A new method of estimation of the box-counting dimension of multivariate objects using space-filling curves
نویسنده
چکیده
Box-counting dimension is one of the most widely used fractal dimensions, because it is relatively easy for empirical estimation. Unfortunately, the task is simple only if one operates on oneor twodimensional data. Otherwise, the amount of computation grows exponentially with the number of space coordinates.A newmethod of estimation of the box-counting dimension of multivariate objects using space-filling curves is presented. The method is based on a quasi-inverse to a space-filling curve which maps data to one dimension. Such a transformation retains box-counting dimension up to a known factor. This factor equals the embedding dimension. Thus, the box-counting dimension of multidimensional objects can be estimated by means of a one-dimensional procedure. 2005 Elsevier Ltd. All rights reserved.
منابع مشابه
Analysis of Resting-State fMRI Topological Graph Theory Properties in Methamphetamine Drug Users Applying Box-Counting Fractal Dimension
Introduction: Graph theoretical analysis of functional Magnetic Resonance Imaging (fMRI) data has provided new measures of mapping human brain in vivo. Of all methods to measure the functional connectivity between regions, Linear Correlation (LC) calculation of activity time series of the brain regions as a linear measure is considered the most ubiquitous one. The strength of the dependence obl...
متن کاملApproximation of arbitrary polygonal objects using space filling curves versus a bounding box approach
Using multiple intervals on space filling curves has a benefit to merely approximating the polygon by a bounding box for indexing purposes. These intervals feature a shapes closer to those of arbitrary, non rectangular polygons. In this paper we examine whether SCUBA (Space filling Curves versus Unsophisticated Bounding box Approximation) is a feasible approach in comparison to a simple boundin...
متن کاملOptimizing image steganography by combining the GA and ICA
In this study, a novel approach which uses combination of steganography and cryptography for hiding information into digital images as host media is proposed. In the process, secret data is first encrypted using the mono-alphabetic substitution cipher method and then the encrypted secret data is embedded inside an image using an algorithm which combines the random patterns based on Space Fillin...
متن کاملAccurate Estimation of Fractal Dimension of Binary Images by Box-Counting Method with Automatic Scale Selection
Fractal dimension can be used to describe the self-similarity, the complexity, or the irregularity of images. One of the most popular ways to estimate the fractal dimension of images is the box-counting method (BCM). Its naive estimates, however, tend to be inaccurate. This paper gives careful consideration to the sources of inaccurate estimates and modifies Buczkowski's method for accurate est...
متن کاملA Variation of the Box-Counting Algorithm Applied to Colour Images
The box counting method for fractal dimension estimation had not been applied to large or colour images thus far due to the processing time required. In this letter we present a fast, easy to implement and very easily expandable to any number of dimensions variation, the box merging method. It is applied here in RGB images which are considered as sets in 5-D space.
متن کامل