相关论文: A Variation of the Box-Counting Algorithm Applied …
While the numerical methods which utilizes partitions of equal-size, including the box-counting method, remain the most popular choice for computing the generalized dimension of multifractal sets, two mass- oriented methods are investigated…
The box-counting (BC) algorithm is applied to calculate fractal dimensions of four fractal sets. The sets are contaminated with an additive noise with amplitude $\gamma = 10^{-5} \div 10^{-1}$. The accuracy of calculated numerical values of…
Fractal dimension is widely adopted in spatial databases and data mining, among others as a measure of dataset skewness. State-of-the-art algorithms for estimating the fractal dimension exhibit linear runtime complexity whether based on…
Fractal Image Compression (FIC) is a lossy image compression technique that leverages self-similarity within an image to achieve high compression ratios. However, the process of compressing the image is computationally expensive. This paper…
This work presents a new Visual Basic 6.0 application for estimating the fractal dimension of images, based on an optimized version of the box-counting algorithm. Following the attempt to separate the real information from noise, we…
Covering a network with the minimum possible number of boxes can reveal interesting features for the network structure, especially in terms of self-similar or fractal characteristics. Considerable attention has been recently devoted to this…
An alternate definition of the box-counting dimension is proposed, to provide a better approximation for fractals involving rotation such as the 'Bradley Spiral' structure. A curve fitting comparison of this definition with the box-counting…
Accuracy of the box-counting algorithm for numerical computation of the fractal exponents is investigated. To this end several sample mathematical fractal sets are analyzed. It is shown that the standard deviation obtained for the fit of…
We estimate a Box-counting dimension of fractal surfaces which are generated by iterated function systems with a vertical contraction factor function on an arbitrary data set over rectangular grids and can express well a lot of natural…
We compare different partitioning schemes for the box-counting algorithm in the multifractal analysis by computing the singularity spectrum and the distribution of the box probabilities. As model system we use the Anderson model of…
Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional…
The present work proposes the development of a novel method to provide descriptors for colored texture images. The method consists in two steps. In the first, we apply a linear transform in the color space of the image aiming at…
The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored…
The fractal dimensions of color-specific paint patterns in various Jackson Pollock paintings are calculated using a filtering process which models perceptual response to color differences ($\Lab$ color space). The advantage of the $\Lab$…
In this paper, we discuss the Higuchi algorithm which serves as a widely used estimator for the box-counting dimension of the graph of a bounded function $f : [0,1] \to \R$. We formulate the method in a mathematically precise way and show…
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance…
The light scattering experiment establishes a relationship between refractive index fluctuations and fractal dimension in weakly scattering tissue-like media. Based on the box-counting approach, an analytical model is developed and shows…
Research on fractal networks is a dynamically growing field of network science. A central issue is to analyze fractality with the so-called box-covering method. As this problem is known to be NP-hard, a plethora of approximating algorithms…
A random sequential box-covering algorithm recently introduced to measure the fractal dimension in scale-free networks is investigated. The algorithm contains Monte Carlo sequential steps of choosing the position of the center of each box,…
Fractal analysis has been shown to be useful in image processing for characterizing shape and gray-scale complexity. The fractal feature is a compact descriptor used to give a numerical measure of the degree of irregularity of the medical…