of the two mean va... |

114 |
Moment-preserving thresholding: a new approach
- Tsai
- 1985
(Show Context)
Citation Context ...e to select the optimal threshold value through a discriminant criterion that defines a separability measure between the object and background classes on the basis of second-order statistics. In Ref. =-=[12]-=-, a method based on the moment preserving principle is presented, in which the threshold value is selected in such a way that the first three moments of the original image are preserved in the binary ... |

106 |
Adaptive speckle filters and scene heterogeneity
- Lopes, Touzi, et al.
- 1990
(Show Context)
Citation Context ...se effects that make separation between changed and unchanged classes difficult, we applied two iterations of the enhanced Lee filter with a window size of 5 × 5 pixels to the two original SAR images =-=[39]-=-. Then, according to what usually done in the context of change detection in SAR imagery [40], changes can be identified by thresholding the log-ratio image generated from the filtered images (see Fig... |

97 | Bayesian approaches to Gaussian mixture modeling
- Roberts, Husmeier, et al.
- 1998
(Show Context)
Citation Context ...ods are reported in the literature. Some of these are based on the use of multiple random initial conditions to generate multiple solutions and then chose the one that produces the highest likelihood =-=[33,34]-=-. Others are based on initialization by clustering algorithms [33,35] or under a tree structure scheme [27]. In this paper, we propose to use GAs as an alternative solution to the problem of initializ... |

92 |
Automatic analysis of the difference image for unsupervised change detection
- Bruzzone, Prieto
- 2005
(Show Context)
Citation Context ...ion. In the literature, the EM algorithm has already been used for global image histogram thresholding [27] and for the complex problem of change detection in multitemporal remote-sensing (RS) images =-=[4]-=- by assuming that the two above classes follow a Gaussian distribution. In order to cope with the limitations of the Gaussian model, an approach combining the EM algorithm with a semi-parametric model... |

85 | A comparative performance study of several global thresholding techniques for segmentation - Lee, Shung, et al. - 1990 |

62 |
Automatic Target Recognition: State of the Art Survey
- Bhanu
- 1986
(Show Context)
Citation Context ...as object (or vice versa). Image thresholding is widely used in many application domains, such as biomedical image analysis [1], handwritten character identification [2], automatic target recognition =-=[3]-=-, change-detection applications [4–6], etc. In general, automatic thresholding techniques are classified into two main groups: global methods and local methods. Global methods adopt a fixed threshold ... |

54 | Evaluation of global image thresholding for change detection - Rosin, Ioannidis - 2003 |

53 |
An adaptive semiparametric and context-based approach to unsupervised change detection in multitemporal remote-sensing images
- Bruzzone, Prieto
- 2002
(Show Context)
Citation Context ...Gaussian distribution. In order to cope with the limitations of the Gaussian model, an approach combining the EM algorithm with a semi-parametric model based on the Parzen window was proposed in Ref. =-=[5]-=-. In spite of the fact that this approach has proved effective in many thresholding problems for complex cases, it may exhibit problems of stability due: (i) to the relatively large number of paramete... |

47 |
Automatic thresholding of gray-level pictures using twodimensional entropy
- Abutaleb
- 1989
(Show Context)
Citation Context ... [15], the optimal threshold is determined by maximizing the posterior entropy subject to inequality constraints derived from measures of the uniformity and shape of the regions in the image. In Ref. =-=[16]-=-, an extension of the methods presented in Refs. [13,15] using 2-D entropies is proposed. The 2-D entropies are obtained from a bi-dimensional histogram constructed using the gray-level values and the... |

37 |
Abdelmalek , Maximum likelihood thresholding based on population mixture models
- Kurita, Otsu, et al.
- 1992
(Show Context)
Citation Context ...ted in Refs. [13,15] using 2-D entropies is proposed. The 2-D entropies are obtained from a bi-dimensional histogram constructed using the gray-level values and the local average gray values. In Ref. =-=[17]-=-, a maximum likelihood (ML) thresholding method based on a population of Gaussian mixtures is introduced. In this work, the authors show that the maximization of the likelihood of the conditional dist... |

34 | Image segmentation by histogram thresholding using fuzzy sets - Tobias, Seara |

31 |
Integral Ratio: A New Class of Global Thresholding Techniques for Handwriting Images
- Solihin, Leedham
- 1999
(Show Context)
Citation Context ...ove this threshold are classified as object (or vice versa). Image thresholding is widely used in many application domains, such as biomedical image analysis [1], handwritten character identification =-=[2]-=-, automatic target recognition [3], change-detection applications [4–6], etc. In general, automatic thresholding techniques are classified into two main groups: global methods and local methods. Globa... |

21 |
Adaptive thresholding by variational method
- Chan, Lam, et al.
- 1995
(Show Context)
Citation Context ...d and object classes have statistical properties that are not stationary in the different portions of the analyzed image (for example, due to nonhomogeneous light conditions) (see, for example, Refs. =-=[7,8]-=-). In this paper, we address the former group, i.e. global thresholding methods. Many techniques for global image thresholding have been proposed in the literature [9–22]. They are generally based on ... |

