Relevant bibliographies by topics / Box counting fractal dimension

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Academic literature on the topic 'Box counting fractal dimension'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Box counting fractal dimension"

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Maryenko, N. І., and O. Yu Stepanenko. "Fractal analysis of anatomical structures linear contours: modified Caliper method vs Box counting method." Reports of Morphology 28, no. 1 (2022): 17–26. http://dx.doi.org/10.31393/morphology-journal-2022-28(1)-03.

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Fractal analysis estimates the metric dimension and complexity of the spatial configuration of different anatomical structures. This allows the use of this mathematical method for morphometry in morphology and clinical medicine. Two methods of fractal analysis are most often used for fractal analysis of linear fractal objects: the Box counting method (Grid method) and the Caliper method (Richardson’s method, Perimeter stepping method, Ruler method, Divider dimension, Compass dimension, Yard stick method). The aim of the research is a comparative analysis of two methods of fractal analysis – Bo
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Chen, Xiang, Jingchao Li, Hui Han, and Yulong Ying. "Improving the signal subtle feature extraction performance based on dual improved fractal box dimension eigenvectors." Royal Society Open Science 5, no. 5 (2018): 180087. http://dx.doi.org/10.1098/rsos.180087.

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Because of the limitations of the traditional fractal box-counting dimension algorithm in subtle feature extraction of radiation source signals, a dual improved generalized fractal box-counting dimension eigenvector algorithm is proposed. First, the radiation source signal was preprocessed, and a Hilbert transform was performed to obtain the instantaneous amplitude of the signal. Then, the improved fractal box-counting dimension of the signal instantaneous amplitude was extracted as the first eigenvector. At the same time, the improved fractal box-counting dimension of the signal without the H
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CHEN, WEN-SHIUNG, and SHANG-YUAN YUAN. "SOME FRACTAL DIMENSION ESTIMATE ALGORITHMS AND THEIR APPLICATIONS TO ONE-DIMENSIONAL BIOMEDICAL SIGNALS." Biomedical Engineering: Applications, Basis and Communications 14, no. 03 (2002): 100–108. http://dx.doi.org/10.4015/s1016237202000152.

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Fractals can model many classes of time-series data. The fractal dimension is an important characteristic of fractals that contains information about their geometrical structure at multiple scales. The covering methods are a class of efficient approaches, e.g., box-counting (BC) method, to estimate the fractal dimension. In this paper, the differential box-counting (DBC) approach, originally for 2-D applications, is modified and applied to 1-D case. In addition, two algorithms, called 1-D shifting-DBC (SDBC-1D) and 1-D scanning-BC (SBC-1D), are also proposed for 1-D signal analysis. The fracta
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Meng, Xianmeng, Pengju Zhang, Jing Li, Chuanming Ma, and Dengfeng Liu. "The linkage between box-counting and geomorphic fractal dimensions in the fractal structure of river networks: the junction angle." Hydrology Research 51, no. 6 (2020): 1397–408. http://dx.doi.org/10.2166/nh.2020.082.

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Abstract In the past, a great deal of research has been conducted to determine the fractal properties of river networks, and there are many kinds of methods calculating their fractal dimensions. In this paper, we compare two most common methods: one is geomorphic fractal dimension obtained from the bifurcation ratio and the stream length ratio, and the other is box-counting method. Firstly, synthetic fractal trees are used to explain the role of the junction angle on the relation between two kinds of fractal dimensions. The obtained relationship curves indicate that box-counting dimension is d
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Jiang, Shiguo, and Desheng Liu. "Box-Counting Dimension of Fractal Urban Form." International Journal of Artificial Life Research 3, no. 3 (2012): 41–63. http://dx.doi.org/10.4018/jalr.2012070104.

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The difficulty to obtain a stable estimate of fractal dimension for stochastic fractal (e.g., urban form) is an unsolved issue in fractal analysis. The widely used box-counting method has three main issues: 1) ambiguities in setting up a proper box cover of the object of interest; 2) problems of limited data points for box sizes; 3) difficulty in determining the scaling range. These issues lead to unreliable estimates of fractal dimensions for urban forms, and thus cast doubt on further analysis. This paper presents a detailed discussion of these issues in the case of Beijing City. The authors
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FATHALLAH-SHAYKH, HASSAN M. "FRACTAL DIMENSION OF THE DROSOPHILA CIRCADIAN CLOCK." Fractals 19, no. 04 (2011): 423–30. http://dx.doi.org/10.1142/s0218348x11005476.

