Related papers: Fractional Calculus In Image Processing: A Review
There are many resources useful for processing images, most of them freely available and quite friendly to use. In spite of this abundance of tools, a study of the processing methods is still worthy of efforts. Here, we want to discuss the…
This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…
In a recent paper, published at arXiv:0910.2381, we started a discussion on the new possibilities arising from the use of fractional differential calculus in image processing. We have seen that the fractional calculation is able to enhance…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
Fractional gradient descent has been studied extensively, with a focus on its ability to extend traditional gradient descent methods by incorporating fractional-order derivatives. This approach allows for more flexibility in navigating…
The implementation of fractional differential calculations can give new possibilities for image processing tools, in particular for those that are devoted to astronomical images analysis. As discussed in arxiv:0910.2381, the fractional…
This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…
This contribution deals with the creation of numerical models for the simulation of the dynamic characteristics of fractional-order control systems and their comparison with analytical models. We give the results of the comparison of…
In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional…
To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order…
This paper deals with fractional-order controlled systems and fractional-order controllers in the frequency domain. The mathematical description by fractional transfer functions and properties of these systems are presented. The new ways…
Identification of fractional order systems is considered from an algebraic point of view. It allows for a simultaneous estimation of model parameters and fractional (or integer) orders from input and output data. It is exact in that no…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…
Estimates of image gradients play a ubiquitous role in image segmentation and classification problems since gradients directly relate to the boundaries or the edges of a scene. This paper proposes an unified approach to gradient estimation…
Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and…
Viscoelasticity and related phenomena are of great importance in the study of mechanical properties of material especially, biological materials. Certain materials show some complex effects in mechanical tests, which cannot be described by…