21 |
Image thresholding by minimizing the measures of fuzziness, Pattern Recognit
- Huang, Wang
- 1995
(Show Context)
Citation Context ...e results provided by the proposed method were compared with those yielded by a set of four thresholding techniques widely used in the literature, i.e. Otsu’s [11], K&I’s [14], Kapur’s [13] and H&W’s =-=[20]-=- techniques. In all experiments, we adopted the following parameters for the GA-based initialization procedure: population size S = 50, crossover probability PC = 0.9, mutation probability PM = 0.1, a... |

20 |
Minimum error thresholding [J]. Pattern Recognition
- Kittler, Illingworth
- 1986
(Show Context)
Citation Context ...ents of the original image are preserved in the binary image. In Ref. [13], the threshold value is identified by maximizing the sum of entropies of object and background classes of the image. In Ref. =-=[14]-=-, a method that optimizes a criterion function based on the Bayes classification rule for minimum error and on the Gaussian assumption for object and background classes is presented. In Ref. [15], the... |

17 | A gray-level threshold selection method based on maximum entropy principle - Wong, Sahoo - 1989 |

13 |
Comments on 'picture thresholding using an iterative selection method
- Trussell
- 1979
(Show Context)
Citation Context ...c approach does not make any assumption about the class statistical distributions. Among the early global thresholding techniques available in the literature, one can find the work presented in Refs. =-=[9,10]-=-. In this iterative method, the threshold value is first initialized with the mean of the entire histogram. Then at each iteration the new threshold value is computed as the average of the two mean va... |

13 |
Zyl, “Change detection techniques for ERS 1
- Rignot, Van
- 1993
(Show Context)
Citation Context ...wo iterations of the enhanced Lee filter with a window size of 5 × 5 pixels to the two original SAR images [39]. Then, according to what usually done in the context of change detection in SAR imagery =-=[40]-=-, changes can be identified by thresholding the log-ratio image generated from the filtered images (see Fig. 14). Table 5 shows the results achieved with the different thresholding methods. The thresh... |

11 | Thresholding using two dimensional histogram and fuzzy entropy principle - Cheng, Chen, et al. - 2000 |

11 | Unsupervised change-detection methods for remote-sensing images - Melgani, Moser, et al. - 2002 |

7 | Glasbey, "An analysis of histogram based thresholding algorithms - A - 1993 |

5 |
An algorithm for fast adaptive binarization with applications in radiotherapy imaging
- Sund, Eilertsen
(Show Context)
Citation Context ...ssified as background, while the values above this threshold are classified as object (or vice versa). Image thresholding is widely used in many application domains, such as biomedical image analysis =-=[1]-=-, handwritten character identification [2], automatic target recognition [3], change-detection applications [4–6], etc. In general, automatic thresholding techniques are classified into two main group... |

3 |
algorithm for image segmentation initialized by a tree structure scheme
- Fwu, Djuric, et al.
- 1997
(Show Context)
Citation Context ... object and background classes, which are assumed to follow a generalized Gaussian (GG) distribution. In the literature, the EM algorithm has already been used for global image histogram thresholding =-=[27]-=- and for the complex problem of change detection in multitemporal remote-sensing (RS) images [4] by assuming that the two above classes follow a Gaussian distribution. In order to cope with the limita... |

2 |
Maximum entropy segmentation based on the autocorrelation function of the image histogram
- Brink
- 1994
(Show Context)
Citation Context ...is) between the object and background classes. An algorithm that maximizes the sum of the entropies computed from the autocorrelation functions of the thresholded image histogram is presented in Ref. =-=[19]-=-. More recently, other global thresholding procedures based on fuzzy logic have been introduced [20–22]. Their underlying idea is to determine the best threshold value by minimizing a measure of fuzzi... |

1 |
Adaptive thresholding based on variational background, Electron
- Liu, Song, et al.
- 2002
(Show Context)
Citation Context ...d and object classes have statistical properties that are not stationary in the different portions of the analyzed image (for example, due to nonhomogeneous light conditions) (see, for example, Refs. =-=[7,8]-=-). In this paper, we address the former group, i.e. global thresholding methods. Many techniques for global image thresholding have been proposed in the literature [9–22]. They are generally based on ... |

1 |
Minimum entropy thresholding, Pattern Recognition 26
- Li, Lee
- 1993
(Show Context)
Citation Context ...tion of the likelihood of the conditional distributions under the Gaussian assumption with equal and different variances is equivalent to the methods developed in Refs. [11,14], respectively. In Ref. =-=[18]-=-, a technique based on Kullback’s minimum cross-entropy principle is described. The optimum threshold is obtained by minimizing the aforementioned cross entropy (formulated on a pixelto-pixel basis) b... |