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Fractal geometry can adequately represent many complex and irregular objects in nature. The fractal dimension is typically computed by the box-counting procedure. Here I compute the box-counting and the Kaplan-Yorke dimensions of the 14-dimensional models of the Drosophila circadian clock. Clockwork Orange (CWO) is transcriptional repressor of direct target genes that appears to play a key role in controlling the dynamics of the clock. The findings identify these models as strange attractors and highlight the complexity of the time-keeping actions of CWO in light-day cycles. These fractals are
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PERFECT, E., and B. DONNELLY. "BI-PHASE BOX COUNTING: AN IMPROVED METHOD FOR FRACTAL ANALYSIS OF BINARY IMAGES." Fractals 23, no. 01 (2015): 1540010. http://dx.doi.org/10.1142/s0218348x15400101.

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Many natural systems are irregular and/or fragmented, and have been interpreted to be fractal. An important parameter needed for modeling such systems is the fractal dimension, D. This parameter is often estimated from binary images using the box-counting method. However, it is not always apparent which fractal model is the most appropriate. This has led some researchers to report different D values for different phases of an analyzed image, which is mathematically untenable. This paper introduces a new method for discriminating between mass fractal, pore fractal, and Euclidean scaling in imag
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Górski, A. Z., M. Stróż, P. Oświȩcimka, and J. Skrzat. "Accuracy of the box-counting algorithm for noisy fractals." International Journal of Modern Physics C 27, no. 10 (2016): 1650112. http://dx.doi.org/10.1142/s0129183116501126.

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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 [Formula: see text]. The accuracy of calculated numerical values of the fractal dimensions is analyzed as a function of [Formula: see text] for different sizes of the data sample. In particular, it has been found that even in case of pure fractals ([Formula: see text]) as well as for tiny noise ([Formula: see text]) one has considerable error for the calculated exponents of order 0.01. For larger noise the error is growing up to 0.1 an
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MASTERS, BARRY R. "FRACTAL ANALYSIS OF NORMAL HUMAN RETINAL BLOOD VESSELS." Fractals 02, no. 01 (1994): 103–10. http://dx.doi.org/10.1142/s0218348x94000090.

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The fractal dimension of the pattern of retinal blood vessels in the normal human eye was calculated. Photomontages were constructed from 10 red-free retinal photographs. Manual tracings of the vessels were made. Digital images of the tracings were analyzed on a computer using the box-counting method to determine the fractal dimension. The mean value and standard deviation of the fractal dimension (box-counting dimension), computed as described in the Methods section, is 1.70 ± 0.02 (N = 10). The use of standard methods for both data acquisition and computer assisted box-counting to determine
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Yang, Zon-Yee, and Jian-Liang Juo. "Interpretation of sieve analysis data using the box-counting method for gravelly cobbles." Canadian Geotechnical Journal 38, no. 6 (2001): 1201–12. http://dx.doi.org/10.1139/t01-052.

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In fractal theory, the fractal dimension (D) is a measure of the complexity of particle distribution in nature. It can provide a description of how much space a particle set fills. The box-counting method uses squared grids of various sizes to cover the particles to obtain a box dimension. This sequential counting concept is analogous to the sieve analysis test using stacked sieves. In this paper the box-counting method is applied to describe the particle-size distribution of gravelly cobbles. Three approaches to obtain the fractal dimension are presented. In the first approach the data obtain
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Dissertations / Theses on the topic "Box counting fractal dimension"

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Brandão, Daniela Teresa Quaresma Santos. "Dimensões fractais e dimensão de correlação." Master's thesis, Universidade de Évora, 2008. http://hdl.handle.net/10174/17740.

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O objetivo deste trabalho é o estudo da dimensão fractal, nomeadamente a dimensão de Hausdorff, dimensão de capacidade e dimensão de correlação, relacionando-as e efetuando o cálculo em alguns exemplos. Sempre que se considera indispensável, são apresentadas noções introdutórias para uma melhor compreensão dos conceitos analisados. O Capítulo 2 é dedicado ao estudo da dimensão de Hausdorff, introduzindo, previamente, uma noção de medida, de Hausdorff. No Capítulo 3 analisamos a dimensão de capacidade, suas propriedades e inconvenientes, relacionando, no final, esta dimensão com a dimensão de H
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Simonini, Marina. "Fractal sets and their applications in medicine." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/8763/.

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La geometria euclidea risulta spesso inadeguata a descrivere le forme della natura. I Frattali, oggetti interrotti e irregolari, come indica il nome stesso, sono più adatti a rappresentare la forma frastagliata delle linee costiere o altri elementi naturali. Lo strumento necessario per studiare rigorosamente i frattali sono i teoremi riguardanti la misura di Hausdorff, con i quali possono definirsi gli s-sets, dove s è la dimensione di Hausdorff. Se s non è intero, l'insieme in gioco può riconoscersi come frattale e non presenta tangenti e densità in quasi nessun punto. I frattali più classici
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HUANG, KUAN-YU. "Fractal or Scaling Analysis of Natural Cities Extracted from Open Geographic Data Sources." Thesis, Högskolan i Gävle, Avdelningen för Industriell utveckling, IT och Samhällsbyggnad, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-19386.

