Modeling Quantized Coefficients with Generalized Gaussian Distribution with Exponent 1 / m, $$m=2,3,\ldots $$

Krupiński, Robert

doi:10.1007/978-3-319-67792-7_23

Cited by 7 publications

(3 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

Self Cite

View full text Add to dashboard Cite

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(OMR), which may also be applied for unevenly illuminated natural images, as well as for challenging degraded historical document images, considered as typical benchmarking tools for image binarization algorithms.To face the still valid challenge of relatively fast and simple, but robust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.

show abstract

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…In order to validate the analytical calculations, we have investigated the minimum energy configuration of a cobalt dot of radius R = 120 nm and length L = 70 nm by micromagnetic simulations [38]. In this article we have considered an out-of-plane magnetic anisotropy, which is generally obtained when the cobalt is deposited on a platinum or palladium substrate [39][40][41][42]. We have used a saturation magnetization M 0 = 1.4 × 10 6 A/m, an exchange stiffness A = 3 × 10 −11 J/m and a Gilbert damping constant α= 0.5.…”

Section: Micromagnetic Simulationsmentioning

confidence: 99%

Analytical and numericalKu-Bphase diagrams for cobalt nanostructures: Stability region for a Bloch skyrmion

Riveros

Vidal-Silva

Tejo

et al. 2018

Journal of Magnetism and Magnetic Materials

View full text Add to dashboard Cite

In this letter we calculate the energies corresponding to the different magnetic phases present in a ferromagnetic cylinder by means of analytical calculations. From the comparison of these energies, it is possible to construct magnetic phase diagrams as a function of the uniaxial anisotropy of the sample and the external magnetic field applied. As proof of concept, we analyzed the magnetic phase diagrams for a cobalt dot of 240 nm in diameter and 70 nm in length, with an easy axis parallel to the dot axis, and with a magnetic field applied towards or perpendicular to this axis. From these diagrams we have obtained the stability regions for a Bloch skyrmion (Sk), a vortex core (VC) and a ferromagnetic (F) configuration, which can point in any ψ direction. Our results provide a pathway to engineer the formation and controllability of a skyrmion in a ferromagnetic dot to different anisotropy constants and magnetic fields.

show abstract

“…. : covered in [8]. Based on special cases, the analysis and calculations can be simplified and equations can be determined in closed form.…”

Section: Introductionmentioning

confidence: 99%

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

Krupiński,

Marciniak,

Oyerinde

2024

IEEE Access

View full text Add to dashboard Cite

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.

show abstract

Modeling Quantized Coefficients with Generalized Gaussian Distribution with Exponent 1 / m, $$m=2,3,\ldots $$

Cited by 7 publications

References 14 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

Analytical and numericalKu-Bphase diagrams for cobalt nanostructures: Stability region for a Bloch skyrmion

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

Contact Info

Product

Resources

About