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Related papers: Fractional Calculus In Image Processing: A Review

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In this paper we will present some alternative types of mathematical description and methods of solution of the fractional-order dynamical system in the state space. We point out the difference in the true sense of the name "state" space…

Optimization and Control · Mathematics 2007-05-23 L. Dorcak , I. Petras , I. Kostial , J. Terpak

Image segmentation is a key topic in image processing and computer vision with applications such as scene understanding, medical image analysis, robotic perception, video surveillance, augmented reality, and image compression, among many…

Computer Vision and Pattern Recognition · Computer Science 2020-11-17 Shervin Minaee , Yuri Boykov , Fatih Porikli , Antonio Plaza , Nasser Kehtarnavaz , Demetri Terzopoulos

Image processing is an important research area in computer vision. Image segmentation plays the vital rule in image processing research. There exist so many methods for image segmentation. Clustering is an unsupervised study. Clustering can…

Computer Vision and Pattern Recognition · Computer Science 2014-07-31 Dibya Jyoti Bora , Anil Kumar Gupta

Image ordinal estimation is to predict the ordinal label of a given image, which can be categorized as an ordinal regression problem. Recent methods formulate an ordinal regression problem as a series of binary classification problems. Such…

Computer Vision and Pattern Recognition · Computer Science 2021-02-23 Haiping Zhu , Hongming Shan , Yuheng Zhang , Lingfu Che , Xiaoyang Xu , Junping Zhang , Jianbo Shi , Fei-Yue Wang

Fractional differential equations are powerful mathematical descriptors for intricate physical phenomena in a compact form. However, compared to integer ordinary or partial differential equations, solving fractional differential equations…

Analysis of PDEs · Mathematics 2025-06-16 Donya Dabiri , Joshua DaRosa , Milad Saadat , Deepak Mangal , Safa Jamali

The aim of this work is to show, based on concrete data observation, that the choice of the fractional derivative when modelling a problem is relevant for the accuracy of a method. Using the least squares fitting technique, we determine the…

Other Statistics · Statistics 2017-04-04 Ricardo Almeida

Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…

Numerical Analysis · Mathematics 2022-04-11 Kai Diethelm

The technology of image segmentation is widely used in medical image processing, face recognition pedestrian detection, etc. The current image segmentation techniques include region-based segmentation, edge detection segmentation,…

Computer Vision and Pattern Recognition · Computer Science 2017-07-10 Song Yuheng , Yan Hao

In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…

Numerical Analysis · Mathematics 2018-01-23 Seshu Kumar Damarla , Madhusree Kundu

In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…

Statistical Mechanics · Physics 2016-08-31 Fevzi Buyukkilic , Zahide Ok Bayrakdar , Dogan Demirhan

In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…

Chaotic Dynamics · Physics 2014-08-20 Marius-F. Danca

Image segmentation is a central topic in image processing and computer vision and a key issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote sensing. According to the human perception, image…

Numerical Analysis · Mathematics 2022-06-24 Laura Antonelli , Valentina De Simone , Daniela di Serafino

Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains…

Optimization and Control · Mathematics 2013-05-10 Shakoor Pooseh , Ricardo Almeida , Delfim F. M. Torres

The Proportional-Integral-Derivative Controller is widely used in industries for process control applications. Fractional-order PID controllers are known to outperform their integer-order counterparts. In this paper, we propose a new…

Other Computer Science · Computer Science 2008-11-04 Mithun Chakraborty , Deepyaman Maiti , Amit Konar

Many image segmentation techniques have been developed over the past two decades for segmenting the images, which help for object recognition, occlusion boundary estimation within motion or stereo systems, image compression, image editing.…

Computer Vision and Pattern Recognition · Computer Science 2014-06-03 Shradha Dakhare , Harshal Chowhan , Manoj B. Chandak

Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…

Graphics · Computer Science 2025-02-25 Adarsh Djeacoumar , Felix Mujkanovic , Hans-Peter Seidel , Thomas Leimkühler

The interference of fluorescence signals and noise remains a significant challenge in Raman spectrum analysis, often obscuring subtle spectral features that are critical for accurate analysis. Inspired by variational methods similar to…

Image and Video Processing · Electrical Eng. & Systems 2025-12-08 Nelson H. T. Lemes , José Claudinei Ferreira , Higor V. M. Ferreira

In the present work, we propose a new parameterization for the concentration flux using fractional derivatives. The fractional order differential equation in the longitudinal and vertical directions is used to obtain the concentration…

Atmospheric and Oceanic Physics · Physics 2018-12-26 A. G. Goulart , M. J. Lazo , J. M. S. Suarez

The current digital era, driven by growing threats to data security, requires a robust image encryption technique. Classical encryption algorithms suffer from a trade-off among security, image fidelity, and computational efficiency. This…

Fractional-order differentiation has many characteristics different from integer-order differentiation. These characteristics can be applied to the optimization algorithms of artificial neural networks to obtain better results. However, due…

Machine Learning · Computer Science 2025-06-10 Xiaojun zhou , Chunna Zhao , Yaqun Huang , Chengli Zhou , Junjie Ye , Kemeng Xiang