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A city consists of many elements such as humans, buildings, and roads. The complexity of cities is difficult to measure using Euclidean geometry. In this study, we use fractal geometry (scaling analysis) to measure the complexity of urban areas. We observe urban development from different perspectives using the bottom-up approach. In a bottom-up approach, we observe an urban region from a basic to higher level from our daily life perspective to an overall view. Furthermore, an urban environment is not constant, but it is complex; cities with greater complexity are more prosperous. There are ma
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Berlinkov, Artemi. "Dimensions in Random Constructions." Thesis, University of North Texas, 2002. https://digital.library.unt.edu/ark:/67531/metadc3160/.

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We consider random fractals generated by random recursive constructions, prove zero-one laws concerning their dimensions and find their packing and Minkowski dimensions. Also we investigate the packing measure in corresponding dimension. For a class of random distribution functions we prove that their packing and Hausdorff dimensions coincide.
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Le, Huy. "Numerické metody měření fraktálních dimenzí a fraktálních měr." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-417160.

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Tato diplomová práce se zabývá teorií fraktálů a popisuje patričné potíže při zavedení pojmu fraktál. Dále se v práci navrhuje několik metod, které se použijí na aproximaci fraktálních dimenzí různých množin zobrazených na zařízeních s konečným rozlišením. Tyto metody se otestují na takových množinách, jejichž dimenze známe, a na závěr se výsledky porovnávají.
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ZANINI, ALESSANDRO. "Analisi dei dati da emissione acustica per la valutazione del danneggiamento strutturale." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2008. http://hdl.handle.net/2108/686.

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Viene studiata una nuova metodologia di diagnostica, basata sull’analisi di dati derivanti dall’Emissione Acustica (EA), per lo studio della nucleazione e della propagazione di difetti durante prove di laboratorio su provino sotto carico e serbatoi in pressione. L’applicazione dell’analisi frattale al segnale di EA risulta particolarmente efficace e permette di identificare la distribuzione spaziale delle sorgenti stesse, esplicitandone la correlazione tra gli eventi. E’ così possibile ottenere molte informazioni associate al danneggiamento dei differenti casi studiati. L’intensità della solle
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Dathe, Annette. "Digitale Bildanalyse zur Messung fraktaler Eigenschaften der Bodenstruktur." Doctoral thesis, [S.l.] : [s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=965898083.

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Leifsson, Patrik. "Fractal sets and dimensions." Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-7320.

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<p>Fractal analysis is an important tool when we need to study geometrical objects less regular than ordinary ones, e.g. a set with a non-integer dimension value. It has developed intensively over the last 30 years which gives a hint to its young age as a branch within mathematics.</p><p>In this thesis we take a look at some basic measure theory needed to introduce certain definitions of fractal dimensions, which can be used to measure a set's fractal degree. Comparisons of these definitions are done and we investigate when they coincide. With these tools different fractals are studied and com
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Fraser, Jonathan M. "Dimension theory and fractal constructions based on self-affine carpets." Thesis, University of St Andrews, 2013. http://hdl.handle.net/10023/3869.

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The aim of this thesis is to develop the dimension theory of self-affine carpets in several directions. Self-affine carpets are an important class of planar self-affine sets which have received a great deal of attention in the literature on fractal geometry over the last 30 years. These constructions are important for several reasons. In particular, they provide a bridge between the relatively well-understood world of self-similar sets and the far from understood world of general self-affine sets. These carpets are designed in such a way as to facilitate the computation of their dimensions, an
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Wang, Nancy. "Fractal Sets: Dynamical, Dimensional and Topological Properties." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-233147.

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Fractals is a relatively new mathematical topic which received thorough treatment only starting with 1960's. Fractals can be observed everywhere in nature and in day-to-day life. To give a few examples, common fractals are the spiral cactus, the romanesco broccoli, human brain and the outline of the Swedish map. Fractal dimension is a dimension which need not take integer values. In fractal geometry, a fractal dimension is a ratio providing an index of the complexity of fractal pattern with regard to how the local geometry changes with the scale at which it is measured. In recent years, fracta
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Book chapters on the topic "Box counting fractal dimension"

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Rosenberg, Eric. "Network Box Counting Dimension." In Fractal Dimensions of Networks. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43169-3_7.

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Rosenberg, Eric. "Computing the Box Counting Dimension." In Fractal Dimensions of Networks. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43169-3_6.

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Ostwald, Michael J., and Josephine Vaughan. "Introducing the Box-Counting Method." In The Fractal Dimension of Architecture. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32426-5_3.

