A new method of estimation of the box-counting dimension of multivariate objects using space-filling curves

被引：15
|
作者：
Skubalska-Rafajlowicz, Ewa [1 ]
机构：
[1] Wroclaw Univ Technol, Inst Engn Cybernet, PL-50370 Wroclaw, Poland
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2005年 / 63卷 / 5-7期
关键词：
Box-counting dimension; Fractal dimension; Space-filling curve;
D O I：
10.1016/j.na.2005.02.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 one- or two-dimensional data. Otherwise, the amount of computation grows exponentially with the number of space coordinates. A new method 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. (C) 2005 Elsevier Ltd. All rights reserved.
引用
收藏
页码：E1281 / E1287
页数：7
相关论文
共 38 条
  • [21] Estimation of Citarum Watershed Boundary's Length Based on Fractal's Power Law by the Modified Box-Counting Dimension Algorithm
    Lim, Michael
    Kartiwa, Alit
    Napitupulu, Herlina
    MATHEMATICS, 2023, 11 (02)
  • [22] Realizing the Box-counting Method for Calculating Fractal Dimension of Urban Form Based on Remote Sensing Image
    Ge Meiling
    Lin Qizhong
    GEO-SPATIAL INFORMATION SCIENCE, 2009, 12 (04) : 265 - 270
  • [23] Realizing the Box-counting Method for Calculating the Fractal Dimension of the Urban Form Based on the Remote Sensing Image
    Ge Meiling
    Lin Qizhong
    Lu Wang
    2006 IEEE INTERNATIONAL GEOSCIENCE AND REMOTE SENSING SYMPOSIUM, VOLS 1-8, 2006, : 1423 - 1426
  • [24] Interpretation of sieve analysis data using the box-counting method for gravelly cobbles
    Yang, ZY
    Juo, JL
    CANADIAN GEOTECHNICAL JOURNAL, 2001, 38 (06) : 1201 - 1212
  • [25] CONSTRUCTION OF RECURRENT FRACTAL INTERPOLATION SURFACES WITH FUNCTION SCALING FACTORS AND ESTIMATION OF BOX-COUNTING DIMENSION ON RECTANGULAR GRIDS
    Yun, Chol-Hui
    Choi, Hui-Chol
    Hyong-Chol, O.
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2015, 23 (04)
  • [26] Detection and classification of pavement damages using wavelet scattering transform, fractal dimension by box-counting method and machine learning algorithms
    Tello-Cifuentes, Lizette
    Marulanda, Johannio
    Thomson, Peter
    ROAD MATERIALS AND PAVEMENT DESIGN, 2024, 25 (03) : 566 - 584
  • [27] A New Space-Filling Curve Based Method for the Traveling Salesman Problems
    Hsieh, Yi-Chih
    You, Peng-Sheng
    APPLIED MATHEMATICS & INFORMATION SCIENCES, 2012, 6 (02): : 371S - 377S
  • [28] Using space-filling curves and fractals to reveal spatial and temporal patterns in neuroimaging data
    Grela, Jacek
    Drogosz, Zbigniew
    Janarek, Jakub
    Ochab, Jeremi K.
    Cifre, Ignacio
    Gudowska-Nowak, Ewa
    Nowak, Maciej A.
    Oswiecimka, Pawel
    Chialvo, Dante R.
    Alzheimers Disease Neuroimaging Initiative
    JOURNAL OF NEURAL ENGINEERING, 2025, 22 (01)
  • [29] Efficient Flexible M-Tree Bulk Loading Using FastMap and Space-Filling Curves
    Loh, Woong-Kee
    CMC-COMPUTERS MATERIALS & CONTINUA, 2021, 66 (02): : 1251 - 1267
  • [30] A BOX-COUNTING METHOD TO CHARACTERIZE DEGREES OF FOLIAGE CLUMPING USING AIRBORNE AND SIMULATED LIDAR DATA
    van Leeuwen, M.
    van Aardt, J. A. N.
    Kampe, T.
    Krause, K.
    36TH INTERNATIONAL SYMPOSIUM ON REMOTE SENSING OF ENVIRONMENT, 2015, 47 (W3): : 1325 - 1331
1234