Reconstructed Quantized Coefficients Modeled with Generalized Gaussian Distribution with Exponent 1/3

Krupiński, Robert

doi:10.1515/ipc-2016-0019

Cited by 11 publications

(2 citation statements)

References 23 publications

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“…One of the main advantages of the GGD is the coverage of the other popular distributions, namely Gaussian distribution, Laplacian distribution, a uniform one, an impulse function, as well as some other special cases [9,10]. Estimation of its parameters is possible using various methods [37].…”

Section: Generalized Gaussian Distribution and Gaussian Mixture Modelmentioning

confidence: 99%

Improved Two-Step Binarization of Degraded Document Images Based on Gaussian Mixture Model

Krupiński

Lech

Okarma

2020

Lecture Notes in Computer Science

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Image binarization is one of the most relevant preprocessing operations influencing the results of further image analysis conducted for many purposes. During this step a significant loss of information occurs and the use of inappropriate thresholding methods may cause difficulties in further shape analysis or even make it impossible to recognize different shapes of objects or characters. Some of the most typical applications utilizing the analysis of binary images are Optical Character Recognition (OCR) and Optical Mark Recognition (OMR), which may also be applied for unevenly illuminated natural images, as well as for challenging degraded historical document images, considered as typical benchmarking tools for image binarization algorithms.To face the still valid challenge of relatively fast and simple, but robust binarization of degraded document images, a novel two-step algorithm utilizing initial thresholding, based on the modelling of the simplified image histogram using Gaussian Mixture Model (GMM) and the Monte Carlo method, is proposed in the paper. This approach can be considered as the extension of recently developed image preprocessing method utilizing Generalized Gaussian Distribution (GGD), based on the assumption of its similarity to the histograms of ground truth binary images distorted by Gaussian noise. The processing time of the first step, producing the intermediate images with partially removed background information, may be significantly reduced due to the use of the Monte Carlo method.The proposed improved approach leads to even better results, not only for well-known DIBCO benchmarking databases, but also for more demanding Bickley Diary dataset, allowing the use of some well-known classical binarization methods, including the global ones, in the second step of the algorithm.

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Section: Generalized Gaussian Distribution and Gaussian Mixture Modelmentioning

confidence: 99%

Improved Two-Step Binarization of Degraded Document Images Based on Gaussian Mixture Model

Krupiński

Lech

Okarma

2020

Lecture Notes in Computer Science

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“…Many articles have been published presenting the applications of GGD in many research areas, e.g., in image segmentation [9], stereoscopic images [10], image synthesis [11], the binarization of historical degraded document images [12], image compression [7], [13], [14], in testing adaptive filters [15], and the vibroacoustic method of detecting damage to the power transformer core [16]. In [17] the probabilistic function as a mixture of generalized Gaussian distributions was built in order to predict the failure of rotating machines.…”

Section: Introductionmentioning

confidence: 99%

Maximum Likelihood Estimators of Generalized Gaussian Distribution With an ℍ-Proper Quaternion Random Variable

Krupiński,

Marciniak,

Oyerinde

2024

IEEE Access

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The currently known generalized Gaussian distributions (GGD) with an augmented quaternion random variable are based on the 3D GGD distribution. That is, they are based on random variables with three components. In this article, GGD for an augmented quaternion random variable based on GGD for a random variable with four components is given. Then the distribution obtained is simplified for an Hproper quaternion random variable. For this simplified distribution the maximum likelihood estimators are presented. The simplification allows the presentation of the ML estimator for the shape parameter of GGD by eliminating the coefficients related to the covariance from the non-linear equation. The performance of the derived ML estimators is examined in the simulations.INDEX TERMS Augmented quaternion statistics, maximum likelihood method, quaternion generalized Gaussian distribution, quaternion random variable.

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Binarization of Degraded Document Images with Generalized Gaussian Distribution

Krupiński

Lech

Tecław

et al. 2019

Lecture Notes in Computer Science

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Reconstructed Quantized Coefficients Modeled with Generalized Gaussian Distribution with Exponent 1/3

Abstract: Abstract.Generalized Gaussian distribution (GGD) includes specials cases when the shape parame-

Cited by 11 publications

References 23 publications

Improved Two-Step Binarization of Degraded Document Images Based on Gaussian Mixture Model

Improved Two-Step Binarization of Degraded Document Images Based on Gaussian Mixture Model

Maximum Likelihood Estimators of Generalized Gaussian Distribution With an ℍ-Proper Quaternion Random Variable

Binarization of Degraded Document Images with Generalized Gaussian Distribution

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