摘要 :
Image sharpening based on the partial differential equations plays an important role in the fields of image processing. It is an effective technique to clear and sharpen image features, and provides a higher resolution for the sub...
展开
Image sharpening based on the partial differential equations plays an important role in the fields of image processing. It is an effective technique to clear and sharpen image features, and provides a higher resolution for the subsequent processing. This paper makes the first attempt to employ the Hausdorff derivative Laplacian operator to sharpen the images. In terms of the visual quality of details, contours and edges, the original images and noisy images were sharpened by using an appropriate Hausdorff derivative order. Numerical results indicate that the Hausdorff derivative Laplacian operator outperforms the high-pass filtering, the Roberts operator and the traditional integer-order Laplacian operator. In comparison with the existing methods for the image sharpening, the proposed new methodology could be considered as a competitive alternative.
收起
摘要 :
Image edge extraction based on the differential equations is an important branch of image processing. This paper makes the first attempt to employ the Hausdorff derivative gradient method (HDHM) to extract the image edge. In terms...
展开
Image edge extraction based on the differential equations is an important branch of image processing. This paper makes the first attempt to employ the Hausdorff derivative gradient method (HDHM) to extract the image edge. In terms of the visual quality of details, contours, edge integrity, and continuity, the original images and noisy images were extracted by using an appropriate fractal dimension. Numerical results indicate that the HDGM outperforms the Sobel operator, Canny algorithm and traditional gradient method. Moreover, it can be confirmed that the proposed method with multiple values is effective for some images on which the gray value in different parts is quite different. This work extends the Hausdorff derivative to a new field and provides an effective methodology for image edge extraction. (C) 2019 Elsevier B.V. All rights reserved.
收起
摘要 :
Let d(c) denote the Hausdorff dimension of the Julia set J_c of the polynomial f_c(z) = z~2 + c. The function c→ d(c) is real-analytic on the interval (-3/4, 1/4), which is included in the main cardioid of the Mandelbrot set. It ...
展开
Let d(c) denote the Hausdorff dimension of the Julia set J_c of the polynomial f_c(z) = z~2 + c. The function c→ d(c) is real-analytic on the interval (-3/4, 1/4), which is included in the main cardioid of the Mandelbrot set. It was shown by G. Havard and M. Zinsmeister that the derivative d'(c) tends to +∞ as fast as (1/4 — c)~(d(1/4)-3/2) when c 1/4. Under numerically verified assumption d(-3/4) < 4/3, we prove that d'(c) tends to-∞ aswhen c ↘-3/4.
收起
摘要 :
Let be a positive singular measure on Euclidean space. If is sufficiently regular, then for any the set where the derivative of is equal to is large in the sense of the Hausdorff dimension.
摘要 :
One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fracta...
展开
One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals. (C) 2015 Elsevier B.V. All rights reserved.
收起
摘要 :
In the present work, we propose an advection-diffusion equation with Hausdorff deformed derivatives to stud the turbulent diffusion of contaminants in the atmosphere. We compare the performance of our model to fit experimental dat...
展开
In the present work, we propose an advection-diffusion equation with Hausdorff deformed derivatives to stud the turbulent diffusion of contaminants in the atmosphere. We compare the performance of our model to fit experimental data against models with classical and Caputo fractional derivatives. We found that the Hausdorff equation gives better results than the tradition advection-diffusion equation when fitting experimental data. Most importantly, we show that our model and the Caputo fractional derivative model display a very similar performance for all experiments. This last result indicates that regardless of the kind of non-classical derivative we use, an advection-diffusion equation with non-classical derivative displaying power-law mean square displacement is more adequate to describe the diffusion of contaminants in the atmosphere than a model with classical derivatives. Furthermore, since Hausdorff derivatives can be related to several deformed operators, and since differential equations with the Hausdorff derivatives are easier to solve than equations with Caputo and other non-local fractional derivatives, our result highlights the potential of deformed derivative models to describe the diffusion of contaminants in the atmosphere. (C) 2020 Elsevier B.V. All rights reserved.
收起
摘要 :
In this article, we introduce a new notion of (strong) absolute derivative, for functions defined between metric spaces, and we investigate various properties and.uses of this concept, especially regarding the geometry of abstract...
展开
In this article, we introduce a new notion of (strong) absolute derivative, for functions defined between metric spaces, and we investigate various properties and.uses of this concept, especially regarding the geometry of abstract metric spaces carrying no other structure.
收起
摘要 :
This study proposes the radial basis function (RBF) based on the Hausdorff fractal distance and then applies it to develop the Kansa method for the solution of the Hausdorff derivative Poisson equations. The Kansa method is a mesh...
展开
This study proposes the radial basis function (RBF) based on the Hausdorff fractal distance and then applies it to develop the Kansa method for the solution of the Hausdorff derivative Poisson equations. The Kansa method is a meshless global technique promising for high-dimensional irregular domain problems. It is, however, noted that the shape parameter of the RBFs can have a significant influence on the accuracy and robustness of the numerical solution. Based on the leave-one-out cross-validation algorithm proposed by Rippa, this study presents a new technique to choose the optimal shape parameter of the RBFs with the Hausdorff fractal distance. Numerical experiments show that the Kansa method based on the Hausdorff fractal distance is highly accurate and computationally efficient for the Hausdorff derivative Poisson equations.
收起
摘要 :
This paper is devoted to the study of weak and strong convergence of derivations, and of the flows associated to them, when dealing with a sequence of metric measure structures (X, d, m(n)), m(n) weakly convergent to m. In particu...
展开
This paper is devoted to the study of weak and strong convergence of derivations, and of the flows associated to them, when dealing with a sequence of metric measure structures (X, d, m(n)), m(n) weakly convergent to m. In particular, under curvature assumptions, either only on the limit metric structure (X, d, m) or on the whole sequence of metric measure spaces, we provide several stability results. (C) 2016 Elsevier Inc. All rights reserved.
收起
原文获取