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Rosenberg, Eric. "Network Box Counting Heuristics." In Fractal Dimensions of Networks. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43169-3_8.

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Rosenberg, Eric. "Topological and Box Counting Dimensions." In Fractal Dimensions of Networks. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43169-3_4.

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Rosenberg, Eric. "Network Box Counting Heuristics." In A Survey of Fractal Dimensions of Networks. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-90047-6_3.

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Rosenberg, Eric. "Lower Bounds on Box Counting." In A Survey of Fractal Dimensions of Networks. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-90047-6_4.

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Che Azemin, Mohd Zulfaezal, Fadilah Ab Hamid, Jie Jin Wang, Ryo Kawasaki, and Dinesh Kant Kumar. "Box-Counting Fractal Dimension Algorithm Variations on Retina Images." In Lecture Notes in Electrical Engineering. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24584-3_27.

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Kaewaramsri, Yothin, and Kuntpong Woraratpanya. "Improved Triangle Box-Counting Method for Fractal Dimension Estimation." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19024-2_6.

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Șerbănescu, Mircea-Sebastian. "Fractal Dimension Box-Counting Algorithm Optimization Through Integral Images." In IFMBE Proceedings. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-93564-1_11.

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Conference papers on the topic "Box counting fractal dimension"

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Jie Feng, Wei-Chung Lin, and Chin-Tu Chen. "Fractional box-counting approach to fractal dimension estimation." In Proceedings of 13th International Conference on Pattern Recognition. IEEE, 1996. http://dx.doi.org/10.1109/icpr.1996.547197.

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Attikos, Christos, and Michael Doumpos. "Faster Estimation of the Correlation Fractal Dimension Using Box-counting." In 2009 Fourth Balkan Conference in Informatics. IEEE, 2009. http://dx.doi.org/10.1109/bci.2009.6.

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Xue, Song, Xinsheng Jiang, and Jimiao Duan. "A new box-counting method for image fractal dimension estimation." In 2017 3rd IEEE International Conference on Computer and Communications (ICCC). IEEE, 2017. http://dx.doi.org/10.1109/compcomm.2017.8322847.

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Wada, Yukari, and Kazunori Kuwana. "Flame Fractal Dimension Induced by Hydrodynamic Instability." In ASME/JSME 2011 8th Thermal Engineering Joint Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajtec2011-44222.

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Premixed flames self-turbulized due to hydrodynamic instability have self-similar, fractal-like structures as evidenced by the acceleration of spherically-propagating flames. The fractal dimension of a self-turbulized premixed flame needs to be known if its apparent flame speed is to be estimated. CFD simulations of outwardly-propagating flames have been conducted to predict their fractal dimensions. There are, however, difficulties in accurately determining fractal dimension based on the flame-propagation behavior of such an outwardly-propagating flame. This paper demonstrates a newly propose
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Panigrahy, Chinmaya, Ayan Seal, and Nihar Kumar Mahato. "Is Box-Height Really a Issue in Differential Box Counting Based Fractal Dimension?" In 2019 International Conference on Information Technology (ICIT). IEEE, 2019. http://dx.doi.org/10.1109/icit48102.2019.00073.

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Kraitong, Atikarn, Sanpachai Huvanandana, and Settapong Malisuwan. "A box-counting fractal dimension for feature extraction in iris recognition." In 2011 International Symposium on Intelligent Signal Processing and Communications Systems (ISPACS 2011). IEEE, 2011. http://dx.doi.org/10.1109/ispacs.2011.6146121.

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Ivanovici, Mihai, Irina Nicolae, and Radu-Mihai Coliban. "Umbra-based Improvement of the Probabilistic Box-Counting Fractal Dimension Estimation." In 2021 International Symposium on Signals, Circuits and Systems (ISSCS). IEEE, 2021. http://dx.doi.org/10.1109/isscs52333.2021.9497383.

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Li, Jian, Caixin Sun, and Qian Du. "A New Box-Counting Method for Estimation of Image Fractal Dimension." In 2006 International Conference on Image Processing. IEEE, 2006. http://dx.doi.org/10.1109/icip.2006.313005.

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Gang Wei and Ju Tang. "Study of Minimum Box-Counting Method for image fractal dimension estimation." In 2008 China International Conference on Electricity Distribution (CICED 2008). IEEE, 2008. http://dx.doi.org/10.1109/ciced.2008.5211829.

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Wu, Longwen, Yaqin Zhao, Zhao Wang, Fakheraldin Y. O. Abdalla, and Guanghui Ren. "Specific emitter identification using fractal features based on box-counting dimension and variance dimension." In 2017 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT). IEEE, 2017. http://dx.doi.org/10.1109/isspit.2017.8388646.

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